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Sample records for buckling topology optimization

  1. On Compliance and Buckling Objective Functions in Topology Optimization of Snap-Through Problems

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Dahl, Jonas

    2013-01-01

    optimized design. A well-known issue in buckling topology optimization is artificial buckling modes in low density regions. The typical remedy applied for linear buckling does not have a natural extension to nonlinear problems, and we propose an alternative approach. Some possible negative implications...... of the analysis method and optimization formulation. We apply a nonlinear path tracing algorithm capable of detecting different types of stability points and an optimization formulation that handles possible mode switching. This is an extension into the topology optimization realm of a method developed, and used......This paper deals with topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied for topology optimization of a point loaded curved beam problem with the aim of maximizing...

  2. Plate/shell structure topology optimization of orthotropic material for buckling problem based on independent continuous topological variables

    Science.gov (United States)

    Ye, Hong-Ling; Wang, Wei-Wei; Chen, Ning; Sui, Yun-Kang

    2017-03-01

    The purpose of the present work is to study the buckling problem with plate/shell topology optimization of orthotropic material. A model of buckling topology optimization is established based on the independent, continuous, and mapping method, which considers structural mass as objective and buckling critical loads as constraints. Firstly, composite exponential function (CEF) and power function (PF) as filter functions are introduced to recognize the element mass, the element stiffness matrix, and the element geometric stiffness matrix. The filter functions of the orthotropic material stiffness are deduced. Then these filter functions are put into buckling topology optimization of a differential equation to analyze the design sensitivity. Furthermore, the buckling constraints are approximately expressed as explicit functions with respect to the design variables based on the first-order Taylor expansion. The objective function is standardized based on the second-order Taylor expansion. Therefore, the optimization model is translated into a quadratic program. Finally, the dual sequence quadratic programming (DSQP) algorithm and the global convergence method of moving asymptotes algorithm with two different filter functions (CEF and PF) are applied to solve the optimal model. Three numerical results show that DSQP&CEF has the best performance in the view of structural mass and discretion.

  3. Exploiting Additive Manufacturing Infill in Topology Optimization for Improved Buckling Load

    Directory of Open Access Journals (Sweden)

    Anders Clausen

    2016-06-01

    Full Text Available Additive manufacturing (AM permits the fabrication of functionally optimized components with high geometrical complexity. The opportunity of using porous infill as an integrated part of the manufacturing process is an example of a unique AM feature. Automated design methods are still incapable of fully exploiting this design freedom. In this work, we show how the so-called coating approach to topology optimization provides a means for designing infill-based components that possess a strongly improved buckling load and, as a result, improved structural stability. The suggested approach thereby addresses an important inadequacy of the standard minimum compliance topology optimization approach, in which buckling is rarely accounted for; rather, a satisfactory buckling load is usually assured through a post-processing step that may lead to sub-optimal components. The present work compares the standard and coating approaches to topology optimization for the MBB beam benchmark case. The optimized structures are additively manufactured using a filamentary technique. This experimental study validates the numerical model used in the coating approach. Depending on the properties of the infill material, the buckling load may be more than four times higher than that of solid structures optimized under the same conditions.

  4. Aerothermoelastic Topology Optimization with Flutter and Buckling Metrics (Postprint)

    Science.gov (United States)

    2013-07-01

    this work, as drawn in Fig. 1), an analytical value of R∗ = 4 · π2 is obtained ( Shigley and Mishke 2001). Alternatively, if TL is set to 0 and TU = 1...of the panel ( Shigley and Mishke 2001). Except for R∗, this latter boundary is of no interest for the current topological design study, but does...tural optimization problems. Struct Optim 8(4):207–227 Shigley J, Mishke C (2001) Mechanical engineering design. McGraw Hill, New York Sigmund O (2001

  5. Exploiting Additive Manufacturing Infill in Topology Optimization for Improved Buckling Load

    DEFF Research Database (Denmark)

    Clausen, Anders; Aage, Niels; Sigmund, Ole

    2016-01-01

    Additive manufacturing (AM) permits the fabrication of functionally optimized components with high geometrical complexity. The opportunity of using porous infill as an integrated part of the manufacturing process is an example of a unique AM feature. Automated design methods are still incapable...... addresses an important inadequacy of the standard minimum compliance topology optimization approach, in which buckling is rarely accounted for; rather, a satisfactory buckling load is usually assured through a post-processing step that may lead to sub-optimal components. The present work compares...... the standard and coating approaches to topology optimization for the MBB beam benchmark case. The optimized structures are additively manufactured using a filamentary technique. This experimental study validates the numerical model used in the coating approach. Depending on the properties of the infill...

  6. Plate/shell topological optimization subjected to linear buckling constraints by adopting composite exponential filtering function

    Institute of Scientific and Technical Information of China (English)

    Hong-Ling Ye; Wei-Wei Wang; Ning Chen; Yun-Kang Sui

    2016-01-01

    In this paper, a model of topology optimization with linear buckling constraints is established based on an independent and continuous mapping method to minimize the plate/shell structure weight. A composite exponential function (CEF) is selected as filtering functions for element weight, the element stiffness matrix and the element geomet-ric stiffness matrix, which recognize the design variables, and to implement the changing process of design variables from“discrete”to“continuous”and back to“discrete”. The buck-ling constraints are approximated as explicit formulations based on the Taylor expansion and the filtering function. The optimization model is transformed to dual programming and solved by the dual sequence quadratic programming algo-rithm. Finally, three numerical examples with power function and CEF as filter function are analyzed and discussed to demonstrate the feasibility and efficiency of the proposed method.

  7. Topology Optimization of Periodic Microstructures with a Penalization of Highly Localized Buckling Modes

    DEFF Research Database (Denmark)

    Neves, Miguel M.; Sigmund, Ole; Bendsøe, Martin P.

    2002-01-01

    The problem of determining highly localized buckling modes in perfectly periodic cellular microstructures of infinite extent is addressed. A double scale asymptotic technique is applied to the linearized stability problem for a periodic structure built from linearly elastic microstructures...... to design materials with optimal elastic properties that are less prone to localized instability in the form of local buckling modes at the scale of the micro structure. Copyright (C) 2002 John Wiley Sons, Ltd....

  8. Topology Optimization

    DEFF Research Database (Denmark)

    A. Kristensen, Anders Schmidt; Damkilde, Lars

    2007-01-01

    . A way to solve the initial design problem namely finding a form can be solved by so-called topology optimization. The idea is to define a design region and an amount of material. The loads and supports are also fidefined, and the algorithm finds the optimal material distribution. The objective function...... dictates the form, and the designer can choose e.g. maximum stiness, maximum allowable stresses or maximum lowest eigenfrequency. The result of the topology optimization is a relatively coarse map of material layout. This design can be transferred to a CAD system and given the necessary geometrically...... refinements, and then remeshed and reanalysed in other to secure that the design requirements are met correctly. The output of standard topology optimization has seldom well-defined, sharp contours leaving the designer with a tedious interpretation, which often results in less optimal structures. In the paper...

  9. Topology optimization

    DEFF Research Database (Denmark)

    Bendsøe, Martin P.; Sigmund, Ole

    2007-01-01

    Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...

  10. Issues related to topology optimization of snap-through problems

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Dahl, Jonas

    2012-01-01

    This work focuses on issues related to topology optimization of static geometrically nonlinear structures experiencing snap-through behaviour. Different compliance and buckling criterion functions are studied and applied to topology optimization of a point loaded curved beam problem with the aim ...

  11. Interactive Topology Optimization

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten

    software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based......Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...

  12. Topology optimized microbioreactors

    DEFF Research Database (Denmark)

    Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna

    2011-01-01

    . Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement...... in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced....

  13. Topology optimization approaches

    DEFF Research Database (Denmark)

    Sigmund, Ole; Maute, Kurt

    2013-01-01

    Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...

  14. Effect of Topological Defects on Buckling Behavior of Single-walled Carbon Nanotube

    Directory of Open Access Journals (Sweden)

    Wang Guoxiu

    2011-01-01

    Full Text Available Abstract Molecular dynamic simulation method has been employed to consider the critical buckling force, pressure, and strain of pristine and defected single-walled carbon nanotube (SWCNT under axial compression. Effects of length, radius, chirality, Stone–Wales (SW defect, and single vacancy (SV defect on buckling behavior of SWCNTs have been studied. Obtained results indicate that axial stability of SWCNT reduces significantly due to topological defects. Critical buckling strain is more susceptible to defects than critical buckling force. Both SW and SV defects decrease the buckling mode of SWCNT. Comparative approach of this study leads to more reliable design of nanostructures.

  15. Topology optimized microbioreactors.

    Science.gov (United States)

    Schäpper, Daniel; Lencastre Fernandes, Rita; Lantz, Anna Eliasson; Okkels, Fridolin; Bruus, Henrik; Gernaey, Krist V

    2011-04-01

    This article presents the fusion of two hitherto unrelated fields--microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein. Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced.

  16. Manufacturing tolerant topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2009-01-01

    In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick...... (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization...... approach, under- and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show...

  17. Filters in topology optimization

    DEFF Research Database (Denmark)

    Bourdin, Blaise

    1999-01-01

    In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...

  18. Filters in topology optimization

    DEFF Research Database (Denmark)

    Bourdin, Blaise

    1999-01-01

    In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...

  19. Manufacturing tolerant topology optimization

    Institute of Scientific and Technical Information of China (English)

    Ole Sigmund

    2009-01-01

    In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded)or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization.

  20. Topology Optimization with Stress Constraints

    NARCIS (Netherlands)

    Verbart, A.

    2015-01-01

    This thesis contains contributions to the development of topology optimization techniques capable of handling stress constraints. The research that led to these contributions was motivated by the need for topology optimization techniques more suitable for industrial applications. Currently, topolo

  1. A topological derivative method for topology optimization

    DEFF Research Database (Denmark)

    Norato, J.; Bendsøe, Martin P.; Haber, RB;

    2007-01-01

    resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void......We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...... regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures....

  2. Topology optimization of viscoelastic rectifiers

    DEFF Research Database (Denmark)

    Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin

    2012-01-01

    An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...

  3. OPTIMAL NETWORK TOPOLOGY DESIGN

    Science.gov (United States)

    Yuen, J. H.

    1994-01-01

    This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.

  4. Topology Mining for Optimization of Framed Structures

    Science.gov (United States)

    Hagishita, Takao; Ohsaki, Makoto

    A new heuristic method called Topology Mining (TM) is proposed for topology optimization of framed structures, where the problem is formulated as 0-1 mixed-integer optimization problem. TM uses the apriori algorithm, developed in the field of data mining, to efficiently extract the bar sets that frequently appears among superior solutions, and proceeds so as to preserve the sets. Hence, the process of optimization can be investigated by tracing the frequent bar sets, accordingly, the parameters for optimization can easily be adjusted. It is pointed out that the ground structure method based on nonlinear programming is not effective for finding optimal placement of braces for a given frame under local buckling constraints. We propose an integrated approach to obtain an accurate solution of this problem, where optimal placement of braces is searched by TM, and the sizing optimization is performed by nonlinear programming. Three numerical examples are solved to demonstrate the performance of TM in comparison with another heuristic method called tabu search.

  5. Acoustic design by topology optimization

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard; Jensen, Jakob Søndergaard; Sigmund, Ole

    2008-01-01

    To bring down noise levels in human surroundings is an important issue and a method to reduce noise by means of topology optimization is presented here. The acoustic field is modeled by Helmholtz equation and the topology optimization method is based on continuous material interpolation functions...

  6. Level-Set Topology Optimization with Aeroelastic Constraints

    Science.gov (United States)

    Dunning, Peter D.; Stanford, Bret K.; Kim, H. Alicia

    2015-01-01

    Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

  7. Combined Shape and Topology Optimization

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman

    Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead...

  8. Bifurcations in the optimal elastic foundation for a buckling column

    Energy Technology Data Exchange (ETDEWEB)

    Rayneau-Kirkhope, Daniel, E-mail: ppxdr@nottingham.ac.u [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom); Farr, Robert [Unilever R and D, Olivier van Noortlaan 120, AT3133, Vlaardingen (Netherlands); London Institute for Mathematical Sciences, 22 South Audley Street, Mayfair, London (United Kingdom); Ding, K. [Department of Physics, Fudan University, Shanghai, 200433 (China); Mao, Yong [School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD (United Kingdom)

    2010-12-01

    We investigate the buckling under compression of a slender beam with a distributed lateral elastic support, for which there is an associated cost. For a given cost, we study the optimal choice of support to protect against Euler buckling. We show that with only weak lateral support, the optimum distribution is a delta-function at the centre of the beam. When more support is allowed, we find numerically that the optimal distribution undergoes a series of bifurcations. We obtain analytical expressions for the buckling load around the first bifurcation point and corresponding expansions for the optimal position of support. Our theoretical predictions, including the critical exponent of the bifurcation, are confirmed by computer simulations.

  9. Selective buckling via states of self-stress in topological metamaterials

    Science.gov (United States)

    Paulose, Jayson; Meeussen, Anne S.; Vitelli, Vincenzo

    2015-01-01

    States of self-stress—tensions and compressions of structural elements that result in zero net forces—play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices. PMID:26056303

  10. Selective buckling via states of self-stress in topological metamaterials.

    Science.gov (United States)

    Paulose, Jayson; Meeussen, Anne S; Vitelli, Vincenzo

    2015-06-23

    States of self-stress--tensions and compressions of structural elements that result in zero net forces--play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self-stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely hinged joints, they leave a distinct signature in the nonlinear buckling behavior of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.

  11. Topology optimization for coated structures

    DEFF Research Database (Denmark)

    Clausen, Anders; Andreassen, Erik; Sigmund, Ole

    2015-01-01

    This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....

  12. Topology Optimization for Convection Problems

    DEFF Research Database (Denmark)

    Alexandersen, Joe

    2011-01-01

    This report deals with the topology optimization of convection problems.That is, the aim of the project is to develop, implement and examine topology optimization of purely thermal and coupled thermomechanical problems,when the design-dependent eects of convection are taken into consideration.......This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...

  13. Topology optimized permanent magnet systems

    CERN Document Server

    Bjørk, R; Insinga, A R

    2016-01-01

    Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. First, the Halbach cylinder is topology optimized with iron and an increase of 15% in magnetic efficiency is shown, albeit with an increase of 3.8 pp. in field inhomogeneity - a value compared to the inhomogeneity in a 16 segmented Halbach cylinder. Following this a topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111% for the chosen dimensions. Finally, a permanent magnet with alternating high and low field regions is considered. Here a $\\Lambda_\\mathrm{cool}$ figure of merit of 0.472 is reached, which is an increase of 100% compared to a previous optimized design.

  14. Topology Optimized Photonic Wire Splitters

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Borel, Peter Ingo; Jensen, Jakob Søndergaard;

    2006-01-01

    Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm.......Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm....

  15. Robust buckling optimization of laminated composite structures using discrete material optimization considering “worst” shape imperfections

    DEFF Research Database (Denmark)

    Henrichsen, Søren Randrup; Lindgaard, Esben; Lund, Erik

    2015-01-01

    Robust buckling optimal design of laminated composite structures is conducted in this work. Optimal designs are obtained by considering geometric imperfections in the optimization procedure. Discrete Material Optimization is applied to obtain optimal laminate designs. The optimal geometric...... example. The imperfection sensitivity of the optimized structure decreases during the recurrence optimization for both examples, hence robust buckling optimal structures are designed....

  16. Time-Space Topology Optimization

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2008-01-01

    A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....

  17. Topology optimized RF MEMS switches

    DEFF Research Database (Denmark)

    Philippine, M. A.; Zareie, H.; Sigmund, Ole

    2013-01-01

    Topology optimization is a rigorous and powerful method that should become a standard MEMS design tool - it can produce unique and non-intuitive designs that meet complex objectives and can dramatically improve the performance and reliability of MEMS devices. We present successful uses of topology...... optimization for an RF MEM capacitive switch. Extensive experimental data confirms that the switches perform as designed by the optimizations, and that our simulation models are accurate. A subset of measurements are presented here. Broader results have been submitted in full journal format....

  18. Approximate Reanalysis in Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole

    2009-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...

  19. Topological Derivatives in Shape Optimization

    CERN Document Server

    Novotny, Antonio André

    2013-01-01

    The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, sensitivity analysis in fracture mechanics and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intende...

  20. Topology optimization of flexoelectric structures

    Science.gov (United States)

    Nanthakumar, S. S.; Zhuang, Xiaoying; Park, Harold S.; Rabczuk, Timon

    2017-08-01

    We present a mixed finite element formulation for flexoelectric nanostructures that is coupled with topology optimization to maximize their intrinsic material performance with regards to their energy conversion potential. Using Barium Titanate (BTO) as the model flexoelectric material, we demonstrate the significant enhancement in energy conversion that can be obtained using topology optimization. We also demonstrate that non-smooth surfaces can play a key role in the energy conversion enhancements obtained through topology optimization. Finally, we examine the relative benefits of flexoelectricity, and surface piezoelectricity on the energy conversion efficiency of nanobeams. We find that the energy conversion efficiency of flexoelectric nanobeams is comparable to the energy conversion efficiency obtained from nanobeams whose electromechanical coupling occurs through surface piezoelectricity, but are ten times thinner. Overall, our results not only demonstrate the utility and efficiency of flexoelectricity as a nanoscale energy conversion mechanism, but also its relative superiority as compared to piezoelectric or surface piezoelectric effects.

  1. Topology optimization of flow problems

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund

    2007-01-01

    of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the thesis also contains examples with the 2D Navier-Stokes equation as well as an example with convection dominated....... Although the study of the FVM is carried out using a simple heat conduction problem, the work illuminates and discusses the technicalities of employing the FVM in connection with topology optimization. Finally, parallelized solution methods are investigated using the high performance computing facility...

  2. Topology optimization for acoustic problems

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard

    2006-01-01

    In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...

  3. Topology optimization of microfluidic mixers

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe; Gersborg, Allan Roulund; Sigmund, Ole

    2009-01-01

    This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering...

  4. Topology optimized electrothermal polysilicon microgrippers

    DEFF Research Database (Denmark)

    Sardan Sukas, Özlem; Petersen, Dirch Hjorth; Mølhave, Kristian

    2008-01-01

    This paper presents the topology optimized design procedure and fabrication of electrothermal polysilicon microgrippers for nanomanipulation purposes. Performance of the optimized microactuators is compared with a conventional three-beam microactuator design through finite element analysis....... The accuracy of the finite element model is verified by comparison of simulated and measured displacement vs. bias voltage curves. A considerable improvement in the mechanical stiffness is indicated by AFM force measurements, being 9 times higher compared to the conventional three-beam actuator. (C) 2008...

  5. Benchmarking optimization solvers for structural topology optimization

    DEFF Research Database (Denmark)

    Rojas Labanda, Susana; Stolpe, Mathias

    2015-01-01

    The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different...... sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point...... profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving...

  6. Topology Optimization for Additive Manufacturing

    DEFF Research Database (Denmark)

    Clausen, Anders

    This PhD thesis deals with the combination of topology optimization and additive man-ufacturing (AM, also known as 3D-printing). In addition to my own works, the thesis contains a broader review and assessment of the literature within the field. The thesis first presents a classification...... of the various AM technologies, a review of relevant manufacturing materials, the properties of these materials in the additively manufactured part, as well as manufacturing constraints with a potential for design optimization. Subsequently, specific topology optimization formulations relevant for the most im......-portant AM-related manufacturing constraints are presented. These constraints are di-vided into directional and non-directional constraints. Non-directional constraints include minimum/uniform length scale and a cavity constraint. It is shown that modified filter boundary conditions are required in order...

  7. Wave Manipulation by Topology Optimization

    DEFF Research Database (Denmark)

    Andkjær, Jacob Anders

    Sound and light propagate as waves and are scattered, reflected and change direction when encountering other media and obstacles. By optimizing the spatial placement and distribution of the media, which the waves encounter, one can obtain useful and interesting effects. This thesis describes how...... topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...

  8. Topology Optimization using a Topology Description Function Approach

    NARCIS (Netherlands)

    de Ruiter, M.J.

    2005-01-01

    During the last two decades, computational structural optimization methods have emerged, as computational power increased tremendously. Designers now have topological optimization routines at their disposal. These routines are able to generate the entire geometry of structures, provided only with in

  9. Improving Topology Optimization using Games

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas

    free of charge on iOS and Android devices1. The TopOptGame is inspired by puzzle-games (a genre of computer games), which constantly challenges the players and gives rewards when progress is made. This engagement loop will take the player on a journey starting with simple problems with few supports......, this will allow us to analyze the data to measure human performance of topology optimization and more importantly, in which cases people's intuition succeed or fail. The game is currently a working prototype and is scheduled for final release on both iOS and Android before WCSMO-10....

  10. Topology Optimization of Thermal Heat Sinks

    DEFF Research Database (Denmark)

    Klaas Haertel, Jan Hendrik; Engelbrecht, Kurt; Lazarov, Boyan Stefanov

    2015-01-01

    In this paper, topology optimization is applied to optimize the cooling performance of thermal heat sinks. The coupled two-dimensional thermofluid model of a heat sink cooled with forced convection and a density-based topology optimization including density filtering and projection are implemented...... in COMSOL Multiphysics. The optimization objective is to minimize the heat sink’s temperature for a prescribed pressure drop and fixed heat generation. To conduct the optimization, COMSOL’s Optimization Module with GCMMA as the optimization method is used. The implementation of this topology optimization...

  11. Simultaneous topology optimization of structures and supports

    DEFF Research Database (Denmark)

    Buhl, Thomas

    2002-01-01

    The purpose of this paper is to demonstrate a method for and the benefits of simultaneously designing structure and support distribution using topology optimization. The support conditions are included in the topology optimization by introducing, a new set of design variables that represents...... cost of supports in a design domain. Other examples show that more efficient mechanisms are obtained by introducing the support conditions in the topology optimization problem....

  12. Improving topology optimization intuition through games

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten; Malmgren-Hansen, David; Bærentzen, J. Andreas

    2016-01-01

    This paper describes the educational game, TopOpt Game, which invites the player to solve various optimization challenges. The main purpose of gamifying topology optimization is to create a supplemental educational tool which can be used to introduce concepts of topology optimization to newcomers...

  13. Topological Optimization of Rod Mixers

    Science.gov (United States)

    Finn, Matthew D.; Thiffeault, Jean-Luc

    2006-11-01

    Stirring of fluid with moving rods is necessary in many practical applications to achieve homogeneity. These rods are topological obstacles that force stretching of fluid elements. The resulting stretching and folding is commonly observed as filaments and striations, and is a precursor to mixing. In a space-time diagram, the trajectories of the rods form a braid [1], and the properties of this braid impose a minimal complexity in the flow. We discuss how optimal mixing protocols can be obtained by a judicious choice of braid, and how these protocols can be implemented using simple gearing [2].[12pt] [1] P. L. Boyland, H. Aref, and M. A. Stremler, JFM 403, 277 (2000).[8pt] [2] J.-L. Thiffeault and M. D. Finn, http://arxiv.org/nlin/0603003

  14. Adjoint Techniques for Topology Optimization of Structures Under Damage Conditions

    Science.gov (United States)

    Akgun, Mehmet A.; Haftka, Raphael T.

    2000-01-01

    The objective of this cooperative agreement was to seek computationally efficient ways to optimize aerospace structures subject to damage tolerance criteria. Optimization was to involve sizing as well as topology optimization. The work was done in collaboration with Steve Scotti, Chauncey Wu and Joanne Walsh at the NASA Langley Research Center. Computation of constraint sensitivity is normally the most time-consuming step of an optimization procedure. The cooperative work first focused on this issue and implemented the adjoint method of sensitivity computation (Haftka and Gurdal, 1992) in an optimization code (runstream) written in Engineering Analysis Language (EAL). The method was implemented both for bar and plate elements including buckling sensitivity for the latter. Lumping of constraints was investigated as a means to reduce the computational cost. Adjoint sensitivity computation was developed and implemented for lumped stress and buckling constraints. Cost of the direct method and the adjoint method was compared for various structures with and without lumping. The results were reported in two papers (Akgun et al., 1998a and 1999). It is desirable to optimize topology of an aerospace structure subject to a large number of damage scenarios so that a damage tolerant structure is obtained. Including damage scenarios in the design procedure is critical in order to avoid large mass penalties at later stages (Haftka et al., 1983). A common method for topology optimization is that of compliance minimization (Bendsoe, 1995) which has not been used for damage tolerant design. In the present work, topology optimization is treated as a conventional problem aiming to minimize the weight subject to stress constraints. Multiple damage configurations (scenarios) are considered. Each configuration has its own structural stiffness matrix and, normally, requires factoring of the matrix and solution of the system of equations. Damage that is expected to be tolerated is local

  15. Topology optimization of wave-propagation problems

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2006-01-01

    Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures.......Topology optimization is demonstrated as a useful tool for systematic design of wave-propagation problems. We illustrate the applicability of the method for optical, acoustic and elastic devices and structures....

  16. Topology optimization of two-dimensional waveguides

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2003-01-01

    In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss.......In this work we use the method of topology optimization to design two-dimensional waveguides with low transmission loss....

  17. Topology optimization of reinforced concrete structures

    DEFF Research Database (Denmark)

    Amir, Oded

    Recent advances regarding topology optimization procedures of reinforced concrete structures are presented. We discuss several approaches to the challenging problem of optimizing the distribution of concrete and steel reinforcement. In particular, the consideration of complex nonlinear constitutive...

  18. Generalized Benders’ Decomposition for topology optimization problems

    DEFF Research Database (Denmark)

    Munoz Queupumil, Eduardo Javier; Stolpe, Mathias

    2011-01-01

    This article considers the non-linear mixed 0–1 optimization problems that appear in topology optimization of load carrying structures. The main objective is to present a Generalized Benders’ Decomposition (GBD) method for solving single and multiple load minimum compliance (maximum stiffness......–1 semi definite programming formulation of the considered problem. Several ways to accelerate the method are suggested and an implementation is described. Finally, a set of truss topology optimization problems are numerically solved to global optimality....

  19. Topology optimization using an explicit interface representation

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman; Nobel-Jørgensen, Morten; Aage, Niels

    2014-01-01

    used for both finite element calculations and shape representation. In addition, the approach unifies shape and topology optimization in a complementary optimization strategy. The shape is optimized on the basis of the gradient-based optimization algorithm MMA whereas holes are introduced using......We introduce the Deformable Simplicial Complex method to topology optimization as a way to represent the interface explicitly yet being able to handle topology changes. Topology changes are handled by a series of mesh operations, which also ensures a well-formed mesh. The same mesh is therefore...... topological derivatives. The presented method is tested on two standard minimum compliance problems which demonstrates that it is both simple to apply, robust and efficient....

  20. Optimization Formulations for the Maximum Nonlinear Buckling Load of Composite Structures

    DEFF Research Database (Denmark)

    Lindgaard, Esben; Lund, Erik

    2011-01-01

    , benchmarked on a number of numerical examples of laminated composite structures for the maximization of the buckling load considering fiber angle design variables. The optimization formulations are based on either linear or geometrically nonlinear analysis and formulated as mathematical programming problems...... solved using gradient based techniques. The developed local criterion is formulated such it captures nonlinear effects upon loading and proves useful for both analysis purposes and as a criterion for use in nonlinear buckling optimization. © 2010 Springer-Verlag....

  1. Numerical topology optimization of heat sinks

    OpenAIRE

    Van Oevelen, Tijs; Baelmans, Martine

    2014-01-01

    The availability of flexible production techniques challenges their full exploitation during thermo-hydraulic design of micro heat sinks. In this context, a systematic approach capable to take advantage of the practically unlimited design freedom is highly desirable. Therefore, we propose to use topology optimization, a numerical design optimization method well-established in structural mechanics problems. In this paper, the fundamentals of topology optimization, and its application in thermo...

  2. Design of microfluidic bioreactors using topology optimization

    DEFF Research Database (Denmark)

    Okkels, Fridolin; Bruus, Henrik

    2007-01-01

    We address the design of optimal reactors for supporting biological cultures using the method of topology optimization. For some years this method have been used to design various optimal microfluidic devices.1-4 We apply this method to distribute optimally biologic cultures within a flow of nutr...

  3. Topology optimization of microwave waveguide filters

    CERN Document Server

    Aage, Niels

    2016-01-01

    We present a density based topology optimization approach for the design of metallic microwave insert filters. A two-phase optimization procedure is proposed in which we, starting from a uniform design, first optimize to obtain a set of spectral varying resonators followed by a band gap optimization for the desired filter characteristics. This is illustrated through numerical experiments and comparison to a standard band pass filter design. It is seen that the carefully optimized topologies can sharpen the filter characteristics and improve performance. Furthermore, the obtained designs share little resemblance to standard filter layouts and hence the proposed design method offers a new design tool in microwave engineering.

  4. Topology optimization of fluid mechanics problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan

    While topology optimization for solid continuum structures have been studied for about 20 years and for the special case of trusses for many more years, topology optimization of fluid mechanics problems is more recent. Borrvall and Petersson [1] is the seminal reference for topology optimization...... with respect to minimizing the energy loss, characteristic properties of the velocity field or mixing properties. To reduce the computational complexity of the topology optimization problems the primary focus is put on the Stokes equation in 2D and in 3D. However, the the talk also contains examples with the 2......D Navier-Stokes equation as well as an example with convection dominated transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the present work gives a proof-of-concept for the application of the method within fluid mechanics problems and it remains...

  5. Reliability-based design optimization of composite stiffened panels in post-buckling regime

    OpenAIRE

    Lopez, C.; Bacarreza Nogales, OR; Baldomir, A.; Hernandez, S; Aliabadi, MH

    2016-01-01

    This paper focuses on Deterministic and Reliability Based Design Optimization (DO and RBDO) of composite stiffened panels considering post-buckling regime and progressive failure analysis. The ultimate load that a post-buckled panel can hold is to be maximised by changing the stacking sequence of both skin and stringers composite layups. The RBDO problem looks for a design that collapses beyond the shortening of failure obtained in the DO phase with a target reliability while considering unce...

  6. Multiobjective Topology Optimization of Energy Absorbing Materials

    Science.gov (United States)

    2015-08-01

    125–143 DOI 10.1007/s00158-014-1117-8 RESEARCH PAPER Multiobjective topology optimization of energy absorbing materials Raymond A. Wildman · George A...recent developments. J Multiscale Model 3(4):1–42 Qiao P, Yang M, Bobaru F (2008) Impact mechanics and high-energy absorbing materials: review . J Aerosp...ARL-RP-0533 ● AUG 2015 US Army Research Laboratory Multiobjective Topology Optimization of Energy Absorbing Materials by

  7. Topology optimization for simplified structural fire safety

    DEFF Research Database (Denmark)

    Madsen, Søren; Lange, Nis P.; Giuliani, Luisa;

    2016-01-01

    Topology optimization is applied in an idealized structural fire safety model, where the minimum compliance problem is constrained by temperature-controlled structural degradation. The constraint ensures a certain structural stiffness after a prescribed time. As this time period is extended......, resulting optimized topologies tend to become thicker or introduce redundant members that can take over when structural parts near the origin of the fire lose their load carrying capability. Hence, the structural degradation model acts as an erosion operator on the topology and indirectly enforces a minimum...

  8. Topology Optimization for Transient Wave Propagation Problems

    DEFF Research Database (Denmark)

    Matzen, René

    as for vectorial elastic wave propagation problems using finite element analysis [P2], [P4]. The concept is implemented in a parallel computing code that includes efficient techniques for performing gradient based topology optimization. Using the developed computational framework the thesis considers four...... new technology, by designing new materials and their layout. The thesis presents a general framework for applying topology optimization in the design of material layouts for transient wave propagation problems. In contrast to the high level of modeling in the frequency domain, time domain topology...

  9. Topology Optimization for Architected Materials Design

    Science.gov (United States)

    Osanov, Mikhail; Guest, James K.

    2016-07-01

    Advanced manufacturing processes provide a tremendous opportunity to fabricate materials with precisely defined architectures. To fully leverage these capabilities, however, materials architectures must be optimally designed according to the target application, base material used, and specifics of the fabrication process. Computational topology optimization offers a systematic, mathematically driven framework for navigating this new design challenge. The design problem is posed and solved formally as an optimization problem with unit cell and upscaling mechanics embedded within this formulation. This article briefly reviews the key requirements to apply topology optimization to materials architecture design and discusses several fundamental findings related to optimization of elastic, thermal, and fluidic properties in periodic materials. Emerging areas related to topology optimization for manufacturability and manufacturing variations, nonlinear mechanics, and multiscale design are also discussed.

  10. Topology Optimization of Structure Using Differential Evolution

    Directory of Open Access Journals (Sweden)

    Chun-Yin Wu

    2008-02-01

    Full Text Available The population-based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems. A promising new evolutionary algorithm, differential evolution, has garnered significant attention in the engineering optimization research. Differential evolution has the advantage of incorporating a relatively simple and efficient form of mutation and crossover. This paper aims at introducing differential evolution as an alternative approach for topology optimization of truss and continuous structure with stress and displacement constraints. In comparison the results with other studies, it shows that differential evolution algorithms are very effective and efficient in solving topology optimization problem of structure.

  11. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole

    Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see......, e.g. [2]) in order to develop methods for topology design for applications where conservation laws are critical such that element--wise conservation in the discretized models has a high priority. This encompasses problems involving for example mass and heat transport. The work described...... in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...

  12. Topology optimization for nano-photonics

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2011-01-01

    applications. Topology optimization may be based on finite element and finite difference type modeling methods in both frequency and time domain. The basic idea is that the material density of each element or grid point is a design variable, hence the geometry is parameterized in a pixel-like fashion......Topology optimization is a computational tool that can be used for the systematic design of photonic crystals, waveguides, resonators, filters and plasmonics. The method was originally developed for mechanical design problems but has within the last six years been applied to a range of photonics....... The optimization problem is efficiently solved using mathematical programming-based optimization methods and analytical gradient calculations. The paper reviews the basic procedures behind topology optimization, a large number of applications ranging from photonic crystal design to surface plasmonic devices...

  13. Efficient reanalysis techniques for robust topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Sigmund, Ole; Lazarov, Boyan Stefanov

    2012-01-01

    efficient robust topology optimization procedures based on reanalysis techniques. The approach is demonstrated on two compliant mechanism design problems where robust design is achieved by employing either a worst case formulation or a stochastic formulation. It is shown that the time spent on finite......The article focuses on the reduction of the computational effort involved in robust topology optimization procedures. The performance of structures designed by means of topology optimization may be seriously degraded due to fabrication errors. Robust formulations of the optimization problem were...... shown to yield optimized designs that are tolerant with respect to such manufacturing uncertainties. The main drawback of such procedures is the added computational cost associated with the need to evaluate a set of designs by performing multiple finite element analyses. In this article, we propose...

  14. On topology optimization of plates with prestress

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard

    2001-01-01

    In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the original stiffness matrix. The calculation...... of the sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA...

  15. Topology optimization design of space rectangular mirror

    Science.gov (United States)

    Qu, Yanjun; Wang, Wei; Liu, Bei; Li, Xupeng

    2016-10-01

    A conceptual lightweight rectangular mirror is designed based on the theory of topology optimization and the specific structure size is determined through sensitivity analysis and size optimization in this paper. Under the load condition of gravity along the optical axis, compared with the mirrors designed by traditional method using finite element analysis method, the performance of the topology optimization reflectors supported by peripheral six points are superior in lightweight ratio, structure stiffness and the reflective surface accuracy. This suggests that the lightweight method in this paper is effective and has potential value for the design of rectangular reflector.

  16. Improving topology optimization intuition through games

    DEFF Research Database (Denmark)

    Nobel-Jørgensen, Morten; Malmgren-Hansen, David; Bærentzen, J. Andreas

    2016-01-01

    This paper describes the educational game, TopOpt Game, which invites the player to solve various optimization challenges. The main purpose of gamifying topology optimization is to create a supplemental educational tool which can be used to introduce concepts of topology optimization to newcomers...... that players achieve higher scores the more they play the game. The game is freely available for the iOS platform at Apple's App Store and at http://www.topopt.dtu.dk/?q=node/909 for Win-dows and OSX....

  17. Topology optimization of inertia driven dosing units

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe

    2016-01-01

    This paper presents a methodology for optimizing inertia driven dosing units, sometimes referred to as eductors, for use in small scale flow applications. The unit is assumed to operate at low to moderate Reynolds numbers and under steady state conditions. By applying topology optimization...

  18. Robust topology optimization accounting for geometric imperfections

    DEFF Research Database (Denmark)

    Schevenels, M.; Jansen, M.; Lombaert, Geert

    2013-01-01

    performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... of imperfections) and a vertical load carrying system (for the second type). © 2013 Taylor & Francis Group, London....

  19. Tailoring group velocity by topology optimization

    DEFF Research Database (Denmark)

    Stainko, Roman; Sigmund, Ole

    2007-01-01

    The paper describes a systematic method for the tailoring of dispersion properties of slab-based photonic crystal waveguides. The method is based on the topology optimization method which consists in repeated finite element frequency domain analyses. The goal of the optimization process is to come...

  20. Topology Optimization of Sub-Wavelength Antennas

    DEFF Research Database (Denmark)

    Erentok, Aycan; Sigmund, Ole

    2011-01-01

    We propose a topology optimization strategy for the systematic design of a three-dimensional (3D), conductor-based sub-wavelength antenna. The post-processed finite-element (FE) models of the optimized structure are shown to be self-resonant, efficient and exhibit distorted omnidirectional...

  1. Shape and topology optimization of enzymatic microreactors

    DEFF Research Database (Denmark)

    Pereira Rosinha, Ines

    configuration. In this thesis structural optimization methods were exclusively applied to enzymatic microreactors. The case studies were chosen such that they can be experimentally tested afterwards. In this way, the design of the reactor is customized to the reaction system and itcontributes to the reduction......Structural optimization methods have been used by mechanical and civil engineers over the yearsto find the optimal structures. Structural optimization is a series of computational techniqueswhich include shape and topology optimization. Shape optimization is directly applied to theboundaries...... in a chemical process do not always yield in the best reaction conditions.This thesis develops an innovative application of topology and shape optimization methods to achemical engineering problem. The main goal is to design a reactor according to the limitations of the reaction system by modifying the reactor...

  2. Topology Optimization of Nanophotonic Devices

    DEFF Research Database (Denmark)

    Yang, Lirong

    are appropriate for problems where the power is to be maximized or minimized at a few frequencies, without regards on the detailed profile of the optical pulse or the need of large amount of frequency samplings. The design of slow light couplers connecting ridge waveguides and the photonic crystal waveguides...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....

  3. Topology optimization of microwave waveguide filters

    DEFF Research Database (Denmark)

    Aage, Niels; Johansen, Villads Egede

    2017-01-01

    We present a density based topology optimization approach for the design of metallic microwave insert filters. A two-phase optimization procedure is proposed in which we, starting from a uniform design, first optimize to obtain a set of spectral varying resonators followed by a band gap optimizat......We present a density based topology optimization approach for the design of metallic microwave insert filters. A two-phase optimization procedure is proposed in which we, starting from a uniform design, first optimize to obtain a set of spectral varying resonators followed by a band gap...... little resemblance to standard filter layouts and hence the proposed design method offers a new design tool in microwave engineering....

  4. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see...... in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... derivative of the system matrix K and in how one computes the discretized version of certain objective functions. Thus for a cost function for minimum dissipated energy (like minimum compliance for an elastic structure) one obtains an expression c = u^\\T \\tilde{K}u $, where \\tilde{K} is different from K...

  5. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole

    Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see...... in this presentation is focused on a prototype model for topology optimization of steady heat diffusion. This allows for a study of the basic ingredients in working with FVM methods when dealing with topology optimization problems. The FVM and FEM based formulations differ both in how one computes the design...... $, where $\\tilde{\\mathbf K}$ is different from $\\mathbf K $; in a FEM scheme these matrices are equal following the principle of virtual work. Using a staggered mesh and averaging procedures consistent with the FVM the checkerboard problem is eliminated. Two averages are compared to FE solutions, being...

  6. State space Newton's method for topology optimization

    DEFF Research Database (Denmark)

    Evgrafov, Anton

    2014-01-01

    We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem in the algori......We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem...

  7. Systematic design of microstructures by topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2003-01-01

    The topology optimization method can be used to determine the material distribution in a design domain such that an objective function is maximized and constraints are fulfilled. The method which is based on Finite Element Analysis may be applied to all kinds of material distribution problems like...... extremal material design, sensor and actuator design and MEMS synthesis. The state-of-the-art in topology optimization will be reviewed and older as well as new applications in phononic and photonic crystals design will be presented....

  8. Implementation of Molding Constraints in Topology Optimization

    DEFF Research Database (Denmark)

    Marx, S.; Kristensen, Anders Schmidt

    2009-01-01

    In many cases the topology optimization method yield inadmissible solutions in respect to a particular manufacturing process, e.g. injection molding. In the present work it is chosen to focus on the most common injection molding parameters/factors determining the quality of the mold geometry, i.......e. uniform thickness, filling of the die and ejection of the molded item, i.e. extrusion. The mentioned injection mold parameters/factors are introduced in the topology optimization by defining a centerline of the initial domain and then penalize elements in respect to the distance to the defined centerline...

  9. Topology optimization of laminated plates with prestress

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard

    2002-01-01

    Laminated plates with different prestress in the layers are topology optimized. The objectives are to minimize the deflection due to the prestress or to minimize ordinary compliance. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress...... stiffness matrix to the structural stiffness. The calculations of sensitivities are complicated not only by the prestress but also because we are dealing with laminates. The topology optimization problem is solved using a new penalization scheme as an alternative to the SIMP (power law) approach...

  10. Topology optimization of nano-photonic systems

    DEFF Research Database (Denmark)

    Elesin, Yuriy; Wang, Fengwen; Andkjær, Jacob Anders;

    2012-01-01

    We describe recent developments within nano-photonic systems design based on topology optimization. Applications include linear and non-linear optical waveguides, slow-light waveguides, as well as all-dielectric cloaks that minimize scattering or back-scattering from hard obstacles.......We describe recent developments within nano-photonic systems design based on topology optimization. Applications include linear and non-linear optical waveguides, slow-light waveguides, as well as all-dielectric cloaks that minimize scattering or back-scattering from hard obstacles....

  11. STACKING SEQUENCE OPTIMIZATION OF LAMINATED COMPOSITE CYLINDER SHELL FOR MAXIMAL BUCKLING LOAD

    Institute of Scientific and Technical Information of China (English)

    TANG Qian; LIAO Xiaoyun; GAO Zhan

    2008-01-01

    A new optimization method for the optimization of stacking of composite glass fiber laminates is developed. The fiber orientation and angle of the layers of the cylindrical shells are sought considering the buckling load. The proposed optimization algorithm applies both finite element analysis and the mode-pursuing sampling (MPS)method. The algorithms suggest the optimal stacking sequence for achieving the maximal buckling load. The procedure is implemented by integrating ANSYS and MATLAB. The stacking sequence designing for the symmetric angle-ply three-layered and five-layered composite cylinder shells is presented to illustrate the optimization process, respectively. Compared with the genetic algorithms, the proposed optimization method is much faster and efficient for composite staking sequence plan.

  12. Topology Optimization using an Explicit Interface Representation

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman; Nobel-Jørgensen, Morten; Bærentzen, J. Andreas;

    Current methods for topology optimization primarily represent the interface between solid and void implicitly on fixed grids. In contrast, shape optimization methods represent the interface explicitly, but do not allow for any topological changes to the structure. Using an explicit interface...... to handle topology changes. It does so by discretizing the entire design domain into an irregular adaptive triangle mesh and thereby explicitly representing both the structure and the embedding space. In other words, the entire design domain is divided into triangles, where the interface is represented...... the final design. The status of the work is that the method has been developed and is showing promising results. For instance, the cantilever beam problem has been solved to a high precision using a fine discretization by evaluating the objective function approximately 500 times. This took around 100...

  13. Topology optimization using the finite volume method

    DEFF Research Database (Denmark)

    Computational procedures for topology optimization of continuum problems using a material distribution method are typically based on the application of the finite element method (FEM) (see, e.g. [1]). In the present work we study a computational framework based on the finite volume method (FVM, see...... the well known Reuss lower bound. [1] Bendsøe, M.P.; Sigmund, O. 2004: Topology Optimization - Theory, Methods, and Applications. Berlin Heidelberg: Springer Verlag [2] Versteeg, H. K.; W. Malalasekera 1995: An introduction to Computational Fluid Dynamics: the Finite Volume Method. London: Longman......, e.g. [2]) in order to develop methods for topology design for applications where conservation laws are critical such that element--wise conservation in the discretized models has a high priority. This encompasses problems involving for example mass and heat transport. The work described...

  14. Structural and Topology Optimization of Complex Civil Engineering Structures

    DEFF Research Database (Denmark)

    Hald, Frederik; Kirkegaard, Poul Henning; Andersen, Lars Vabbersgaard

    2013-01-01

    This paper shows the use of topology optimization for finding an optimized form for civil engineering structures. Today topology optimization and shape optimization have been integrated in several commercial finite element codes. Here, the topology of two complex civil engineering structures...

  15. STUDY OF TOPOLOGY OPTIMIZATION FOR THERMO-STRUCTURAL COUPLING FIELD

    Institute of Scientific and Technical Information of China (English)

    Zuo Kongtian; Qian Qin; Zhao Yudong; Chen Liping

    2005-01-01

    A number of critical problems of topology optimization concerning the thermostructural coupling field are studied at length. The governing equations and topology optimization model for the thermal-structural coupling field are derived, with an adjoint method for sensitivity analysis of the thermo-structural coupling field proposed. The optimization algorithm for coupling field topology optimization is investigated and a flowchart of coupling field topology optimization presented. The theory and algorithms are implemented and verified by two numerical examples.

  16. Topology Optimization including Inequality Buoyancy Constraints

    NARCIS (Netherlands)

    Picelli, R.; Van Dijk, R.; Vicente, W.M.; Pavanello, R.; Langelaar, M.; Van Keuen, A.

    2014-01-01

    This paper presents an evolutionary topology optimization method for applications in design of completely submerged buoyant devices with design-dependent fluid pressure loading. This type of structures aid rig installations and pipeline transportation in all water depths in offshore structural

  17. Topology optimization for biocatalytic microreactor configurations

    DEFF Research Database (Denmark)

    Pereira Rosinha, Ines; Gernaey, Krist; Woodley, John

    2015-01-01

    The aim of this study is to present an innovative strategy for selecting a reactor for a specific process. Instead of adapting the process to a well-known reactor shape, a topology optimization method is used to obtain the best reactor configuration, and is applied to a biocatalyic reaction system...

  18. Topology Optimization including Inequality Buoyancy Constraints

    NARCIS (Netherlands)

    Picelli, R.; Van Dijk, R.; Vicente, W.M.; Pavanello, R.; Langelaar, M.; Van Keuen, A.

    2014-01-01

    This paper presents an evolutionary topology optimization method for applications in design of completely submerged buoyant devices with design-dependent fluid pressure loading. This type of structures aid rig installations and pipeline transportation in all water depths in offshore structural engin

  19. Maximization of eigenvalues using topology optimization

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard

    2000-01-01

    Topology optimization is used to optimize the eigenvalues of plates. The results are intended especially for MicroElectroMechanical Systems (MEMS) but call be seen as more general. The problem is not formulated as a case of reinforcement of an existing structure, so there is a problem related...... to localized modes in low density areas. The topology optimization problem is formulated using the SIMP method. Special attention is paid to a numerical method for removing localized eigenmodes in low density areas. The method is applied to numerical examples of maximizing the first eigenfrequency, One example...... is a practical MEMS application; a probe used in an Atomic Force Microscope (AFM). For the AFM probe the optimization is complicated by a constraint on the stiffness and constraints on higher order eigenvalues....

  20. Topological and parametric optimization of gear trains

    Science.gov (United States)

    Swantner, Albert; Campbell, Matthew I.

    2012-11-01

    A method for automating the design of gear trains comprised of simple, compound, bevel and worm is described. The search process combines topological changes, discrete variable choices and continuous variable optimization. By combing best-first search, implicit enumeration, automated optimization invocation and gradient-based optimization, a near guarantee of the optimal solution can be made. While the combination of methods is specific to gear trains, there are aspects of the work that make it amenable to other engineering design problems. In addition, the topological and discrete modifications to the candidate solutions are specific to gear trains, but the graph grammar methodology that is adopted has been tailored to other problems. This article presents details on the rules that generate feasible gear trains, the evaluation routines used in determining the objective functions and constraints, and the interaction among the three search methods. Resulting gear trains are presented for a variety of gear problems.

  1. Optimization of practical trusses with constraints on eigenfrequencies, displacements, stresses, and buckling

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard; Nielsen, A.

    2004-01-01

    and the objective of the optimizations is minimum mass with constraints on (possibly multiple) eigenfrequencies, displacements, and stresses. For the case of stress constraints, we deal differently with tensile and compressive stresses, for which we control buckling on the element level. The stress constraints...

  2. Topology Optimization - broadening the areas of application

    DEFF Research Database (Denmark)

    Bendsøe, Martin P.; Lund, Erik; Olhoff, Niels;

    2005-01-01

    This paper deals with recent developments of topology optimization techniques for application in some new types of design problems. The emphasis is on recent work of the Danish research groups at Aalborg University and at the Technical University of Denmark and focus is on the central role......, design in fluids, design in acoustics, and design in photonics. A short outline of other design optimization activities is also given....

  3. Topology optimization of Channel flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Sigmund, Ole; Haber, R. B.

    2005-01-01

    ]. Further, the inclusion of inertia effects significantly alters the physics, enabling solutions of new classes of optimization problems, such as velocity--driven switches, that are not addressed by the earlier method. Specifically, we determine optimal layouts of channel flows that extremize a cost...... sensitivities. Our target application is optimal layout design of channels in fluid network systems. Using concepts borrowed from topology optimization of compliant mechanisms in solid mechanics, we introduce a method for the synthesis of fluidic components, such as switches, diodes, etc....

  4. The Optimizer Topology Characteristics in Seismic Hazards

    Science.gov (United States)

    Sengor, T.

    2015-12-01

    The characteristic data of the natural phenomena are questioned in a topological space approach to illuminate whether there is an algorithm behind them bringing the situation of physics of phenomena to optimized states even if they are hazards. The optimized code designing the hazard on a topological structure mashes the metric of the phenomena. The deviations in the metric of different phenomena push and/or pull the fold of the other suitable phenomena. For example if the metric of a specific phenomenon A fits to the metric of another specific phenomenon B after variation processes generated with the deviation of the metric of previous phenomenon A. Defining manifold processes covering the metric characteristics of each of every phenomenon is possible for all the physical events; i.e., natural hazards. There are suitable folds in those manifold groups so that each subfold fits to the metric characteristics of one of the natural hazard category at least. Some variation algorithms on those metric structures prepare a gauge effect bringing the long time stability of Earth for largely scaled periods. The realization of that stability depends on some specific conditions. These specific conditions are called optimized codes. The analytical basics of processes in topological structures are developed in [1]. The codes are generated according to the structures in [2]. Some optimized codes are derived related to the seismicity of NAF beginning from the quakes of the year 1999. References1. Taner SENGOR, "Topological theory and analytical configuration for a universal community model," Procedia- Social and Behavioral Sciences, Vol. 81, pp. 188-194, 28 June 2013, 2. Taner SENGOR, "Seismic-Climatic-Hazardous Events Estimation Processes via the Coupling Structures in Conserving Energy Topologies of the Earth," The 2014 AGU Fall Meeting, Abstract no.: 31374, ABD.

  5. Multistep Optimization of Composite Drive Shaft Subject to Strength, Buckling, Vibration and Manufacturing Constraints

    Science.gov (United States)

    Cherniaev, Aleksandr; Komarov, Valeriy

    2015-10-01

    Composite drive shafts are extensively used in automotive and aeronautical applications due to lightweight combined with exceptional strength and stiffness. Complexity of the drive shaft design problem associated with the need to determine rational values for multiple parameters characterizing composite material (fiber orientation angles, stacking sequence and ply thicknesses), as well as with the fact that multiple conflicting design constraints should be considered simultaneously. In this paper we approach this problem considering carbon/epoxy drive shaft design as a multistep optimization process. It includes the following steps: 1) determination of fiber orientation angles and laminate stacking sequence based on analysis of loading conditions and analytical expressions predicting buckling load and minimal natural frequency of idealized drive shaft; 2) finding rational ply thicknesses using formal optimization procedure utilizing response surface approximations and gradient-based optimization algorithm; and 3) verification analysis of the optimized configuration with the use of nonlinear buckling analysis to ensure satisfaction of stability constraint.

  6. Topology Optimization for Urban Traffic Sensor Network

    Institute of Scientific and Technical Information of China (English)

    HU Jianming; SONG Jingyan; ZHANG Mingchen; KANG Xiaojing

    2008-01-01

    This paper presents an optimized topology for urban traffic sensor networks. Small world theory is used to improve the performance of the wireless communication system with a heterogeneous transmission model and an optimal transmission radius. Furthermore, a series of simulations based on the actual road network around the 2nd Ring Road in Beijing demonstrate the practicability of constructing artificial "small worlds". Moreover, the particle swarm optimization method is used to calculate the globally best distribution of the nodes with the large radius. The methods proposed in this paper will be helpful to the sensor nodes deployment of the new urban traffic sensor networks.

  7. Topology optimization of robust superhydrophobic surfaces

    DEFF Research Database (Denmark)

    Cavalli, Andrea; Bøggild, Peter; Okkels, Fridolin

    2013-01-01

    the space between the posts, we search for an optimal post cross-section that minimizes the vertical displacement of the liquid–air interface at the base of the drop when a pressure difference is applied. Topology optimisation proves effective in this framework, showing that posts with a branching cross......-section are optimal, which is consistent with several biologic strategies to achieve superhydrophobicity. Through a filtering technique, we can also control the characteristic length scale of the optimal design, thus obtaining geometries feasible via standard lithography....

  8. Reliability-Based Topology Optimization With Uncertainties

    Energy Technology Data Exchange (ETDEWEB)

    Bae, Kyoungryun [JAEIK Information and Communication Co. Ltd., Seoul (Korea, Republic of); Wang, Semyung [Kwangju Institute of Science and Technology, Kwangju (Korea, Republic of); Choi, Kyung K. [Univ. of Iowa, Iowa (United States)

    2002-11-15

    A probabilistic optimal design modeled with finite elements is presented. A 2-D finite element model is constructed for topology optimization. Young's modulus, thickness and loading are considered as uncertain variables. The uncertain variable means that the variable has a variance on a certain point. In order to compute reliability constraints, two methods-RIA, PMA-are widely used. To find reliability index easily, the limit state function is linearly approximated at the each iteration. This approximation method is called as the first order reliability method (FORM), which is widely used in reliability based design optimizations (RBDO)

  9. NEW HMM ALGORITHM FOR TOPOLOGY OPTIMIZATION

    Institute of Scientific and Technical Information of China (English)

    Zuo Kongtian; Zhao Yudong; Chen Liping; Zhong Yifang; Huang Yuying

    2005-01-01

    A new hybrid MMA-MGCMMA (HMM) algorithm for solving topology optimization problems is presented. This algorithm combines the method of moving asymptotes (MMA) algorithm and the modified globally convergent version of the method of moving asymptotes (MGCMMA) algorithm in the optimization process. This algorithm preserves the advantages of both MMA and MGCMMA. The optimizer is switched from MMA to MGCMMA automatically, depending on the numerical oscillation value existing in the calculation. This algorithm can improve calculation efficiency and accelerate convergence compared with simplex MMA or MGCMMA algorithms, which is proven with an example.

  10. Design and fabrication of topologically optimized structures;

    DEFF Research Database (Denmark)

    Feringa, Jelle; Søndergaard, Asbjørn

    2012-01-01

    Integral structural optimization and fabrication seeks the synthesis of two original approaches; that of topological optimization (TO) and robotic hotwire cutting (HWC) (Mcgee 2011). TO allows for the reduction of up to 70% of the volume of concrete to support a given structure (Sondergaard...... & Dombernowsky 2011). A strength of the method is that it allows to come up with structural designs that lie beyond the grasp of traditional means of design. A design space is a discretized volume, delimiting where the optimization will take place. The number of cells used to discretize the design space thus...

  11. Topology optimization for transient heat transfer problems

    DEFF Research Database (Denmark)

    Zeidan, Said; Sigmund, Ole; Lazarov, Boyan Stefanov

    The focus of this work is on passive control of transient heat transfer problems using the topology optimization (TopOpt) method [1]. The goal is to find distributions of a limited amount of phase change material (PCM), within a given design domain, which optimizes the heat energy storage [2]. Our......, TopOpt has later been extended to transient problems in mechanics and photonics (e.g. [5], [6] and [7]). In the presented approach, the optimization is gradient-based, where in each iteration the non-steady heat conduction equation is solved,using the finite element method and an appropriate time...

  12. Efficient Reanalysis Procedures in Structural Topology Optimization

    DEFF Research Database (Denmark)

    Amir, Oded

    of the analysis equations. For demonstrative purposes, the discussion is limited to topology optimization problems within the field of structural mechanics. Nevertheless, the results can be relevant for a wide range of problems in structural and topology optimization. The main focus of the thesis...... effort invested in the solution of the nested problem is even more dominant since nonlinear equation systems are to be solved repeatedly. Efficient procedures for nonlinear structural analysis are proposed, based on transferring solutions and factorized tangent stiffnesses from one design cycle...... to the following one. This approach is demonstrated on several design problems involving either geometric or material nonlinearities. The suggested procedures are shown to be effective mainly for problems that do not involve path-dependent solutions....

  13. Topology optimization in structural and continuum mechanics

    CERN Document Server

    Lewiński, Tomasz

    2014-01-01

    The book covers new developments in structural topology optimization. Basic features and limitations of Michell’s truss theory, its extension to a broader class of support conditions, generalizations of truss topology optimization, and Michell continua are reviewed. For elastic bodies, the layout problems in linear elasticity are discussed and the method of relaxation by homogenization is outlined. The classical problem of free material design is shown to be reducible to a locking material problem, even in the multiload case. For structures subjected to dynamic loads, it is explained how they can be designed so that the structural eigenfrequencies of vibration are as far away as possible from a prescribed external excitation frequency (or a band of excitation frequencies) in order to avoid resonance phenomena with high vibration and noise levels. For diffusive and convective transport processes and multiphysics problems, applications of the density method are discussed. In order to take uncertainty in mater...

  14. Robust topology optimization accounting for geometric imperfections

    DEFF Research Database (Denmark)

    Schevenels, M.; Jansen, M.; Lombaert, Geert

    2013-01-01

    performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... is modeled by means of a scalar non-Gaussian random field, which is represented as a translation process. The underlying Gaussian field is simulated by means of the EOLE method. The second type of imperfections is modeled as a Gaussian vector-valued random field, which is simulated directly by means...

  15. Topology optimized cloak for airborne sound

    DEFF Research Database (Denmark)

    Andkjær, Jacob Anders; Sigmund, Ole

    2013-01-01

    Directional acoustic cloaks that conceal an aluminum cylinder for airborne sound waves are presented in this paper. Subwavelength cylindrical aluminum inclusions in air constitute the cloak design to aid practical realizations. The positions and radii of the subwavelength cylinders are determined...... by minimizing scattering from the cloak-structure and cylinder using the gradient-based topology optimization method. In the final optimization step, the radii of the subwavelength cylinders are constrained to three discrete values. A near-perfect narrow-banded and angular cloaking effect is obtained...

  16. Topological Optimization of Continuum Structure based on ANSYS

    Directory of Open Access Journals (Sweden)

    Li Xue-ping

    2017-01-01

    Full Text Available Topology optimization is at the phase of structural concept design and the result of it is foundation for succeeding design, therefore, structural topology optimization is more important to engineering design. in this thesis, in order to seek the optimal structure shape of the winch’s mounting bracket of ROV simulator, topology optimization design of it by finite element analysis software ANSYS was carried out. the results show that the topology optimization method is an effective optimization method and indicate that the method is correct and effective, it has a certain engineering application prospect.

  17. Crashworthiness design of transient frame structures using topology optimization

    DEFF Research Database (Denmark)

    Pedersen, Claus B. Wittendorf

    2004-01-01

    The aim of this paper is to present topology optimization as a method to obtain conceptual designs for crash-worthiness. The topology optimization formulation uses rigorously computed sensitivities. The large displacements and plasticity of the 2D beam elements are modelled with the co-rotational......-rotational formulation and the plastic zone formulation, respectively. Three examples are presented to show the results of combining topology optimization and crashworthiness optimization. (C) 2003 Elsevier B.V. All rights reserved....

  18. Binary discrete method of topology optimization

    Institute of Scientific and Technical Information of China (English)

    MEI Yu-lin; WANG Xiao-ming; CHENG Geng-dong

    2007-01-01

    The numerical non-stability of a discrete algorithm of topology optimization can result from the inaccurate evaluation of element sensitivities. Especially, when material is added to elements, the estimation of element sensitivities is very inaccurate,even their signs are also estimated wrong. In order to overcome the problem, a new incremental sensitivity analysis formula is constructed based on the perturbation analysis of the elastic equilibrium increment equation, which can provide us a good estimate of the change of the objective function whether material is removed from or added to elements,meanwhile it can also be considered as the conventional sensitivity formula modified by a non-local element stiffness matrix. As a consequence, a binary discrete method of topology optimization is established, in which each element is assigned either a stiffness value of solid material or a small value indicating no material, and the optimization process can remove material from elements or add material to elements so as to make the objective function decrease. And a main advantage of the method is simple and no need of much mathematics, particularly interesting in engineering application.

  19. A new topology optimization scheme for nonlinear structures

    Energy Technology Data Exchange (ETDEWEB)

    Eim, Young Sup; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)

    2014-07-15

    A new topology optimization algorithm based on artificial bee colony algorithm (ABCA) was developed and applied to geometrically nonlinear structures. A finite element method and the Newton-Raphson technique were adopted for the nonlinear topology optimization. The distribution of material is expressed by the density of each element and a filter scheme was implemented to prevent a checkerboard pattern in the optimized layouts. In the application of ABCA for long structures or structures with small volume constraints, optimized topologies may be obtained differently for the same problem at each trial. The calculation speed is also very slow since topology optimization based on the roulette-wheel method requires many finite element analyses. To improve the calculation speed and stability of ABCA, a rank-based method was used. By optimizing several examples, it was verified that the developed topology scheme based on ABCA is very effective and applicable in geometrically nonlinear topology optimization problems.

  20. On filter boundary conditions in topology optimization

    DEFF Research Database (Denmark)

    Clausen, Anders; Andreassen, Erik

    2017-01-01

    we define three requirements that boundary conditions must fulfill in order to eliminate boundary effects. Previously suggested approaches are briefly reviewed in the light of these requirements. A new approach referred to as the “domain extension approach” is suggested. It effectively eliminates......Most research papers on topology optimization involve filters for regularization. Typically, boundary effects from the filters are ignored. Despite significant drawbacks the inappropriate homogeneous Neumann boundary conditions are used, probably because they are trivial to implement. In this paper...

  1. Linux software for large topology optimization problems

    DEFF Research Database (Denmark)

    evolving product, which allows a parallel solution of the PDE, it lacks the important feature that the matrix-generation part of the computations is localized to each processor. This is well-known to be critical for obtaining a useful speedup on a Linux cluster and it motivates the search for a COMSOL......-like package for large topology optimization problems. One candidate for such software is developed for Linux by Sandia Nat’l Lab in the USA being the Sundance system. Sundance also uses a symbolic representation of the PDE and a scalable numerical solution is achieved by employing the underlying Trilinos...

  2. Finite Volumes Discretization of Topology Optimization Problems

    DEFF Research Database (Denmark)

    Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

    such a mature and versatile technique for discretiz- ing partial dierential equations in the form of conservation laws of varying types. Advantages of FVMs include the simplicity of implementation, their local conservation properties, and the ease of coupling various PDEs in a multi-physics setting. In fact...... attractive, as all involved PDEs on a given domain are discretized using the same and the low- est possible number of degrees of freedom. In spite of their numerous favourable advantages, FVMs have seen very little adoption within the topology optimization community, where the absolute majority of numerical...

  3. Advanced Topology Optimization Methods for Conceptual Architectural Design

    DEFF Research Database (Denmark)

    Aage, Niels; Amir, Oded; Clausen, Anders

    2015-01-01

    in topological optimization: Interactive control and continuous visualization; embedding flexible voids within the design space; consideration of distinct tension / compression properties; and optimization of dual material systems. In extension, optimization procedures for skeletal structures such as trusses...

  4. Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework

    DEFF Research Database (Denmark)

    Aage, Niels; Andreassen, Erik; Lazarov, Boyan Stefanov

    2015-01-01

    This paper presents a flexible framework for parallel and easy-to-implement topology optimization using the Portable and Extendable Toolkit for Scientific Computing (PETSc). The presented framework is based on a standardized, and freely available library and in the published form it solves the mi...

  5. SIMULTANEOUS SHAPE AND TOPOLOGY OPTIMIZATION OF TRUSS UNDER LOCAL AND GLOBAL STABILITY CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    GuoXu; LiuWei; LiHongyan

    2003-01-01

    A new approach for the solution of truss shape and topology optimization problem sunder local and global stability constraints is proposed. By employing the cross sectional areas of each bar and some shape parameters as topology design variables, the difficulty arising from the jumping of buckling length phenomenon can be easily overcome without the necessity of introducing the overlapping bars into the initial ground structure. Therefore computational efforts can be saved for the solution of this kind of problem. By modifying the elements of the stiffness matrix using Sigmoid function, the continuity of the objective and constraint functions with respect to shape design parameters can be restored to some extent. Some numerical examples demonstrate the effectiveness of the proposed method.

  6. Mixed methods for viscoelastodynamics and topology optimization

    Directory of Open Access Journals (Sweden)

    Giacomo Maurelli

    2014-07-01

    Full Text Available A truly-mixed approach for the analysis of viscoelastic structures and continua is presented. An additive decomposition of the stress state into a viscoelastic part and a purely elastic one is introduced along with an Hellinger-Reissner variational principle wherein the stress represents the main variable of the formulation whereas the kinematic descriptor (that in the case at hand is the velocity field acts as Lagrange multiplier. The resulting problem is a Differential Algebraic Equation (DAE because of the need to introduce static Lagrange multipliers to comply with the Cauchy boundary condition on the stress. The associated eigenvalue problem is known in the literature as constrained eigenvalue problem and poses several difficulties for its solution that are addressed in the paper. The second part of the paper proposes a topology optimization approach for the rationale design of viscoelastic structures and continua. Details concerning density interpolation, compliance problems and eigenvalue-based objectives are given. Worked numerical examples are presented concerning both the dynamic analysis of viscoelastic structures and their topology optimization.

  7. Topology Optimization for Energy Management in Underwater Sensor Networks

    Science.gov (United States)

    2015-02-01

    1 To appear in International Journal of Control as a regular paper Topology Optimization for Energy Management in Underwater Sensor Networks⋆ Devesh... topology that maximizes the probability of successful search (of a target) over a surveillance region. In a two-stage optimization, a genetic algorithm (GA...Adaptation to energy variations across the network is shown to be manifested as a change in the optimal network topology by using sensing and

  8. On CAD-integrated Structural Topology and Design Optimization

    DEFF Research Database (Denmark)

    Olhoff, Niels; Bendsøe, M.P.; Rasmussen, John

    1991-01-01

    Concepts underlying an interactive CAD-based engineering design optimization system are developed, and methods of optimizing the topology, shape and sizing of mechanical components are presented. These methods are integrated in the system, and the method for determining the optimal topology is used...

  9. Topology optimization of two-dimensional elastic wave barriers

    DEFF Research Database (Denmark)

    Van Hoorickx, C.; Sigmund, Ole; Schevenels, M.

    2016-01-01

    Topology optimization is a method that optimally distributes material in a given design domain. In this paper, topology optimization is used to design two-dimensional wave barriers embedded in an elastic halfspace. First, harmonic vibration sources are considered, and stiffened material is insert...

  10. Topology Optimization of Metamaterial-Based Electrically Small Antennas

    DEFF Research Database (Denmark)

    Erentok, Aycan; Sigmund, Ole

    2007-01-01

    A topology optimized metamaterial-based electrically small antenna configuration that is independent of a specific spherical and/or cylindrical metamaterial shell design is demonstrated. Topology optimization is shown to provide the optimal value and placement of a given ideal metamaterial in space...

  11. On CAD-integrated Structural Topology and Design Optimization

    DEFF Research Database (Denmark)

    Olhoff, Niels; Bendsøe, M.P.; Rasmussen, John

    1991-01-01

    Concepts underlying an interactive CAD-based engineering design optimization system are developed, and methods of optimizing the topology, shape and sizing of mechanical components are presented. These methods are integrated in the system, and the method for determining the optimal topology is used...

  12. Topology Optimization of Spacecraft Transfer Compartment

    Directory of Open Access Journals (Sweden)

    A. A. Borovikov

    2016-01-01

    Full Text Available IntroductionThe subject of this research is topology optimization of the adapter of a spacecraft transfer compartment. The finite element topology optimization [1] is widely used for simple structure elements [6, 7]. It is argued that using this method in conjunction with additive technology (3D - printing it is possible to create construction designs with the best weight characteristics. However, the paper shows that when applying this method to a complex construction design the optimization results are highly sensitive to optimization algorithm parameters. The goal of this research is to study parameters of the topology optimization algorithm and the influence of their variations on results.1.      Problem formulation   A commercial software Altair HyperWorks/OptiStruct (student’s license performed numerical calculations. The paper presents a detailed description of the finite element model.The main features of the proposed model are as follows:-          Simplicity with non-complicated geometry;-          Building a finite element model in terms of computing time minimization;-          Using the lumped mass elements to simulate the impacts of the conjugates on the adapter;-          A limit of material strength, decreased by an order of magnitude, to eliminate stress concentrators;-          The gravitational load applied corresponds to the loads for the Angara-A5 launcher [8]. 2.      Method of solutionA brief description of the SIMP-method realized in the Altair HyperWorks/OptiStruct software is given.3.      ResultsPerformed numerical calculations, and shown the influence of variations of algorithm parameters (DISCRETE, MATINIT, MINDIM, MAXDIM on construction design as well as the parameters SINGLE and SPLIT used to reveal restrictions on manufacturing.Shown that, depending on variations of parameters, an adapter construction strives to «truss» or «shell» type. Described

  13. Optimal design of a smart post-buckled beam actuator using bat algorithm: simulations and experiments

    Science.gov (United States)

    Mallick, Rajnish; Ganguli, Ranjan; Kumar, Ravi

    2017-05-01

    The optimized design of a smart post-buckled beam actuator (PBA) is performed in this study. A smart material based piezoceramic stack actuator is used as a prime-mover to drive the buckled beam actuator. Piezoceramic actuators are high force, small displacement devices; they possess high energy density and have high bandwidth. In this study, bench top experiments are conducted to investigate the angular tip deflections due to the PBA. A new design of a linear-to-linear motion amplification device (LX-4) is developed to circumvent the small displacement handicap of piezoceramic stack actuators. LX-4 enhances the piezoceramic actuator mechanical leverage by a factor of four. The PBA model is based on dynamic elastic stability and is analyzed using the Mathieu-Hill equation. A formal optimization is carried out using a newly developed meta-heuristic nature inspired algorithm, named as the bat algorithm (BA). The BA utilizes the echolocation capability of bats. An optimized PBA in conjunction with LX-4 generates end rotations of the order of 15° at the output end. The optimized PBA design incurs less weight and induces large end rotations, which will be useful in development of various mechanical and aerospace devices, such as helicopter trailing edge flaps, micro and nano aerial vehicles and other robotic systems.

  14. Mathematical programming methods for large-scale topology optimization problems

    DEFF Research Database (Denmark)

    Rojas Labanda, Susana

    , and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second......This thesis investigates new optimization methods for structural topology optimization problems. The aim of topology optimization is finding the optimal design of a structure. The physical problem is modelled as a nonlinear optimization problem. This powerful tool was initially developed...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...

  15. Optimization-based topology identification of complex networks

    Institute of Scientific and Technical Information of China (English)

    Tang Sheng-Xue; Chen Li; He Yi-Gang

    2011-01-01

    In many cases,the topological structures of a complex network are unknown or uncertain,and it is of significance to identify the exact topological structure.An optimization-based method of identifying the topological structure of a complex network is proposed in this paper.Identification of the exact network topological structure is converted into a minimal optimization problem by using the estimated network.Then,an improved quantum-behaved particle swarm optimization algorithm is used to solve the optimization problem.Compared with the previous adaptive synchronizationbased method,the proposed method is simple and effective and is particularly valid to identify the topological structure of synchronization complex networks.In some cases where the states of a complex network are only partially observable,the exact topological structure of a network can also be identified by using the proposed method.Finally,numerical simulations are provided to show the effectiveness of the proposed method.

  16. Topology optimization problems with design-dependent sets of constraints

    DEFF Research Database (Denmark)

    Schou, Marie-Louise Højlund

    Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...... using both discrete and continuous design variables. Using discrete design variables is the natural modeling frame. However, we cannot solve real-size problems with the technological limits of today. Using continuous design variables makes it possible to also study topology optimization problems...

  17. Topology optimization for optical microlithography with partially coherent illumination

    DEFF Research Database (Denmark)

    Zhou, Mingdong; Lazarov, Boyan Stefanov; Sigmund, Ole

    2017-01-01

    This article revisits a topology optimization design approach for micro-manufacturing and extends it to optical microlithography with partially coherent illumination. The solution is based on a combination of two technologies, the topology optimization and the proximity error correction in microl......This article revisits a topology optimization design approach for micro-manufacturing and extends it to optical microlithography with partially coherent illumination. The solution is based on a combination of two technologies, the topology optimization and the proximity error correction...... in microlithography/nanolithography. The key steps include (i) modeling the physical inputs of the fabrication process, including the ultraviolet light illumination source and the mask, as the design variables in optimization and (ii) applying physical filtering and heaviside projection for topology optimization...

  18. Topology optimization with flexible void area

    DEFF Research Database (Denmark)

    Clausen, Anders; Aage, Niels; Sigmund, Ole

    2014-01-01

    This paper presents a methodology for including fixed-area flexible void domains into the minimum compliance topology optimization problem. As opposed to the standard passive elements approach of rigidly specifying void areas within the design domain, the suggested approach allows these areas...... to be flexibly reshaped and repositioned subject to penalization on their moments of inertia, the positions of their centers of mass, and their shapes. The flexible void areas are introduced through a second, discrete design variable field, using the same discretization as the standard field of continuous...... density variables. The formulation is based on a combined approach: The primary sub-problem is to minimize compliance, subject to a volume constraint, with a secondary sub-problem of minimizing the disturbance from the flexible void areas. The design update is performed iteratively between the two...

  19. Topology Optimized Architectures with Programmable Poisson's Ratio over Large Deformations

    DEFF Research Database (Denmark)

    Clausen, Anders; Wang, Fengwen; Jensen, Jakob Søndergaard

    2015-01-01

    Topology optimized architectures are designed and printed with programmable Poisson's ratios ranging from -0.8 to 0.8 over large deformations of 20% or more.......Topology optimized architectures are designed and printed with programmable Poisson's ratios ranging from -0.8 to 0.8 over large deformations of 20% or more....

  20. Topology optimization for optical projection lithography with manufacturing uncertainties

    DEFF Research Database (Denmark)

    Zhou, Mingdong; Lazarov, Boyan Stefanov; Sigmund, Ole

    2014-01-01

    This article presents a topology optimization approach for micro-and nano-devices fabricated by optical projection lithography. Incorporating the photolithography process and the manufacturing uncertainties into the topology optimization process results in a binary mask that can be sent directly...

  1. Time domain topology optimization of 3D nanophotonic devices

    DEFF Research Database (Denmark)

    Elesin, Yuriy; Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard;

    2014-01-01

    We present an efficient parallel topology optimization framework for design of large scale 3D nanophotonic devices. The code shows excellent scalability and is demonstrated for optimization of broadband frequency splitter, waveguide intersection, photonic crystal-based waveguide and nanowire...

  2. Topology and boundary shape optimization as an integrated design tool

    Science.gov (United States)

    Bendsoe, Martin Philip; Rodrigues, Helder Carrico

    1990-01-01

    The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD type input-output facilities.

  3. Depth optimization for topological quantum circuits

    Science.gov (United States)

    AlFailakawi, Mohammad; Ahmad, Imtiaz; AlTerkawi, Laila; Hamdan, Suha

    2015-02-01

    Topological quantum computing (TQC) model is one of the most promising models for quantum computation. A circuit implemented under TQC is optimized by reducing its depth due to special construction requirements in such technology. In this work, we propose a hybrid approach that combines a left-edge greedy heuristic with genetic algorithm (GA) to minimize circuit depth through combined line and gate ordering. In our implementation, GA is used to find line ordering, whereas the left edge is used to reduce circuit depth by taking into consideration overlap constraints imposed by line ordering. Moreover, the proposed algorithm can merge gates together realizing circuit with multi-target gates to provide reduced circuit depth. Experimental results on random benchmark circuits show that the proposed algorithm was able to reduce circuit depth by 42 % on average for CNOT circuits, with additional 5 % savings when multi-target optimization is used. Results on RevLib benchmarks revealed a typical enhancement of 21 % and an additional 11 % when multi-target gates are allowed.

  4. Minimum length scale in topology optimization by geometric constraints

    DEFF Research Database (Denmark)

    Zhou, Mingdong; Lazarov, Boyan Stefanov; Wang, Fengwen

    2015-01-01

    A density-based topology optimization approach is proposed to design structures with strict minimum length scale. The idea is based on using a filtering-threshold topology optimization scheme and computationally cheap geometric constraints. The constraints are defined over the underlying structural...... geometry represented by the filtered and physical fields. Satisfying the constraints leads to a design that possesses user-specified minimum length scale. Conventional topology optimization problems can be augmented with the proposed constraints to achieve minimum length scale on the final design....... No additional finite element analysis is required for the constrained optimization. Several benchmark examples are presented to show the effectiveness of this approach....

  5. Topology optimization of 3D Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan

    to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes......Topology optimization has been applied to a multitude of physical systems and is now a mature technology used in industrial practice, see [1] for an overview. Borrvall and Petersson [2] introduced topology optimization of Stokes flow problems which initiated works on extending topology optimization...... flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...

  6. Advanced Topology Optimization Methods for Conceptual Architectural Design

    DEFF Research Database (Denmark)

    Aage, Niels; Amir, Oded; Clausen, Anders

    2014-01-01

    This paper presents a series of new, advanced topology optimization methods, developed specifically for conceptual architectural design of structures. The proposed computational procedures are implemented as components in the framework of a Grasshopper plugin, providing novel capacities...... in topological optimization: Interactive control and continuous visualization; embedding flexible voids within the design space; consideration of distinct tension / compression properties; and optimization of dual material systems. In extension, optimization procedures for skeletal structures such as trusses...... and frames are implemented. The developed procedures allow for the exploration of new territories in optimization of architectural structures, and offer new methodological strategies for bridging conceptual gaps between optimization and architectural practice....

  7. Topology optimization problems with design-dependent sets of constraints

    DEFF Research Database (Denmark)

    Schou, Marie-Louise Højlund

    Topology optimization is a design tool which is used in numerous fields. It can be used whenever the design is driven by weight and strength considerations. The basic concept of topology optimization is the interpretation of partial differential equation coefficients as effective material...... properties and designing through changing these coefficients. For example, consider a continuous structure. Then the basic concept is to represent this structure by small pieces of material that are coinciding with the elements of a finite element model of the structure. This thesis treats stress constrained...... structural topology optimization problems. For such problems a stress constraint for an element should only be present in the optimization problem when the structural design variable corresponding to this element has a value greater than zero. We model the stress constrained topology optimization problem...

  8. Experimental validation of a topology optimized acoustic cavity

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Sigmund, Ole; Fernandez Grande, Efren

    2015-01-01

    This paper presents the experimental validation of an acoustic cavity designed using topology optimization with the goal of minimizing the sound pressure locally for monochromatic excitation. The presented results show good agreement between simulations and measurements. The effect of damping...

  9. Topology optimization of flexible micro-fluidic devices

    DEFF Research Database (Denmark)

    Kreissl, Sebastian; Pingen, Georg; Evgrafov, Anton;

    2010-01-01

    A multi-objective topology optimization formulation for the design of dynamically tunable fluidic devices is presented. The flow is manipulated via external and internal mechanical actuation, leading to elastic deformations of flow channels. The design objectives characterize the performance...

  10. Topology optimization of vibration and wave propagation problems

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2007-01-01

    The method of topology optimization is a versatile method to determine optimal material layouts in mechanical structures. The method relies on, in principle, unlimited design freedom that can be used to design materials, structures and devices with significantly improved performance and sometimes...... novel functionality. This paper addresses basic issues in simulation and topology design of vibration and wave propagation problems. Steady-state and transient wave propagation problems are addressed and application examples for both cases are presented....

  11. Structural Topology Optimization : Basic Theory, Methods and Applications

    OpenAIRE

    2013-01-01

    The thesis is written as an introduction to topology optimization, aiming to help knowledge development in design optimization techniques, as well as aiding the adaptation of a sustainable culture with direct application to similar products like the two test cases supplied by the EC SuPLight project. These components are; a Door Connection Joint for a business jet and a Front Lower Control Arm from a McPherson suspension. The thesis has no intention of covering all aspects concerning topology...

  12. Topology Optimization as a Conceptual Tool for Designing New Airframes

    OpenAIRE

    2016-01-01

    During the two last decades, topology optimization has grown to be an accepted and used method to produce conceptual designs. Topology optimization is traditionally carried out on a component level, but in this project, the possibility to apply it to airframe design on a full scale aeroplane model is evaluated. The project features a conceptual flying-wing design on which the study is to be carried out. Inertia Relief is used to constrain the aeroplane instead of traditional single point cons...

  13. Systematic design of acoustic devices by topology optimization

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2005-01-01

    We present a method to design acoustic devices with topology optimization. The general algorithm is exemplified by the design of a reflection chamber that minimizes the transmission of acoustic waves in a specified frequency range.......We present a method to design acoustic devices with topology optimization. The general algorithm is exemplified by the design of a reflection chamber that minimizes the transmission of acoustic waves in a specified frequency range....

  14. Systematic design of acoustic devices by topology optimization

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2005-01-01

    We present a method to design acoustic devices with topology optimization. The general algorithm is exemplified by the design of a reflection chamber that minimizes the transmission of acoustic waves in a specified frequency range.......We present a method to design acoustic devices with topology optimization. The general algorithm is exemplified by the design of a reflection chamber that minimizes the transmission of acoustic waves in a specified frequency range....

  15. Maximizing opto‐mechanical interaction using topology optimization

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund; Sigmund, Ole

    2011-01-01

    This paper studies topology optimization of a coupled opto‐mechanical problem with the goal of finding the material layout which maximizes the optical modulation, i.e. the difference between the optical response for the mechanically deformed and undeformed configuration. The optimization is perfo......This paper studies topology optimization of a coupled opto‐mechanical problem with the goal of finding the material layout which maximizes the optical modulation, i.e. the difference between the optical response for the mechanically deformed and undeformed configuration. The optimization...

  16. Topology optimization based on spline-based meshfree method using topological derivatives

    Energy Technology Data Exchange (ETDEWEB)

    Hur, Junyoung; Youn, Sung-Kie [KAIST, Daejeon (Korea, Republic of); Kang, Pilseong [Korea Research Institute of Standards and Science, Daejeon (Korea, Republic of)

    2017-05-15

    Spline-based meshfree method (SBMFM) is originated from the Isogeometric analysis (IGA) which integrates design and analysis through Non-uniform rational B-spline (NURBS) basis functions. SBMFM utilizes trimming technique of CAD system by representing the domain using NURBS curves. In this work, an explicit boundary topology optimization using SBMFM is presented with an effective boundary update scheme. There have been similar works in this subject. However unlike the previous works where semi-analytic method for calculating design sensitivities is employed, the design update is done by using topological derivatives. In this research, the topological derivative is used to derive the sensitivity of boundary curves and for the creation of new holes. Based on the values of topological derivatives, the shape of boundary curves is updated. Also, the topological change is achieved by insertion and removal of the inner holes. The presented approach is validated through several compliance minimization problems.

  17. Compliant topology optimization for planar passive flap micro valve.

    Science.gov (United States)

    Yoon, Gil Ho

    2014-10-01

    This paper reports the compliant topology optimization for planar passive flap micro valve considering fluid-structure interaction with a monolithic approach. Although flap valve type check valve is easy to manufacture and use for the applications for Bio/Nano/MEMS, its structural optimization has been seldom conducted so far. The size of the Bio/Nano/MEMS devices becomes smaller and the simple straight type micro valve structure is required to be optimized considering fluid speed. To address this optimization problem, the structural topology optimization scheme which designs optimal topologies is applied for a flap type check valve structure. To consider the coupling effects of fluid domain and structural domain, the monolithic finite element approach is employed. In the new analysis approach, solid domain is simulated by introducing the inverse permeability in the Navier-Stokes equation and the fluid stress filter in the linear elasticity equation. Also it is a new idea that fluid domain is simulated by finite elements with a weak Young's modulus in the linear elasticity equation. The mutual couplings between fluid and structure are considered by the introduction of the deformation tensor which is one of the basic concepts of the continuum mechanism. By distributing material properties inside a design domain for compliant flap, optimal flap structures can be constructed with different fluid speeds. By investigating the optimal layouts of several passive flap designs, we prove that the structural topology optimization can provide optimal layouts for Bio, Nano, and MEMS applications.

  18. Independent continuous mapping for topological optimization of frame structures

    Institute of Scientific and Technical Information of China (English)

    Yunkang Sui; Jiazheng Du; Yingqiao Guo

    2006-01-01

    Based on the Independent Continuous Mapping method (ICM),a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight,element allowable stress and element stiffness,which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1.Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method.Three criteria (no structural singularity,no violated constraints and no change of structural weight) are introduced to judge iteration convergence.These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure.To improve the efficiency,the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space.By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform.A topological optimization software of frame structures is accomplished.Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.

  19. Experimental Modeling and Optimization of Fatigue Life and Hardness of Carbon Steel CK35 under Dynamic Buckling

    Directory of Open Access Journals (Sweden)

    Ahmed Naif Al-Khazraji

    2014-12-01

    Full Text Available The aim of this paper is to model and optimize the fatigue life and hardness of medium carbon steel CK35 subjected to dynamic buckling. Different ranges of shot peening time (STP and critical points of slenderness ratio which is between the long and intermediate columns, as input factors, were used to obtain their influences on the fatigue life and hardness, as main responses. Experimental measurements of shot peening time and buckling were taken and analyzed using (DESIGN EXPERT 8 experimental design software which was used for modeling and optimization purposes. Mathematical models of responses were obtained and analyzed by ANOVA variance to verify the adequacy of the models. The resultant quadratic models were obtained. A good agreement was found between the results of these models and optimization with the experimental ones with confidence level of 95 %.

  20. Discrete Material Buckling Optimization of Laminated Composite Structures considering "Worst" Shape Imperfections

    DEFF Research Database (Denmark)

    Henrichsen, Søren Randrup; Lindgaard, Esben; Lund, Erik

    2015-01-01

    Robust design of laminated composite structures is considered in this work. Because laminated composite structures are often thin walled, buckling failure can occur prior to material failure, making it desirable to maximize the buckling load. However, as a structure always contains imperfections...

  1. Multiscale topology optimization of solid and fluid structures

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe

    This thesis considers the application of the topology optimization method to multiscale problems, specifically the fluid-structure interaction problem. By multiple-scale methods the governing equations, the Navier-Cauchy and the incompressible Navier-Stokes equations are expanded and separated......, it is shown that the material microstructure can be optimized with respect to application scale properties. A poroelastic actuator consisting of two saturated porous materials is optimized using this approach. Based on the homogenization of a fixed microstructure topology, material design interpolation...... designs a new explicit parametrization is proposed. It allows for casting/milling type manufacturing and ensures a binary design. The method is successfully applied to micromixer design....

  2. Combined shape and topology optimization of 3D structures

    DEFF Research Database (Denmark)

    Christiansen, Asger Nyman; Bærentzen, Jakob Andreas; Nobel-Jørgensen, Morten

    2015-01-01

    We present a method for automatic generation of 3D models based on shape and topology optimization. The optimization procedure, or model generation process, is initialized by a set of boundary conditions, an objective function, constraints and an initial structure. Using this input, the method...... will automatically deform and change the topology of the initial structure such that the objective function is optimized subject to the specified constraints and boundary conditions. For example, this tool can be used to improve the stiffness of a structure before printing, reduce the amount of material needed...

  3. Topology optimization of ultra-fast nano-photonic switches

    DEFF Research Database (Denmark)

    Elesin, Yuriy; Lazarov, Boyan Stefanov; Jensen, Jakob Søndergaard

    2011-01-01

    can be designed using physical considerations and intuition. Alternatively the proposed topology optimization scheme provides a systematic methodology for obtaining and optimizing the layout of the devices. It is shown that the algorithm can efficiently handle more than two materials......The aim of this paper is to demonstrate 1D switch designs obtained by topology optimization which show better performance than the designs considered in the literature. Such devices are non-linear and their performance depends on the efficiency of light-matter interaction. Simple optical switches...

  4. Topology optimization of 3D shell structures with porous infill

    DEFF Research Database (Denmark)

    Clausen, Anders; Andreassen, Erik; Sigmund, Ole

    2017-01-01

    This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same conditions. The study...... indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology optimization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells significantly improves...

  5. Topology optimization for nano-scale heat transfer

    DEFF Research Database (Denmark)

    Evgrafov, Anton; Maute, Kurt; Yang, Ronggui

    2009-01-01

    We consider the problem of optimal design of nano-scale heat conducting systems using topology optimization techniques. At such small scales the empirical Fourier's law of heat conduction no longer captures the underlying physical phenomena because the mean-free path of the heat carriers, phonons...

  6. Frequency response as a surrogate eigenvalue problem in topology optimization

    DEFF Research Database (Denmark)

    Andreassen, Erik; Ferrari, Federico; Sigmund, Ole

    2017-01-01

    This article discusses the use of frequency response surrogates for eigenvalue optimization problems in topology optimization that may be used to avoid solving the eigenvalue problem. The motivation is to avoid complications that arise from multiple eigenvalues and the computational complexity as...

  7. Topology optimization for transient response of photonic crystal structures

    DEFF Research Database (Denmark)

    Matzen, René; Jensen, Jakob Søndergaard; Sigmund, Ole

    2010-01-01

    An optimization scheme based on topology optimization for transient response of photonic crystal structures is developed. The system response is obtained by a finite-element time-domain analysis employing perfectly matched layers as an absorbing boundary condition. As an example a waveguide...

  8. Transient Topology Optimization of Two-Dimensional Elastic Wave Propagation

    DEFF Research Database (Denmark)

    Matzen, René; Jensen, Jakob Søndergaard; Sigmund, Ole

    2008-01-01

    A tapering device coupling two monomodal waveguides is designed with the topology optimization method based on transient wave propagation. The gradient-based optimization technique is applied to predict the material distribution in the tapering area such that the squared output displacement (a...

  9. Topology-optimized broadband surface relief transmission grating

    DEFF Research Database (Denmark)

    Andkjær, Jacob; Ryder, Christian P.; Nielsen, Peter C.

    2014-01-01

    We propose a design methodology for systematic design of surface relief transmission gratings with optimized diffraction efficiency. The methodology is based on a gradient-based topology optimization formulation along with 2D frequency domain finite element simulations for TE and TM polarized pla......% in a broadband range going from the ultraviolet region, through the visible region and into the near-infrared region....

  10. Structural and Topology Optimization of Complex Civil Engineering Structures

    DEFF Research Database (Denmark)

    Hald, Frederik; Kirkegaard, Poul Henning; Andersen, Lars Vabbersgaard

    2013-01-01

    will be optimized using the commercial code Abaqus CAE. The structures are: a bucket foundation for an off-shore submarine structure for a wind turbine, and a pedestrian footbridge over a freeway. The topology optimization method used is the SIMP method, based on minimizing the structures' compliance. Complex load...

  11. Topology optimization for improving the performance of solar cells

    NARCIS (Netherlands)

    Gupta, D.K.; Langelaar, M.; Keulen, F. van; Barink, M.

    2014-01-01

    This work introduces the application of Topology Optimization (TO) to design optimal front metallization patterns for solar cells and increase their power output. A challenging aspect of the solar cell electrode design problem is the strong nonlinear relation between the active layer current and the

  12. Three-dimensional topology optimized electrically-small conformal antenna

    DEFF Research Database (Denmark)

    Erentok, Aycan; Sigmund, Ole

    2008-01-01

    A three-dimensional (3D) conductor-based conformal electrically small antenna is obtained using a topology optimization method. The optimization method distributes a certain amount of conductive material to a designated design domain such that the material layout defines an electrically small...

  13. Topology optimization problems for reflection and dissipation of elastic waves

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2007-01-01

    This paper is devoted to topology optimization problems for elastic wave propagation. The objective of the study is to maximize the reflection or the dissipation in a finite slab of material for pressure and shear waves in a range of frequencies. The optimized designs consist of two or three mate...

  14. Improving resource utilization in hierarchy network by optimizing topological structure

    Science.gov (United States)

    Liu, G. L.; Peng, H. P.; Li, L. X.; Sun, F.; Yang, Y. X.

    2012-02-01

    We study the performance of peer-to-peer (P2P) network built on the top of hierarchy topological structure of local area networks (LAN). We find that the topological structure of the underlying physical network has significant impacts on the resource utilization of the P2P overlay network. The larger size of the physical network is, the lower resource utilization of the overlay network is. Through optimizing the topological structure of physical network, we propose two novel schemes to improve the resource utilization. The experimental results show that in any case the resource utilization of P2P network can always achieve 100% by these two schemes.

  15. A design approach for integrating thermoelectric devices using topology optimization

    DEFF Research Database (Denmark)

    Soprani, Stefano; Haertel, Jan Hendrik Klaas; Lazarov, Boyan Stefanov;

    2016-01-01

    to operate more efficiently. This work proposes and experimentally demonstrates a topology optimization approach as a design tool for efficient integration of thermoelectric modules into systems with specific design constraints. The approach allows thermal layout optimization of thermoelectric systems....... The design method incorporates temperature dependent properties of the thermoelectric device and other materials. The3D topology optimization model developed in this work was used to design a thermoelectric system, complete with insulation and heat sink, that was produced and tested. Good agreement between...... experimental results and model forecasts was obtained and the system was able to maintain the load at more than 33 K below the oil well temperature. Results of this study support topology optimizationas a powerful design tool for thermal design of thermoelectric systems....

  16. TOPOLOGY OPTIMIZATION OF MULTIPLE INPUTS AND MULTIPLE OUTPUTS COMPLIANT MECHANISMS

    Institute of Scientific and Technical Information of China (English)

    ZHANG Xianmin; OUYANG Gaofei; WANG Hua

    2007-01-01

    An optimal topology design method for multiple inputs and multiple outputs compliant micro-manipulation system is presented. Firstly, the topology design problem is posed in terms of a multiple inputs load and several specified output deflections. The compliance and stiffness of the system are expressed by the mutual potential energy and strain energy, respectively, which can be controlled by a multi-criteria objective function. Secondly, based on the optimality criteria method, a model solution algorithm is presented. Finally, a numerical example is presented to show the validity of the presented technique. The optimal topology of a 4 inputs and 4 outputs compliant mechanism is obtained by using the method, and the corresponding micro-positioning stage system is further designed.

  17. Topology Optimized Components for Mode- and Wavelength Division Multiplexing

    DEFF Research Database (Denmark)

    Frellsen, Louise Floor

    This thesis deals with the topic of passive integrated nanophotonic devices realized in silicon on insulator material. The project has been concerned with all the steps of the process: Design, fabrication and characterization. The focus has been on using the inverse design method topology...... optimization.The method has been employed extensively to obtain various nanophotonic components. One of the outcomes of the project has been the development of a solid understanding of the benefits and limitations of topology optimization. This thesis presents numerous designs that have been characterized both...... that topology optimization is a strong method for creating extremely compact devices, the small features do however mean that they are not yet possible to fabricate on a large scale. Complex device functionalities can be obtained. Building on previous work of simpler structures it is comparatively easy...

  18. Truss topology optimization with simultaneous analysis and design

    Science.gov (United States)

    Sankaranarayanan, S.; Haftka, Raphael T.; Kapania, Rakesh K.

    1992-01-01

    Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.

  19. Topology optimization for free vibrations using combined approximations

    DEFF Research Database (Denmark)

    Bogomolny, Michael

    2010-01-01

    This study shows how the Combined Approximations (CA) can be used for reducing the computational effort in Topology Optimization for free vibrations. The previously developed approach is based on the integration of several concepts and methods, including matrix factorization, series expansion......, and reduced basis. In this paper the CA method is used for repeated eigenvalue analysis. Ad joint sensitivity analysis is developed such that the inaccuracies of the approximation are taken into consideration. Several 2-D and 3-D numerical examples show how optimal topology designs can be achieved...

  20. Topology optimization of a gas-turbine engine part

    Science.gov (United States)

    Faskhutdinov, R. N.; Dubrovskaya, A. S.; Dongauzer, K. A.; Maksimov, P. V.; Trufanov, N. A.

    2017-02-01

    One of the key goals of aerospace industry is a reduction of the gas turbine engine weight. The solution of this task consists in the design of gas turbine engine components with reduced weight retaining their functional capabilities. Topology optimization of the part geometry leads to an efficient weight reduction. A complex geometry can be achieved in a single operation with the Selective Laser Melting technology. It should be noted that the complexity of structural features design does not affect the product cost in this case. Let us consider a step-by-step procedure of topology optimization by an example of a gas turbine engine part.

  1. Topology optimization of 3D Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.

    examples relevant for optimal micro fluidic mixer design are shown where the design is planar - compliant with micro fabrication techniques - and where the designs are 3D. In addition issues related to the parallel solution of the linear algebra problems are discussed. The implementation uses...... the commercial COMSOL multiphysics programme which is sufficiently flexible to provide semi--automated analytical sensitivities. 1. M. P. Bendsoe and O. Sigmund, "Topology Optimization - Theory, Methods and Applications", Springer Verlag, Berlin Heidelberg, 2003. 2. T. Borrvall and J. Petersson, "Topology...

  2. Topology Optimization of Large Scale Stokes Flow Problems

    DEFF Research Database (Denmark)

    Aage, Niels; Poulsen, Thomas Harpsøe; Gersborg-Hansen, Allan

    2008-01-01

    This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs.......This note considers topology optimization of large scale 2D and 3D Stokes flow problems using parallel computations. We solve problems with up to 1.125.000 elements in 2D and 128.000 elements in 3D on a shared memory computer consisting of Sun UltraSparc IV CPUs....

  3. Stress-constrained topology optimization for compliant mechanism design

    DEFF Research Database (Denmark)

    de Leon, Daniel M.; Alexandersen, Joe; Jun, Jun S.;

    2015-01-01

    This article presents an application of stress-constrained topology optimization to compliant mechanism design. An output displacement maximization formulation is used, together with the SIMP approach and a projection method to ensure convergence to nearly discrete designs. The maximum stress...... is approximated using a normalized version of the commonly-used p-norm of the effective von Mises stresses. The usual problems associated with topology optimization for compliant mechanism design: one-node and/or intermediate density hinges are alleviated by the stress constraint. However, it is also shown...

  4. Homogenization and structural topology optimization theory, practice and software

    CERN Document Server

    Hassani, Behrooz

    1999-01-01

    Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.

  5. Topology Optimization in Damping Structure Based on ESO

    Institute of Scientific and Technical Information of China (English)

    GUO Zhong-ze; CHEN Yu-ze; HOU Qiang

    2008-01-01

    The damping material optimal placement for the structure with damping layer is studied based on evolutionary structural optimization (ESO) to maximize modal loss factors. A mathematical model is constructed with the objective function defined as the maximum of modal loss factors of the structure and design constraints function defined as volume fraction ofdamping material. The optimal placement is found. Several examples are presented for verification. The results demonstratethat the method based on ESO is effective in solving the topology optimization of the structure with uncon-strained damping layer and constrained damping layer. This optimization method suits for free and constrained damping structures.

  6. Topology Optimization in Electric Car Body Frame Based on Optistruct

    Directory of Open Access Journals (Sweden)

    Ge Dongdong

    2017-01-01

    Full Text Available In order to optimize the structure of the electric car body frame, the static analysis of the car frame were carried on. For the goal of the frame’s weight minimum, OptiStruct software was used to topology optimization design. And the optimal material distribution program of the frame structure was got. Static strength before and after optimization was comprehensive compared through the stress, deformation. The results showed that the weight of frame after optimization was reduced by 18.96%, and the requirements of the strength and stiffness were ensured.

  7. Topological Optimization of Artificial Microstructure Strategies

    Science.gov (United States)

    2015-04-02

    Topographic Optimization Through Artificial Microstructure Strategies During this project as part of DARPA MCMA we aimed to develop and demonstrate...Topographic Optimization Through Artificial Microstructure Strategies Report Title During this project as part of DARPA MCMA we aimed to develop and...Artificial Microstructure Strategies (Yale and Johns Hopkins) During DARPA MCMA we aimed to develop and demonstrate a 3D microstructural

  8. Topology optimization of 3D Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan

    to different flow problems. However, this research has focused on 2D fluid modelling, which limits the practical impact of the computed designs. The explanation of the limitation is that the finite size domain used in topology optimization problems ensures that the velocity components couples, even for Stokes...... flow [3]. Furthermore, it is questionable if such a coupling can be captured by a 2D model especially in non-trivial geometries as typically seen in topology design. This statement is widely accepted in the fluid mechanics community, i.e. that planar fluid models are useful for academic test problems...... fundamental aspects of the topology optimization method applied to the Stokes equations as described below. This work consists of two parts. The main part elaborates on effects caused by 3D fluid modelling on the design. Numerical examples are shown where the design is planar - relevant to micro fluidic...

  9. Topology optimization of 3D Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Sigmund, Ole; Bendsøe, Martin P.

    is caused by the finite size domain used in topology optimization problems which ensures that the velocity components couples, even for Stokes flow [3]. Physically Stokes flow is an exotic inertia free flow, which in practice complicates mixing by passive devices. Passive mixing devices are relevant......The design of MEMS devices have benefitted from the topology optimization tool and complicated layout problems have been solved, see [1] for an overview. This research is aimed at micro fluidic devices known as micro-Total-Analysis-Systems (muTAS) where the main physical phenomena originate from...... fluid mechanics. In future practice a muTAS could be used by doctors, engineers etc. as a hand held device with short reaction time that provides on-site analysis of a flowing substance such as blood, polluted water or similar. Borrvall and Petersson [2] paved the road for using the topology...

  10. A new logistic dynamic particle swarm optimization algorithm based on random topology.

    Science.gov (United States)

    Ni, Qingjian; Deng, Jianming

    2013-01-01

    Population topology of particle swarm optimization (PSO) will directly affect the dissemination of optimal information during the evolutionary process and will have a significant impact on the performance of PSO. Classic static population topologies are usually used in PSO, such as fully connected topology, ring topology, star topology, and square topology. In this paper, the performance of PSO with the proposed random topologies is analyzed, and the relationship between population topology and the performance of PSO is also explored from the perspective of graph theory characteristics in population topologies. Further, in a relatively new PSO variant which named logistic dynamic particle optimization, an extensive simulation study is presented to discuss the effectiveness of the random topology and the design strategies of population topology. Finally, the experimental data are analyzed and discussed. And about the design and use of population topology on PSO, some useful conclusions are proposed which can provide a basis for further discussion and research.

  11. Design of acousto-optical devices by topology optimization

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard

    2009-01-01

    by means of topology optimization is presented. The surface acoustic waves are generated by interdigital transducers in a 2D piezoelectric model, which is coupled to an optical model where the optical mode in the waveguide is found by solving the time-harmonic wave equation for the magnetic field. Only...

  12. On multigrid-CG for efficient topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Aage, Niels; Lazarov, Boyan Stefanov

    2014-01-01

    This article presents a computational approach that facilitates the efficient solution of 3-D structural topology optimization problems on a standard PC. Computing time associated with solving the nested analysis problem is reduced significantly in comparison to other existing approaches. The cos...

  13. Reduction of initial stress stiffening by topology optimization

    DEFF Research Database (Denmark)

    Philippine, M. A.; Sigmund, Ole; Rebeiz, G. M.

    2012-01-01

    Topology optimization is a rigorous method of obtaining non-intuitive designs. We use it to obtain a capacitive RF switch that stiffens little in response to an increase of the in-plane biaxial stresses that typically develop during MEMS fabrication. The actuation voltage is closely related...

  14. Wind load modeling for topology optimization of continuum structures

    NARCIS (Netherlands)

    Zakhama, R.; Abdalla, M.M.; Gürdal, Z.; Smaoui, H.

    2010-01-01

    Topology optimization of two and three dimensional structures subject to dead and wind loading is considered. The wind loading is introduced into the formulation by using standard expressions for the drag force, and a strategy is devised so that wind pressure is ignored where there is no surface obs

  15. Development of a novel ultrasonic motor resonator using topology optimization

    CSIR Research Space (South Africa)

    M'Boungui, G

    2011-01-01

    Full Text Available The use of topology optimization in the design of a novel stator for an ultrasonic motor (USM) is investigated. The design challenge is to produce a stator, with two resonant modes whose frequencies are in a ratio of 1:2. When driven together...

  16. Enhancing the Damping Properties of Viscoelastic Composites by Topology Optimization

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe; Andreassen, Erik; Sigmund, Ole

    techniques. As an example, by the use of e.g. SLM/SLS - Selective Laser Melting/Sintering, an open metallic microstructure can be printed and in a subsequent process the porespace can be filled with a high loss compliant material. Yi and co-workers [6] applied topology optimization to design the 2D...

  17. A topology optimization method for design of negative permeability metamaterials

    DEFF Research Database (Denmark)

    Diaz, A. R.; Sigmund, Ole

    2010-01-01

    A methodology based on topology optimization for the design of metamaterials with negative permeability is presented. The formulation is based on the design of a thin layer of copper printed on a dielectric, rectangular plate of fixed dimensions. An effective media theory is used to estimate...... are presented for illustration. New metamaterial concepts are uncovered, beyond the classical split-ring inspired layouts....

  18. Topology optimization for transient wave propagation problems in one dimension

    DEFF Research Database (Denmark)

    Dahl, Jonas; Jensen, Jakob Søndergaard; Sigmund, Ole

    2008-01-01

    Structures exhibiting band gap properties, i.e., having frequency ranges for which the structure attenuates propagating waves, have applications in damping of acoustic and elastic wave propagation and in optical communication. A topology optimization method for synthesis of such structures, emplo...

  19. Topology Optimized Mode Conversion In a Photonic Crystal Waveguide

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Elesin, Yuriy; Ding, Yunhong;

    2013-01-01

    We experimentally demonstrate an ultra-compact TE0-TE1 mode converter obtained in a photonic crystal waveguide by utilizing topology optimization and show a ~39 nm bandwidth around 1550 nm with an insertion loss lower than ~3 dB....

  20. Topology optimization of front metallization patterns for solar cells

    NARCIS (Netherlands)

    Gupta, D.K.; Langelaar, M.; Barink, M.; Keulen, F. van

    2015-01-01

    This paper presents the application of topology optimization (TO) for designing the front electrode patterns for solar cells. Improving the front electrode design is one of the approaches to improve the performance of the solar cells. It serves to produce the voltage distribution for the front surfa

  1. Topology optimization of radio frequency and microwave structures

    DEFF Research Database (Denmark)

    Aage, Niels

    This thesis focuses on topology optimization of conductor-based microwave and radio frequency electromagnetic devices. The research is motivated by the ever increasing usage of small hand-held, or autonomous, electric devices, which have lead to a series of new challenges for the design...

  2. Design of acousto-optical devices by topology optimization

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard

    2009-01-01

    by means of topology optimization is presented. The surface acoustic waves are generated by interdigital transducers in a 2D piezoelectric model, which is coupled to an optical model where the optical mode in the waveguide is found by solving the time-harmonic wave equation for the magnetic field. Only...

  3. Designing Meta Material Slabs Exhibiting Negative Refraction Using Topology Optimization

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Sigmund, O.

    2016-01-01

    This paper proposes a topology optimization based approach for designing meta materials exhibiting a desired negative refraction with high transmission at a given angle of incidence and frequency. The approach considers a finite slab of meta material consisting of axis-symmetric designable unit...

  4. Tailoring Dispersion properties of photonic crystal waveguides by topology optimization

    DEFF Research Database (Denmark)

    Stainko, Roman; Sigmund, Ole

    2007-01-01

    The paper describes a systematic method for the tailoring of dispersion properties of slab-based photonic crystal waveguides. The method is based on the topology optimization method which consists in repeated finite element frequency domain analyzes, analytical sensitivity analyzes and gradient...

  5. Design of photonic bandgap fibers by topology optimization

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard; Sigmund, Ole; Feurer, Thomas

    2010-01-01

    A method based on topology optimization is presented to design the cross section of hollow-core photonic bandgap fibers for minimizing energy loss by material absorption. The optical problem is modeled by the timeharmonic wave equation and solved with the finite element program Comsol Multiphysics...

  6. Topology Optimization - Improved Checker-Board Filtering With Sharp Contours

    DEFF Research Database (Denmark)

    Pedersen, Christian Gejl; Lund, Jeppe Jessen; Damkilde, Lars

    2006-01-01

    In topology optimization it is mandatory to use a filtering technique in order to prevent checker-boarder solutions. The paper examines a new filtering principle and demonstrates an improved sharpness in the contours. This was not realized in the original proposal of the filter. Furthermore...

  7. Inverse design of dispersion compensating optical fiber using topology optimization

    DEFF Research Database (Denmark)

    Riishede, Jesper; Sigmund, Ole

    2008-01-01

    We present a new numerical method for designing dispersion compensating optical fibers. The method is based on the solving of the Helmholtz wave equation with a finite-difference modesolver and uses topology optimization combined with a regularization filter for the design of the refractive index...

  8. Maximizing opto-elastic interaction using topology optimization

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund; Sigmund, Ole

    When a photonic device is subjected to a mechanical load, there are two effects which change the optical response relative to the reference configuration. First, there is the geometrical effect caused by geometrical changes, i.e. the deformation of the reference geometry to the deformed geometry....... properties when the device is subjected to a static mechanical pre-strain. Material distributions consisting of air inclusions in silicon are considered. The optimized material distributions are computed using topology optimization....

  9. Topology optimization of flexible micro-fluidic devices

    DEFF Research Database (Denmark)

    Kreissl, Sebastian; Pingen, Georg; Evgrafov, Anton

    2010-01-01

    in the undeformed and deformed configurations. The layout of fluid channels is determined by material topology optimization. In addition, the thickness distribution, the distribution of active material for internal actuation, and the support conditions are optimized. The coupled fluid-structure response...... and fluid mesh. The governing and the adjoint equations of the resulting fluid-structure interaction problem are derived. The proposed method is illustrated with the design of tunable manifolds....

  10. Isogeometric Analysis for Topology Optimization with a Phase Field Model

    Science.gov (United States)

    2011-09-01

    been successfully considered. For example, this is the case for applications in fluid dynamics [1], heat conduction [45], vibration [58], multiphysics...Laboratories SAND2006–2649 (2006). [45] A. Gersborg–Hansen, M.P. Bendsøe and O. Sigmund, Topology optimization of heat conduction problems using the...novel stent platform with drug reservoirs, Med. Eng. Phys. 30 (2008), 1177–1185. [111] Y.M. Xie and G.P. Steven, Evolutionary Structural Optimization

  11. Robust topology optimization accounting for spatially varying manufacturing errors

    DEFF Research Database (Denmark)

    Schevenels, M.; Lazarov, Boyan Stefanov; Sigmund, Ole

    2011-01-01

    This paper presents a robust approach for the design of macro-, micro-, or nano-structures by means of topology optimization, accounting for spatially varying manufacturing errors. The focus is on structures produced by milling or etching; in this case over- or under-etching may cause parts...... optimization problem is formulated in a probabilistic way: the objective function is defined as a weighted sum of the mean value and the standard deviation of the structural performance. The optimization problem is solved by means of a Monte Carlo method: in each iteration of the optimization scheme, a Monte...

  12. Inverse design of dielectric materials by topology optimization

    DEFF Research Database (Denmark)

    Otomori, M.; Andkjær, Jacob Anders; Sigmund, Ole

    2012-01-01

    permittivity. A gradient-based topology optimization method is used to find the distribution of dielectric material for the unit cell of a periodic microstructure composed of one or two dielectric materials. The optimization problem is formulated as a problem to minimize the square of the difference between...... the effective permittivity and a prescribed value. The optimization algorithm uses the adjoint variable method (AVM) for the sensitivity analysis and the finite element method (FEM) for solving the equilibrium and adjoint equations, respectively. A Heaviside projection filter is used to obtain clear optimized...

  13. Topology Optimization of an Aircraft Wing

    Science.gov (United States)

    2015-06-11

    baseline products were built in Solidworks prior to the optimization process. Loading on the wing was applied for multiple aerodynamic profiles generating...redesign and placement of the fuel tank was desired. A simple model of the baseline tank was built in Solidworks to estimate the total volume. Overall

  14. A concept for global optimization of topology design problems

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Achtziger, Wolfgang; Kawamoto, Atsushi

    2006-01-01

    on two applications. The first application is the design of stiff truss structures where the bar areas are chosen from a finite set of available areas. The second considered application is simultaneous topology and geometry design of planar articulated mechanisms. For each application we outline......We present a concept for solving topology design problems to proven global optimality. We propose that the problems are modeled using the approach of simultaneous analysis and design with discrete design variables and solved with convergent branch and bound type methods. This concept is illustrated...

  15. Topology Optimization of Continuum Structures with Local Stress Constraints

    DEFF Research Database (Denmark)

    Duysinx, Pierre; Bendsøe, Martin P

    1997-01-01

    We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank~2 layered m...... of the stress constraints is used. We describe the mathematical programming approach that is used to solve the numerical optimization problems, and show results for a number of example applications.......We introduce an extension of current technologies for topology optimization of continuum structures which allows for treating local stress criteria. We first consider relevant stress criteria for porous composite materials, initially by studying the stress states of the so-called rank~2 layered...... materials. Then, an empirical model is proposed for the power law materials (also called SIMP materials). In a second part, solution aspects of topology problems are considered. To deal with the so-called 'singularity' phenomenon of stress constraints in topology design, an $\\epsilon$ constraint relaxation...

  16. Robust topology optimization accounting for misplacement of material

    DEFF Research Database (Denmark)

    Jansen, Miche; Lombaert, Geert; Diehl, Moritz

    2013-01-01

    into account this type of geometric imperfections. A density filter based approach is followed, and translations of material are obtained by adding a small perturbation to the center of the filter kernel. The spatial variation of the geometric imperfections is modeled by means of a vector valued random field......The use of topology optimization for structural design often leads to slender structures. Slender structures are sensitive to geometric imperfections such as the misplacement or misalignment of material. The present paper therefore proposes a robust approach to topology optimization taking....... The random field is conditioned in order to incorporate supports in the design where no misplacement of material occurs. In the robust optimization problem, the objective function is defined as a weighted sum of the mean value and the standard deviation of the performance of the structure under uncertainty...

  17. Length scale and manufacturability in density-based topology optimization

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Wang, Fengwen; Sigmund, Ole

    2016-01-01

    Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it c......, well-defined designs with robust performances. The overview discusses the limitations, the advantages and the associated computational costs. The review is completed with optimized designs for minimum compliance, mechanism design and heat transfer.......Since its original introduction in structural design, density-based topology optimization has been applied to a number of other fields such as microelectromechanical systems, photonics, acoustics and fluid mechanics. The methodology has been well accepted in industrial design processes where it can...

  18. Topology optimization of 3D shell structures with porous infill

    Science.gov (United States)

    Clausen, Anders; Andreassen, Erik; Sigmund, Ole

    2017-08-01

    This paper presents a 3D topology optimization approach for designing shell structures with a porous or void interior. It is shown that the resulting structures are significantly more robust towards load perturbations than completely solid structures optimized under the same conditions. The study indicates that the potential benefit of using porous structures is higher for lower total volume fractions. Compared to earlier work dealing with 2D topology optimization, we found several new effects in 3D problems. Most notably, the opportunity for designing closed shells significantly improves the performance of porous structures due to the sandwich effect. Furthermore, the paper introduces improved filter boundary conditions to ensure a completely uniform coating thickness at the design domain boundary.

  19. An efficient approach for reliability-based topology optimization

    Science.gov (United States)

    Kanakasabai, Pugazhendhi; Dhingra, Anoop K.

    2016-01-01

    This article presents an efficient approach for reliability-based topology optimization (RBTO) in which the computational effort involved in solving the RBTO problem is equivalent to that of solving a deterministic topology optimization (DTO) problem. The methodology presented is built upon the bidirectional evolutionary structural optimization (BESO) method used for solving the deterministic optimization problem. The proposed method is suitable for linear elastic problems with independent and normally distributed loads, subjected to deflection and reliability constraints. The linear relationship between the deflection and stiffness matrices along with the principle of superposition are exploited to handle reliability constraints to develop an efficient algorithm for solving RBTO problems. Four example problems with various random variables and single or multiple applied loads are presented to demonstrate the applicability of the proposed approach in solving RBTO problems. The major contribution of this article comes from the improved efficiency of the proposed algorithm when measured in terms of the computational effort involved in the finite element analysis runs required to compute the optimum solution. For the examples presented with a single applied load, it is shown that the CPU time required in computing the optimum solution for the RBTO problem is 15-30% less than the time required to solve the DTO problems. The improved computational efficiency allows for incorporation of reliability considerations in topology optimization without an increase in the computational time needed to solve the DTO problem.

  20. Perspective Application of Passive Optical Network with Optimized Bus Topology

    Directory of Open Access Journals (Sweden)

    P. Lafata

    2012-06-01

    Full Text Available Passive optical networks (PONs represent a promising solution for modern access telecommunication networks.These networks are able to meet the increasing demands on transmission rate for demanding multimedia services,while they can offer typical shared transmission speed of 1.25 or 2.5 Gbps. The major role in deploying opticaldistribution networks ODNs plays the maximum attenuable loss, which is caused mainly by passive optical splitters.This paper proposes an innovative application of passive optical networks with optimized bus topology especially forlocal backbone data networks. Due to using only passive components, it is necessary to optimize certain parameters,especially an overall attenuation balance. Considering the possibility of such optimization, the passive optical networkwith optimized bus topology provides several interesting opportunities for specific applications. This paper will presentselected aspects of passive optical networks and splitters with asymmetric splitting ratio. The essential part is focusedon the practical demonstration of their use to optimize the passive optical network with bus topology, which acts as alocal backbone network for structured cabling systems, and for local data networks in large buildings.

  1. Optimal design of virtual topology reconfiguration in WDM optical networks

    Institute of Scientific and Technical Information of China (English)

    Fengqing Liu(刘逢清); Qingji Zeng(曾庆济); Xu Zhu(朱栩); Shilin Xiao(肖石林)

    2003-01-01

    Virtual topology of WDM optical networks is often designed for some specific traffic matrix to get thebest network performance. When traffic demand imposed on WDM optical networks changes, the networkperformance may degrade and even become unacceptable. So virtual topology need to be reconfigured.In previous works, virtual topology is reconfigured to achieve the best network performance, in which alarge number of lightpaths need to be set up or torn down. In this paper, we try to get a tradeoff betweenthe network performance and traffic disruption (or implementing cost). The problem of virtual topologyreconfiguration for changing traffic patterns is formulated as an optimization problem and a mixed integerlinear programming (MILP) algorithm is presented. Numerical results show that a large cost reduction ofreconfiguration can be achieved at the expense of network performance.

  2. Robust Topology Optimization of Truss with regard to Volume

    CERN Document Server

    Mohr, Daniel P; Matzies, Thomas; Knapek, Christina A

    2011-01-01

    A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints have to be approximated by finite expressions to generate a computable problem. Here, using the example of the topology optimization of a truss, a method is proposed to deal with such uncertainties by using robust optimization techniques, leading to an approach without the necessity of any approximation. With adequately chosen load cases, the final expression is equivalent to the multiple load case. Simple numerical examples of typical problems illustrate the application of the method.

  3. Maximum length scale in density based topology optimization

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Wang, Fengwen

    2017-01-01

    The focus of this work is on two new techniques for imposing maximum length scale in topology optimization. Restrictions on the maximum length scale provide designers with full control over the optimized structure and open possibilities to tailor the optimized design for broader range...... of manufacturing processes by fulfilling the associated technological constraints. One of the proposed methods is based on combination of several filters and builds on top of the classical density filtering which can be viewed as a low pass filter applied to the design parametrization. The main idea...

  4. Topology optimum design of compliant mechanisms using modified ant colony optimization

    Energy Technology Data Exchange (ETDEWEB)

    Yoo, Kwang Seon; Han, Seog Young [Hanyang University, Seoul (Korea, Republic of)

    2015-08-15

    A Modified ant colony optimization (MACO) algorithm was suggested for topology optimal design of compliant mechanisms since standard ACO cannot provide an appropriate optimal topology. In order to improve computational efficiency and suitability of standard ACO algorithm in topology optimization for compliant mechanisms, a continuous variable, called the 'Element contribution significance (ECS),'is employed, which serves to replace the positions of ants in the standard ACO algorithm, and assess the importance of each element in the optimization process. MACO algorithm was applied to topology optimizations of both linear and geometrically nonlinear compliant mechanisms using three kinds of objective functions, and optimized topologies were compared each other. From the comparisons, it was concluded that MACO algorithm can effectively be applied to topology optimizations of linear and geometrically nonlinear compliant mechanisms, and the ratio of Mutual potential energy (MPE) to Strain energy (SE) type of objective function is the best for topology optimal design of compliant mechanisms.

  5. NOVEL METHOD SOLVING NUMERICAL INSTABILITIES IN TOPOLOGY OPTIMIZATION

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    Numerical instabilities are often encountered in FE solution of continuum topology optimization. The essence of the numerical instabilities is given from the inverse partial differential equation (PDE) point of view. On the basis of the strict mathematical theory, a novel method, named as window filter and multi-grid method, which solves the numerical instabilities, is proposed. Convergent analyses and a numerical example are presented.

  6. Topology Optimization of Building Blocks for Photonic Integrated Circuits

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2005-01-01

    Photonic integrated circuits are likely candidates as high speed replacements for the standard electrical integrated circuits of today. However, in order to obtain a satisfactorily performance many design prob- lems that up until now have resulted in too high losses must be resolved. In this work...... we demonstrate how the method of topology optimization can be used to design a variety of high performance building blocks for the future circuits....

  7. Topology optimization and fabrication of photonic crystal structures

    DEFF Research Database (Denmark)

    Borel, Peter Ingo; Harpøth, Anders; Frandsen, Lars Hagedorn;

    2004-01-01

    Topology optimization is used to design a planar photonic crystal waveguide component resulting in significantly enhanced functionality. Exceptional transmission through a photonic crystal waveguide Z-bend is obtained using this inverse design strategy. The design has been realized in a silicon......-on-insulator based photonic crystal waveguide. A large low loss bandwidth of more than 200 nm for the TE polarization is experimentally confirmed....

  8. Interactive topology optimization on hand-held devices

    DEFF Research Database (Denmark)

    Aage, Niels; Nobel-Jørgensen, Morten; Andreasen, Casper Schousboe

    2013-01-01

    This paper presents an interactive topology optimization application designed for hand-held devices running iOS or Android. The TopOpt app solves the 2D minimum compliance problem with interactive control of load and support positions as well as volume fraction. Thus, it is possible to change......OS devices from the Apple App Store, at Google Play for the Android platform, and a web-version can be run from www.topopt.dtu.dk....

  9. Fast Micro-Differential Evolution for Topological Active Net Optimization.

    Science.gov (United States)

    Li, Yuan-Long; Zhan, Zhi-Hui; Gong, Yue-Jiao; Zhang, Jun; Li, Yun; Li, Qing

    2016-06-01

    This paper studies the optimization problem of topological active net (TAN), which is often seen in image segmentation and shape modeling. A TAN is a topological structure containing many nodes, whose positions must be optimized while a predefined topology needs to be maintained. TAN optimization is often time-consuming and even constructing a single solution is hard to do. Such a problem is usually approached by a "best improvement local search" (BILS) algorithm based on deterministic search (DS), which is inefficient because it spends too much efforts in nonpromising probing. In this paper, we propose the use of micro-differential evolution (DE) to replace DS in BILS for improved directional guidance. The resultant algorithm is termed deBILS. Its micro-population efficiently utilizes historical information for potentially promising search directions and hence improves efficiency in probing. Results show that deBILS can probe promising neighborhoods for each node of a TAN. Experimental tests verify that deBILS offers substantially higher search speed and solution quality not only than ordinary BILS, but also the genetic algorithm and scatter search algorithm.

  10. Efficient topology optimization in MATLAB using 88 lines of code

    DEFF Research Database (Denmark)

    Andreassen, Erik; Clausen, Anders; Schevenels, Mattias

    2011-01-01

    The paper presents an efficient 88 line MATLAB code for topology optimization. It has been developed using the 99 line code presented by Sigmund (Struct Multidisc Optim 21(2):120–127, 2001) as a starting point. The original code has been extended by a density filter, and a considerable improvemen...... of the basic code to include recent PDE-based and black-and-white projection filtering methods. The complete 88 line code is included as an appendix and can be downloaded from the web site www.topopt.dtu.dk....

  11. 3D Topology optimization of Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Dammann, Bernd

    of energy efficient devices for 2D Stokes flow. Creeping flow problems are described by the Stokes equations which model very viscous fluids at macro scales or ordinary fluids at very small scales. The latter gives the motivation for topology optimization problems based on the Stokes equations being a model...... the designs are 3D. Moreover, preliminary results show that a formulation of an optimization problem that maximizes mixing with a constraint on the pressure drop across the device gives promising results. To measure the mixing a step temperature profile is convected through the design and the resulting...

  12. Topology optimized low-contrast all-dielectric optical cloak

    DEFF Research Database (Denmark)

    Andkjær, Jacob Anders; Sigmund, Ole

    2011-01-01

    A systematic methodology for designing low-contrast all-dielectric cloaks operating in the optical range is presented. Topology optimization is used to find the layout of standard dielectric material that minimizes the norm of the scattered field in the surroundings of the cloak. Rotational...... symmetries are exploited to optimize for multiple angles based on the solution for a single angle of incidence. For a few discrete angles of incidences (1-4) the cloaking is shown to be nearly perfect in a limited frequency range, and even for a rotational symmetric design, cloak and object appear smaller...

  13. Topology optimization of free vibrations of fiber laser packages

    DEFF Research Database (Denmark)

    Hansen, Lars Voxen

    2005-01-01

    The optimization problems described in the present paper are inspired by the problem of fiber laser package design for vibrating environments. The optical frequency of tuned fiber lasers glued to stiff packages is sensitive to acoustic or other mechanical vibrations. The paper presents a method...... for reducing this sensitivity by limiting the glue point movement on the package while using only a limited knowledge of vibrating external forces. By use of topology optimization a density distribution for the package is obtained, where the critical eigenmode of the package only effects a small elongation...

  14. Topology optimization of mass distribution problems in Stokes flow

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Berggren, Martin; Dammann, Bernd

    We consider topology optimization of mass distribution problems in 2D and 3D Stokes flow with the aim of designing devices that meet target outflow rates. For the purpose of validation, the designs have been post processed using the image processing tools available in FEMLAB. In turn, this has...... enabled an evaluation of the design with a body fitted mesh in a standard analysis software relevant in engineering practice prior to design manufacturing. This work investigates the proper choice of a maximum penalization value during the optimization process that ensures that the target outflow rates...

  15. Aerostructural Shape and Topology Optimization of Aircraft Wings

    Science.gov (United States)

    James, Kai

    A series of novel algorithms for performing aerostructural shape and topology optimization are introduced and applied to the design of aircraft wings. An isoparametric level set method is developed for performing topology optimization of wings and other non-rectangular structures that must be modeled using a non-uniform, body-fitted mesh. The shape sensitivities are mapped to computational space using the transformation defined by the Jacobian of the isoparametric finite elements. The mapped sensitivities are then passed to the Hamilton-Jacobi equation, which is solved on a uniform Cartesian grid. The method is derived for several objective functions including mass, compliance, and global von Mises stress. The results are compared with SIMP results for several two-dimensional benchmark problems. The method is also demonstrated on a three-dimensional wingbox structure subject to fixed loading. It is shown that the isoparametric level set method is competitive with the SIMP method in terms of the final objective value as well as computation time. In a separate problem, the SIMP formulation is used to optimize the structural topology of a wingbox as part of a larger MDO framework. Here, topology optimization is combined with aerodynamic shape optimization, using a monolithic MDO architecture that includes aerostructural coupling. The aerodynamic loads are modeled using a three-dimensional panel method, and the structural analysis makes use of linear, isoparametric, hexahedral elements. The aerodynamic shape is parameterized via a set of twist variables representing the jig twist angle at equally spaced locations along the span of the wing. The sensitivities are determined analytically using a coupled adjoint method. The wing is optimized for minimum drag subject to a compliance constraint taken from a 2 g maneuver condition. The results from the MDO algorithm are compared with those of a sequential optimization procedure in order to quantify the benefits of the MDO

  16. Design of multiphysics actuators using topology optimization - Part II

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2001-01-01

    -material structures. The application in mind is the design of thermally and electro thermally driven micro actuators for use in MicroElectroMechanical Systems (MEMS). MEMS are microscopic mechanical systems coupled with electrical circuits. MEMS are fabricated using techniques known from the semi-conductor industry...... of the topology optimization method in this part include design descriptions for two-material structures, constitutive modelling of elements with mixtures of two materials, formulation of optimization problems with multiple constraints and multiple materials and a mesh-independency scheme for two...

  17. Topology optimization of metallic devices for microwave applications

    DEFF Research Database (Denmark)

    Aage, Niels; Mortensen, Asger; Sigmund, Ole

    2010-01-01

    In electromagnetic optimization problems of metallic radio-frequency devices, such as antennas and resonators for wireless energy transfer, the volumetric distribution of good conductors, e.g. copper, has been known to cause numerical bottlenecks. In finite element analysis the limiting factor...... is the skin depth, which calls for highly refined meshing in order to capture the physics. The skin depth problem has therefore prohibited the application of topology optimization to this class of problem. We present a design parameterization that remedies these numerical issues, by the interpolation...

  18. Topology optimization for acoustic-structure interaction problems

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole

    2006-01-01

    We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...... to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz...

  19. Network synchronization: optimal and pessimal scale-free topologies

    Energy Technology Data Exchange (ETDEWEB)

    Donetti, Luca [Departamento de Electronica y Tecnologia de Computadores and Instituto de Fisica Teorica y Computacional Carlos I, Facultad de Ciencias, Universidad de Granada, 18071 Granada (Spain); Hurtado, Pablo I; Munoz, Miguel A [Departamento de Electromagnetismo y Fisica de la Materia and Instituto Carlos I de Fisica Teorica y Computacional Facultad de Ciencias, Universidad de Granada, 18071 Granada (Spain)], E-mail: mamunoz@onsager.ugr.es

    2008-06-06

    By employing a recently introduced optimization algorithm we construct optimally synchronizable (unweighted) networks for any given scale-free degree distribution. We explore how the optimization process affects degree-degree correlations and observe a generic tendency toward disassortativity. Still, we show that there is not a one-to-one correspondence between synchronizability and disassortativity. On the other hand, we study the nature of optimally un-synchronizable networks, that is, networks whose topology minimizes the range of stability of the synchronous state. The resulting 'pessimal networks' turn out to have a highly assortative string-like structure. We also derive a rigorous lower bound for the Laplacian eigenvalue ratio controlling synchronizability, which helps understanding the impact of degree correlations on network synchronizability.

  20. Optimal Design of Modern Transformerless PV Inverter Topologies

    DEFF Research Database (Denmark)

    Saridakis, Stefanos; Koutroulis, Eftichios; Blaabjerg, Frede

    2013-01-01

    The design optimization of H5, H6, neutral point clamped, active-neutral point clamped, and conergy-NPC transformerless photovoltaic (PV) inverters is presented in this paper. The components reliability in terms of the corresponding malfunctions, affecting the PV inverter maintenance cost during...... the operational lifetime period of the PV installation, is also considered in the optimization process. According to the results of the proposed design method, different optimal values of the PV inverter design variables are derived for each PV inverter topology and installation site. The H5, H6, neutral point...... clamped, active-neutral point clamped and conergy-NPC PV inverters designed using the proposed optimization process feature lower levelized cost of generated electricity and lifetime cost, longer mean time between failures and inject more PV-generated energy into the electric grid than their nonoptimized...

  1. Truss topology optimization with discrete design variables by outer approximation

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2015-01-01

    Several variants of an outer approximation method are proposed to solve truss topology optimization problems with discrete design variables to proven global optimality. The objective is to minimize the volume of the structure while satisfying constraints on the global stiffness of the structure...... for classical outer approximation approaches applied to optimal design problems. A set of two- and three-dimensional benchmark problems are solved and the numerical results suggest that the proposed approaches are competitive with other special-purpose global optimization methods for the considered class...... of problems. Numerical comparisons indicate that the suggested outer approximation algorithms can outperform standard approaches suggested in the literature, especially on difficult problem instances. © 2014 Springer Science+Business Media New York....

  2. Constraint-based Hybrid Cellular Automaton Topology Optimization for Advanced Lightweight Blast Resistant Structure Development

    Science.gov (United States)

    2011-11-01

    the desired model. 20 5. References 1. Goetz, J. C.; Tan, H.; Renaud, J. E.; Tovar , A. Structural Topology Optimization for Blast Mitigation...Stander, N. A Topology Optimization Tool for LS-DYNA Users: LS- OPT/Topology. The 7th European LS-DYNA Conference, 2009. 10. Tovar , A.; Patel, N

  3. Numerical optimization approach to modelling delamination and buckling of geometrically constrained structures.

    Science.gov (United States)

    Mullineux, G; Hicks, B J; Berry, C

    2012-04-28

    Understanding what happens in terms of delamination during buckling of laminate materials is of importance across a range of engineering sectors. Normally concern is that the strength of the material is not significantly impaired. Carton-board is a material with a laminate structure and, in the initial creation of carton nets, the board is creased in order to weaken the structure. This means that when the carton is eventually folded into its three-dimensional form, correct folding occurs along the weakened crease lines. Understanding what happens during creasing and folding is made difficult by the nonlinear nature of the material properties. This paper considers a simplified approach which extends the idea of minimizing internal energy so that the effects of delamination can be handled. This allows a simulation which reproduces the form of buckling-delamination observed in practice and the form of the torque-rotation relation.

  4. Topology Optimization for Wave Propagation Problems with Experimental Validation

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk

    from acoustics, however problems for TE or TM polarized electromagnetic waves and shear waves in solids in two dimensions may be treated using the proposed methods with minor modifications. A brief introduction to wave problems and to density-based topology optimizationis included, as is a brief......This Thesis treats the development and experimental validation of density-based topology optimization methods for wave propagation problems. Problems in the frequency regime where design dimensions are between approximately one fourth and ten wavelengths are considered. All examples treat problems...... discussion of the finite element method and a hybrid ofa wave based method and the finite element method, used to discretize the modelproblems under consideration. A short discussion of the benefits and drawbacks of applying the hybrid method compared to the finite element method, used in conjunction...

  5. A System for High-Resolution Topology Optimization.

    Science.gov (United States)

    Wu, Jun; Dick, Christian; Westermann, Rudiger

    2016-03-01

    A key requirement in 3D fabrication is to generate objects with individual exterior shapes and their interior being optimized to application-specific force constraints and low material consumption. Accomplishing this task is challenging on desktop computers, due to the extreme model resolutions that are required to accurately predict the physical shape properties, requiring memory and computational capacities going beyond what is currently available. Moreover, fabrication-specific constraints need to be considered to enable printability. To address these challenges, we present a scalable system for generating 3D objects using topology optimization, which allows to efficiently evolve the topology of high-resolution solids towards printable and light-weight-high-resistance structures. To achieve this, the system is equipped with a high-performance GPU solver which can efficiently handle models comprising several millions of elements. A minimum thickness constraint is built into the optimization process to automatically enforce printability of the resulting shapes. We further shed light on the question how to incorporate geometric shape constraints, such as symmetry and pattern repetition, in the optimization process. We analyze the performance of the system and demonstrate its potential by a variety of different shapes such as interior structures within closed surfaces, exposed support structures, and surface models.

  6. Computer Based Porosity Design by Multi Phase Topology Optimization

    Science.gov (United States)

    Burblies, Andreas; Busse, Matthias

    2008-02-01

    A numerical simulation technique called Multi Phase Topology Optimization (MPTO) based on finite element method has been developed and refined by Fraunhofer IFAM during the last five years. MPTO is able to determine the optimum distribution of two or more different materials in components under thermal and mechanical loads. The objective of optimization is to minimize the component's elastic energy. Conventional topology optimization methods which simulate adaptive bone mineralization have got the disadvantage that there is a continuous change of mass by growth processes. MPTO keeps all initial material concentrations and uses methods adapted from molecular dynamics to find energy minimum. Applying MPTO to mechanically loaded components with a high number of different material densities, the optimization results show graded and sometimes anisotropic porosity distributions which are very similar to natural bone structures. Now it is possible to design the macro- and microstructure of a mechanical component in one step. Computer based porosity design structures can be manufactured by new Rapid Prototyping technologies. Fraunhofer IFAM has applied successfully 3D-Printing and Selective Laser Sintering methods in order to produce very stiff light weight components with graded porosities calculated by MPTO.

  7. Topology optimization of pressure adaptive honeycomb for a morphing flap

    Science.gov (United States)

    Vos, Roelof; Scheepstra, Jan; Barrett, Ron

    2011-03-01

    The paper begins with a brief historical overview of pressure adaptive materials and structures. By examining avian anatomy, it is seen that pressure-adaptive structures have been used successfully in the Natural world to hold structural positions for extended periods of time and yet allow for dynamic shape changes from one flight state to the next. More modern pneumatic actuators, including FAA certified autopilot servoactuators are frequently used by aircraft around the world. Pneumatic artificial muscles (PAM) show good promise as aircraft actuators, but follow the traditional model of load concentration and distribution commonly found in aircraft. A new system is proposed which leaves distributed loads distributed and manipulates structures through a distributed actuator. By using Pressure Adaptive Honeycomb (PAH), it is shown that large structural deformations in excess of 50% strains can be achieved while maintaining full structural integrity and enabling secondary flight control mechanisms like flaps. The successful implementation of pressure-adaptive honeycomb in the trailing edge of a wing section sparked the motivation for subsequent research into the optimal topology of the pressure adaptive honeycomb within the trailing edge of a morphing flap. As an input for the optimization two known shapes are required: a desired shape in cruise configuration and a desired shape in landing configuration. In addition, the boundary conditions and load cases (including aerodynamic loads and internal pressure loads) should be specified for each condition. Finally, a set of six design variables is specified relating to the honeycomb and upper skin topology of the morphing flap. A finite-element model of the pressure-adaptive honeycomb structure is developed specifically tailored to generate fast but reliable results for a given combination of external loading, input variables, and boundary conditions. Based on two bench tests it is shown that this model correlates well

  8. Knowledge Management for Topological Optimization Integration in Additive Manufacturing

    Directory of Open Access Journals (Sweden)

    Nicolas Gardan

    2014-01-01

    Full Text Available Engineering design optimization of mechanical structures is nowadays essential in the mechanical industry (automotive, aeronautics, etc.. To remain competitive in the globalized world, it is necessary to create and design structures that, in addition to complying specific mechanical performance, should be less expensive. Engineers must then design parts or assemblies that are a better compromise between mechanical and functional performance, weight, manufacturing costs, and so forth. In this context Additive Manufacturing (AM process offers the possibility to avoid tools and manufacture directly the part. There are numerous technologies which are using different kind of material. For each of these, there are at least two materials: the production material and the support one. Support material is, in most cases, cleaned and becomes a manufacturing residue. Improving the material volume and the global mass of the product is an essential aim surrounding the integration of simulation in additive manufacturing process. Moreover, the layer-by-layer technology of additive manufacturing allows the design of innovative objects, and the use of topological optimization in this context can create a very interesting combination. The purpose of our paper is to present the knowledge management of an AM trade oriented tool which integrated the topological optimization of parts and internal patterns.

  9. Topology optimized design for silicon-on-insulator mode converter

    DEFF Research Database (Denmark)

    Frellsen, Louise Floor; Frandsen, Lars Hagedorn; Ding, Yunhong

    2015-01-01

    The field of photonic integrated circuits (PICs) has attracted interest in recent years as they allow high device density while requiring only low operating power. The possibility of exploiting mode division multiplexing (MDM) in future optical communication networks is being investigated...... as a potential method for supporting the constantly increasing internet traffic demand [1]. Mode converters are important components necessary to support on-chip processing of MDM signals and multiple approaches has been followed in realizing such devices [2], [3]. Topology optimization (TO) [4] is a powerful...

  10. TOPOLOGY DESIGN OPTIMIZATION BASED ON BIOTIC BRANCH NET

    Institute of Scientific and Technical Information of China (English)

    Ding Xiaohong; Li Guojie; Yamazaki Koestu

    2005-01-01

    The biotic branch nets are extreme high-tech product. In order to achieve a certain functional objective, they can adjust their growth direction and growth velocity by according to the varying growth environment. An innovative and effective methodology of topology design optimization based on the growth mechanism of biotic branch nets is suggested, and it is applied to a layout design problem of a conductive cooling channel in a heat transfer system. The effectiveness of the method is validated by the FEM analysis.

  11. Self-supporting structure design in additive manufacturing through explicit topology optimization

    Science.gov (United States)

    Guo, Xu; Zhou, Jianhua; Zhang, Weisheng; Du, Zongliang; Liu, Chang; Liu, Ying

    2017-08-01

    One of the challenging issues in additive manufacturing (AM) oriented topology optimization is how to design structures that are self-supportive in a manufacture process without introducing additional supporting materials. In the present contribution, it is intended to resolve this problem under an explicit topology optimization framework where optimal structural topology can be found by optimizing a set of explicit geometry parameters. Two solution approaches established based on the Moving Morphable Components (MMC) and Moving Morphable Voids (MMV) frameworks, respectively, are proposed and some theoretical issues associated with AM oriented topology optimization are also analyzed. Numerical examples provided demonstrate the effectiveness of the proposed methods.

  12. Models and Methods for Structural Topology Optimization with Discrete Design Variables

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    Structural topology optimization is a multi-disciplinary research field covering optimal design of load carrying mechanical structures such as bridges, airplanes, wind turbines, cars, etc. Topology optimization is a collection of theory, mathematical models, and numerical methods and is often used...... or stresses, or fundamental frequencies. The design variables are either continuous or discrete and model dimensions, thicknesses, densities, or material properties. Structural topology optimization is a multi-disciplinary research field covering optimal design of load carrying mechanical structures...... in the conceptual design phase to find innovative designs. The strength of topology optimization is the capability of determining both the optimal shape and the topology of the structure. In some cases also the optimal material properties can be determined. Optimal structural design problems are modeled...

  13. A level set method for reliability-based topology optimization of compliant mechanisms

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Based on the level set model and the reliability theory, a numerical approach of reliability-based topology optimization for compliant mechanisms with multiple inputs and outputs is presented. A multi-objective topology optimal model of compliant mechanisms considering uncertainties of the loads, material properties, and member geometries is developed. The reliability analysis and topology optimization are integrated in the optimal iterative process. The reliabilities of the compliant mechanisms are evaluated by using the first order reliability method. Meanwhile, the problem of structural topology optimization is solved by the level set method which is flexible in handling complex topological changes and concise in describing the boundary shape of the mechanism. Numerical examples show the importance of considering the stochastic nature of the compliant mechanisms in the topology optimization process.

  14. Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

    Directory of Open Access Journals (Sweden)

    Qinghai Zhao

    2015-01-01

    Full Text Available A robust topology optimization (RTO approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.

  15. On a multiscale strategy and its optimization for the simulation of combined delamination and buckling

    Science.gov (United States)

    Saavedra, K.; Allix, O.; Gosselet, P.

    2012-08-01

    This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated surfaces. In order to achieve an accurate prediction of the quasi-static response, a very refined discretization of the structure is required, leading to the resolution of very large and highly nonlinear numerical problems. In this paper, a nonlinear finite element formulation along with a parallel iterative scheme based on a multiscale domain decomposition are used for the computation of 3D mesoscale models. Previous works by the authors already dealt with the simulation of multiscale delamination assuming small perturbations. This paper presents the formulation used to include geometric nonlinearities into this existing multiscale framework and discusses the adaptations that need to be made to the iterative process in order to ensure the rapid convergence and the scalability of the method in the presence of buckling and delamination. These various adaptations are illustrated by simulations involving large numbers of DOFs.

  16. Designing Meta Material Slabs Exhibiting Negative Refraction Using Topology Optimization

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Sigmund, O.

    2016-01-01

    This paper proposes a topology optimization based approach for designing meta materials exhibiting a desired negative refraction with high transmission at a given angle of incidence and frequency. The approach considers a finite slab of meta material consisting of axis-symmetric designable unit...... cells subjected to an exterior field. The unit cell is designed to achieve the desired properties based on tailoring the response of the meta material slab underthe exterior field. The approach is directly applicable to physical problems modeled by the Helmholtz equation, such as acoustic, elastic...... and electromagnetic wave problems. Acoustic meta materials with unit cell size on the order of half the wave length are considered as examples. Optimized designs are presented and their performance under varying frequency and angle of incidence is investigated....

  17. Geometric constraints for shape and topology optimization in architectural design

    Science.gov (United States)

    Dapogny, Charles; Faure, Alexis; Michailidis, Georgios; Allaire, Grégoire; Couvelas, Agnes; Estevez, Rafael

    2017-02-01

    This work proposes a shape and topology optimization framework oriented towards conceptual architectural design. A particular emphasis is put on the possibility for the user to interfere on the optimization process by supplying information about his personal taste. More precisely, we formulate three novel constraints on the geometry of shapes; while the first two are mainly related to aesthetics, the third one may also be used to handle several fabrication issues that are of special interest in the device of civil structures. The common mathematical ingredient to all three models is the signed distance function to a domain, and its sensitivity analysis with respect to perturbations of this domain; in the present work, this material is extended to the case where the ambient space is equipped with an anisotropic metric tensor. Numerical examples are discussed in two and three space dimensions.

  18. Topology optimization with geometric uncertainties by perturbation techniques

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Schevenels, M.; Sigmund, Ole

    2012-01-01

    the above assumptions, the proposed algorithm provides a computationally cheap alternative to previously introduced stochastic optimization methods based on Monte Carlo sampling. The method is demonstrated on the design of a minimum compliance cantilever beam and a compliant mechanism. Copyright © 2012 John......The aim of this paper was to present a topology optimization methodology for obtaining robust designs insensitive to small uncertainties in the geometry. The variations are modeled using a stochastic field. The model can represent spatially varying geometry imperfections in devices produced...... by etching techniques. Because of under‐etching or over‐etching parts of the structure may become thinner or thicker than a reference design supplied to the manufacturer. The uncertainties are assumed to be small and their influence on the system response is evaluated using perturbation techniques. Under...

  19. Topology optimization for acoustic-structure interaction problems

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole

    2006-01-01

    We propose a gradient based topology optimization algorithm for acoustic-structure (vibro-acoustic) interaction problems without an explicit interfacing boundary representation. In acoustic-structure interaction problems, the pressure field and the displacement field are governed by the Helmholtz...... equation and the linear elasticity equation, respectively, and it is necessary that the governing equations should be properly evolved with respect to the design variables in the design domain. Moreover, all the boundary conditions obtained by computing surface coupling integrals should be properly imposed...... to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz...

  20. Topological Optimization of the Evaluation of Finite Element Matrices

    CERN Document Server

    Kirby, Robert C; Scott, L Ridgway; Terrel, Andy R; 10.1137/050635547

    2012-01-01

    We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on phrasing the computation on each element as the contraction of each collection of reference element tensors with an element-specific geometric tensor. We then present a new concept of complexity-reducing relations that serve as distance relations between these reference element tensors. This notion sets up a graph-theoretic context in which we may find an optimized algorithm by computing a minimum spanning tree. We present experimental results for some common multilinear forms showing significant reductions in operation count and also discuss some efficient algorithms for building the graph we use for the optimization.

  1. Creating Materials with Negative Refraction Index using Topology Optimization

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Sigmund, Ole

    We apply topology optimization along with full modeling of the electromagnetic (acoustic) field to create metamaterials with negative refraction index. We believe that our approach can be used in the design of metamaterials with specific effective permittivity and permeability e.g. by adapting...... is on the order of the wavelength. We seek a distribution of solid and air in the design cell yielding a prescribed negative refraction index for the slab. Our objective is to minimize the difference in amplitude between the solution to the model problemand a prescribed modulated plane wave behind the slab....... The direction of propagation for the prescribed wave is chosen to match the angle of incidence of the incoming plane wave and its position isused to select the refraction index for the slab. We introducing a continuous design field and apply The Method of Moving Asymptotes to perform the optimization. A filter...

  2. Topology optimization of an electronics cover plate with respect to eigenfrequencies

    DEFF Research Database (Denmark)

    A. Kristensen, Anders Schmidt

    In the present paper it is illustrated how topology optimization with respect to eigenfrequency can be applied effectively in the product development process. The topology optimization code is implemented in ANSYS by a so called UPF. The maximization of eigenfrequency as objective is invoked...... into the existing code. As an example is chosen an electronics cover plate. The resulting design devised by the topology optimization yield a significant higher eigenfrequency than obtained by traditional design methods and experience....

  3. Topology Optimization and Performance Calculation for Control Arms of a Suspension

    OpenAIRE

    2014-01-01

    Control Arm (CA) of a suspension plays an important role in the automotive ride comfort and handling stability. In this paper, the topology optimization model including ball joints and bushing for topology optimization of an aluminium CA is established, where a ball joint is simplified as rigid elements and the elastic properties of a rubber bushing are estimated using Mooney-Rivlin constitutive law. A method for treating with multiple loads in topology optimization of CA is presented. Inerti...

  4. Newton-type method for the variational discretization of topology optimization problems

    DEFF Research Database (Denmark)

    Evgrafov, Anton

    2013-01-01

    We present a locally quadratically convergent optimization algorithm for solving topology optimization problems. The distinguishing feature of the algorithm is to treat the design as a smooth function of the state and not vice versa as in the traditional nested approach to topology optimization, ...

  5. A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    石连栓; 孙焕纯; 冯恩民

    2001-01-01

    A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

  6. Topology optimization of pulse shaping filters using the Hilbert transform envelope extraction

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Matzen, René; Elesin, Yuriy

    2011-01-01

    Time domain topology optimization is applied to design pulse shaping filters. The objective function depends on the pulse envelope, which is extracted by utilizing the Hilbert transform. The gradients with respect to the topology optimization variables are derived, and the optimization methodology...

  7. Models and Methods for Structural Topology Optimization with Discrete Design Variables

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    Structural topology optimization is a multi-disciplinary research field covering optimal design of load carrying mechanical structures such as bridges, airplanes, wind turbines, cars, etc. Topology optimization is a collection of theory, mathematical models, and numerical methods and is often used...... such as bridges, airplanes, wind turbines, cars, etc. Topology optimization is a collection of theory, mathematical models, and numerical methods and is often used in the conceptual design phase to find innovative designs. The strength of topology optimization is the capability of determining both the optimal...... methods. The methods are often based on the concept of divide-and-conquer. Despite the proposed theoretical and numerical advances, this thesis clearly indicates that solving large-scale structural topology optimization problems with discrete design variables to proven global optimality is currently...

  8. EPSILON-CONTINUATION APPROACH FOR TRUSS TOPOLOGY OPTIMIZATION

    Institute of Scientific and Technical Information of China (English)

    GUO Xu; CHENG Gengdong

    2004-01-01

    In the present paper, a so-called epsilon-continuation approach is proposed for the solution of singular optimum in truss topology optimization problems. This approach is an improved version of the epsilon-relaxed approach developed by the authors previously. In the proposed approach,we start the optimization process from a relaxation parameter with a relatively large value and obtain a solution by applying the epsilon-relaxed approach. Then we decrease the value of the relaxation parameter by a small amount and choose the optimal solution found from the previous optimization process as the initial design for the next optimization. This continuation process is continued until a small termination value of the relaxation parameter is reached. Convergence analysis of the proposed approach is also presented. Numerical examples show that this approach can alleviate the dependence of the final solution on the initial choice of the design variable and enhance the probability of finding the singular optimum from rather arbitrary initial designs.

  9. APPLICATION OF VIRTUAL LAMINATED ELEMENT IN THE TOPOLOGY OPTIMIZATION OF STRUCTURES

    Institute of Scientific and Technical Information of China (English)

    徐兴; 李芳; 凌道盛

    2001-01-01

    This paper presents the topology optimization design of structures composed of plane stress elements. The authors' proposed method of topology optimization by virtual laminated element is based on the Evolutionary Structural Optimization (ESO) method of linear elasticity, but dose not require formation of as many elements as the conventional ESO method. The presented method has the important feature of reforming the stiffness matrix in generating optimum topology. Calculation results showed that this algorithm is simple and effective and can be applied for topology optimization of structures.

  10. SOME RESULTS ON OPTIMAL TOPOLOGY DESIGN OF TRUSS WITH UNILATERAL CONTACT CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    Yang Deqing; Liu Zhengxing; Xuan Zhaocheng

    2000-01-01

    The optimal topology design of truss structures concerning stress and frictionless unilateral contact displacement constraints is investigated. The existence of ununique optimal solution under contact gaps is found. This shows that the contact conditions have an effect on structural topology, and different ini tial contact gaps may lead to different structural topologies. To avoid the singular optima in structural topology optimization in multiple loading cases, an ε-relaxed method is adopted to establish the relaxing topology opti mization formulations. The problem is solved by means of a two-level optimization method. In the first sub level, the solution of the frictionless unilateral contact problem is obtained by solving an equivalent quadratic programming. In the second sublevel, topology optimization of truss is carried out by an e-relaxed method. The validity of the method proposed is verified by computational results.

  11. On a multiscale strategy and its optimization for the simulation of combined delamination and buckling

    CERN Document Server

    Saavedra, Karin; Gosselet, Pierre; 10.1002/nme.4305

    2012-01-01

    This paper investigates a computational strategy for studying the interactions between multiple through-the-width delaminations and global or local buckling in composite laminates taking into account possible contact between the delaminated surfaces. In order to achieve an accurate prediction of the quasi-static response, a very refined discretization of the structure is required, leading to the resolution of very large and highly nonlinear numerical problems. In this paper, a nonlinear finite element formulation along with a parallel iterative scheme based on a multiscale domain decomposition are used for the computation of 3D mesoscale models. Previous works by the authors already dealt with the simulation of multiscale delamination assuming small perturbations. This paper presents the formulation used to include geometric nonlinearities into this existing multiscale framework and discusses the adaptations that need to be made to the iterative process in order to ensure the rapid convergence and the scalabi...

  12. Fusion Global-Local-Topology Particle Swarm Optimization for Global Optimization Problems

    Directory of Open Access Journals (Sweden)

    Zahra Beheshti

    2014-01-01

    Full Text Available In recent years, particle swarm optimization (PSO has been extensively applied in various optimization problems because of its structural and implementation simplicity. However, the PSO can sometimes find local optima or exhibit slow convergence speed when solving complex multimodal problems. To address these issues, an improved PSO scheme called fusion global-local-topology particle swarm optimization (FGLT-PSO is proposed in this study. The algorithm employs both global and local topologies in PSO to jump out of the local optima. FGLT-PSO is evaluated using twenty (20 unimodal and multimodal nonlinear benchmark functions and its performance is compared with several well-known PSO algorithms. The experimental results showed that the proposed method improves the performance of PSO algorithm in terms of solution accuracy and convergence speed.

  13. On topology optimization of acoustic metamaterial lattices for locally resonant bandgaps of flexural waves

    CERN Document Server

    Hedayatrasa, Saeid; Uddin, Mohammad

    2016-01-01

    Optimized topology of bi-material acoustic metamaterial lattice plates is studied for maximized locally resonant bandgap of flexural guided waves. Optimized layout of the two relatively stiff and compliant material phases in the design domain is explored, free from any restrictions on the topology and shape of the relevant domains. Multiobjective optimization is performed through which maximized effective stiffness or minimized overall mass of the bandgap topology is additionally ensured. Extreme and selected intermediate optimized topologies of Pareto fronts are presented and their bandgap efficiencies and effective stiffness are compared. The bi-material constitution of selected topologies are further altered and modal band structure of resultant multilateral and porous designs are evaluated. Novel, core-shell like, locally resonant bandgaps are introduced. It is shown that how the bandgap efficiency and structural mass and/or stiffness can be optimized through optimized microstructural design of the matrix...

  14. Topology optimization of coated structures and material interface problems

    DEFF Research Database (Denmark)

    Clausen, Anders; Aage, Niels; Sigmund, Ole

    2015-01-01

    This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...

  15. Topological Effects and Performance Optimization in Transportation Continuous Network Design

    Directory of Open Access Journals (Sweden)

    Jianjun Wu

    2014-01-01

    Full Text Available Because of the limitation of budget, in the planning of road works, increased efforts should be made on links that are more critical to the whole traffic system. Therefore, it would be helpful to model and evaluate the vulnerability and reliability of the transportation network when the network design is processing. This paper proposes a bilevel transportation network design model, in which the upper level is to minimize the performance of the network under the given budgets, while the lower level is a typical user equilibrium assignment problem. A new solution approach based on particle swarm optimization (PSO method is presented. The topological effects on the performance of transportation networks are studied with the consideration of three typical networks, regular lattice, random graph, and small-world network. Numerical examples and simulations are presented to demonstrate the proposed model.

  16. Topology optimization of coated structures and material interface problems

    DEFF Research Database (Denmark)

    Clausen, Anders; Aage, Niels; Sigmund, Ole

    2015-01-01

    This paper presents a novel method for including coated structures and prescribed material interface properties into the minimum compliance topology optimization problem. Several elements of the method are applicable to a broader range of interface problems. The approach extends the standard SIMP...... method by including the normalized norm of the spatial gradient of the design field into the material interpolation function, enforcing coating material at interfaces by attributing particular properties. The length scales of the base structure and the coating are separated by introducing a two......-step filtering/projection approach. The modeled coating thickness is derived analytically, and the coating is shown to be accurately controlled and applied in a highly uniform manner over the structure. An alternative interpretation of the model is to perform single-material design for additive manufacturing...

  17. Lightweight design of the rectangular mirror using topology optimization

    Science.gov (United States)

    Xiang, Meng; Li, Fu

    2014-09-01

    That minimizing the mass of space optical remote sensor at the same time guaranteeing of structural rigidity and surface shape accuracy, became a new critical research topic. This paper achieves detailed design of meniscus rectangular lens body structure by taking the choice of materials, design of supporting structure and lightweight form of mirror into account. And we established lightweight concrete of the mirror under self-weight by the method of topological optimization design. For the optimization, we used a 3-D model of the rectangular mirror and calculated based on that making minimum weight of the mirror as an objective function constrained by the displacement of the mirror surface. Finally finite element analysis method was adopted to get the optimization results analyzed and compared with the traditional triangular lightweight model. Analysis results prove that: the new mirror is superior to the traditional model in surface accuracy and structural rigidity, PV value, RMS value and the lightweight rate. With enough high dynamic-static stiffness and thermal stability, this kind of mirror can meet the demand under the self-weight and the random vibration environment respectively. So this article puts forward a new idea in the lightweight design of rectangular mirror.

  18. Topology optimization of embedded piezoelectric actuators considering control spillover effects

    Science.gov (United States)

    Gonçalves, Juliano F.; De Leon, Daniel M.; Perondi, Eduardo A.

    2017-02-01

    This article addresses the problem of active structural vibration control by means of embedded piezoelectric actuators. The topology optimization method using the solid isotropic material with penalization (SIMP) approach is employed in this work to find the optimum design of actuators taken into account the control spillover effects. A coupled finite element model of the structure is derived assuming a two-phase material and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The undesirable effects of the feedback control on the residual modes are limited by including a spillover constraint term containing the residual controllability Gramian eigenvalues. The optimization of the shape and placement of the conventionally embedded piezoelectric actuators are performed using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the additional constraint.

  19. Topology optimization of Halbach magnet arrays using isoparametric projection

    Science.gov (United States)

    Lee, Jaewook; Nomura, Tsuyoshi; Dede, Ercan M.

    2017-06-01

    Topology optimization using isoparametric projection for the design of permanent magnet patterns in Halbach arrays is proposed. Based on isoparametric shape functions used in the finite element analysis, the permanent magnet strength and magnetization directions in a Halbach array are simultaneously optimized for a given design goal. To achieve fabrication feasibility of a designed Halbach magnet array, two design schemes are combined with the isoparametric projection method. First, a penalization scheme is proposed for designing the permanent magnets to have discrete magnetization direction angles. Second, an extrusion scheme is proposed for the shape regularization of the permanent magnet segments. As a result, the method systematically finds the optimal permanent magnet patterns of a Halbach array considering manufacturing feasibility. In two numerical examples, a circular shaped permanent magnet Halbach array is designed to minimize the magnitude of the magnetic flux density and to maximize the upward direction magnetic flux density inside the magnet array. Logical extension of the method to the design of permanent magnet arrays in linear actuators is provided, where the design goal is to maximize the actuator magnetic force.

  20. Topology optimization of 3D compliant actuators by a sequential element rejection and admission method

    OpenAIRE

    Ansola, R; Vegueria, E; Alonso, C.; Querin, OM

    2016-01-01

    This work presents a sequential element rejection and admission (SERA) method for optimum topology design of three dimensional compliant actuators. The proposed procedure has been successfully applied to several topology optimization problems, but most investigations for compliant devices design have been focused on planar systems. This investigation aims to progress on this line, where a generalization of the method for three dimensional topology optimization is explored. The methodology des...

  1. Truss topology optimization with discrete design variables — Guaranteed global optimality and benchmark examples

    DEFF Research Database (Denmark)

    Achtziger, Wolfgang; Stolpe, Mathias

    2007-01-01

    .e., a 0/1 problem. In contrast to the heuristic methods considered in many other approaches, our goal is to compute guaranteed globally optimal structures. This is done by a branch-and-bound method for which convergence can be proven. In this branch-and-bound framework, lower bounds of the optimal......-integer problems. The main intention of this paper is to provide optimal solutions for single and multiple load benchmark examples, which can be used for testing and validating other methods or heuristics for the treatment of this discrete topology design problem....

  2. Topology

    CERN Document Server

    Lefschetz, Solomon

    1930-01-01

    Lefschetz's Topology was written in the period in between the beginning of topology, by Poincaré, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of

  3. Topology

    CERN Document Server

    Hocking, John G

    1988-01-01

    ""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t

  4. Multi-material topology optimization of laminated composite beams with eigenfrequency constraints

    DEFF Research Database (Denmark)

    Blasques, José Pedro Albergaria Amaral

    2014-01-01

    This paper describes a methodology for simultaneous topology and material optimization in optimal design of laminated composite beams with eigenfrequency constraints. The structural response is analyzed using beam finite elements. The beam sectional properties are evaluated using a finite element...... based cross section analysis tool which is able to account for effects stemming from material anisotropy and inhomogeneity in sections of arbitrary geometry. The optimization is performed within a multi-material topology optimization framework where the continuous design variables represent the volume....... The results suggest that the devised methodology is suitable for simultaneous optimization of the cross section topology and material properties in design of beams with eigenfrequency constraints....

  5. Topology optimized mode conversion in a photonic crystal waveguide fabricated in siliconon-insulator material

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Elesin, Yuriy; Frellsen, Louise Floor;

    2014-01-01

    We have designed and for the first time experimentally verified a topology optimized mode converter with a footprint of ∼6.3 μm × ∼3.6 μm which converts the fundamental even mode to the higher order odd mode of a dispersion engineered photonic crystal waveguide. 2D and 3D topology optimization is...

  6. Topology optimization of heat conduction problems using the finite volume method

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Bendsøe, Martin P.; Sigmund, Ole

    2006-01-01

    This note addresses the use of the finite volume method (FVM) for topology optimization of a heat conduction problem. Issues pertaining to the proper choice of cost functions, sensitivity analysis and example test problems are used to illustrate the effect of applying the FVM as an analysis tool...... checkerboards do not form during the topology optimization process....

  7. Topology optimized design of a transverse electric higher order mode converter

    DEFF Research Database (Denmark)

    Frellsen, Louise Floor; Ding, Yunhong; Sigmund, Ole

    2016-01-01

    present the possibility of employing topology optimization (TO) to design a device that allows for reversible conversion between the transverse electric fundamental even (TE0) mode and the second higher order odd mode (TE2). Topology optimization is an iterative inverse design process, where repeated...

  8. Conceptual design of reinforced concrete structures using topology optimization with elastoplastic material modeling

    DEFF Research Database (Denmark)

    Bogomolny, Michael; Amir, Oded

    2012-01-01

    of topology optimization with elastoplastic material modeling. Concrete and steel are both considered as elastoplastic materials, including the appropriate yield criteria and post‐yielding response. The same approach can be applied also for topology optimization of other material compositions where nonlinear...

  9. Simultaneous Topology and Size Optimization of 2D and 3D Trusses Using Evolutionary Structural Optimization with regard to Commonly Used Topologies

    Directory of Open Access Journals (Sweden)

    Pavel Tomšič

    2014-07-01

    Full Text Available One of many optimization techniques is the evolutionary structural optimization (ESO, based on the idea that an optimal structure can be achieved by gradually removing ineffectively used materials from the design domain. Production of a multistage optimization is often proposed to reach the best overall solution. In the first stage, the structure is optimized according to a topology criterion, and, in the second stage, sizing optimization is carried out. The efficiency of such an approach is questionable as a fixed topology, for the second stage optimization may not be the most favorable before sizing optimization is carried out. In this paper, the simultaneous topology and size optimization of trusses using the ESO algorithm are discussed. A number of numerical examples are presented to research capacity to achieve optimal solutions for a structural problem. The topology design of the initial design domain is based on commonly used designs for multistorey trusses constructed from straight members. Therefore, the cases are of a slender shape and made from a combination of presented internal designs. The case studies will present an evaluation to show whether the described optimization approach can be beneficial in structural design for the purpose of steel framework designs.

  10. Backbone cup – a structure design competition based on topology optimization and 3D printing

    Directory of Open Access Journals (Sweden)

    Zhu Ji-Hong

    2016-01-01

    Full Text Available This paper addresses a structure design competition based on topology optimization and 3D Printing, and proposes an experimental approach to efficiently and quickly measure the mechanical performance of the structures designed using topology optimization. Since the topology optimized structure designs are prone to be geometrically complex, it is extremely inconvenient to fabricate these designs with traditional machining. In this study, we not only fabricated the topology optimized structure designs using one kind of 3D Printing technology known as stereolithography (SLA, but also tested the mechanical performance of the produced prototype parts. The finite element method is used to analyze the structure responses, and the consistent results of the numerical simulations and structure experiments prove the validity of this new structure testing approach. This new approach will not only provide a rapid access to topology optimized structure designs verifying, but also cut the turnaround time of structure design significantly.

  11. Higher-order multi-resolution topology optimization using the finite cell method

    DEFF Research Database (Denmark)

    Groen, Jeroen Peter; Langelaar, Matthijs; Sigmund, Ole

    2017-01-01

    This article presents a detailed study on the potential and limitations of performing higher-order multi-resolution topology optimization with the finite cell method. To circumvent stiffness overestimation in high-contrast topologies, a length-scale is applied on the solution using filter methods....... The relations between stiffness overestimation, the analysis system, and the applied length-scale are examined, while a high-resolution topology is maintained. The computational cost associated with nested topology optimization is reduced significantly compared with the use of first-order finite elements...

  12. Topology

    CERN Document Server

    Kuratowski, Kazimierz

    1966-01-01

    Topology, Volume I deals with topology and covers topics ranging from operations in logic and set theory to Cartesian products, mappings, and orderings. Cardinal and ordinal numbers are also discussed, along with topological, metric, and complete spaces. Great use is made of closure algebra. Comprised of three chapters, this volume begins with a discussion on general topological spaces as well as their specialized aspects, including regular, completely regular, and normal spaces. Fundamental notions such as base, subbase, cover, and continuous mapping, are considered, together with operations

  13. Topology

    CERN Document Server

    Kuratowski, Kazimierz

    1968-01-01

    Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte

  14. LEVEL SET METHOD FOR TOPOLOGICAL OPTIMIZATION APPLYING TO STRUCTURE,MECHANISM AND MATERIAL DESIGNS

    Institute of Scientific and Technical Information of China (English)

    Mei Yulin; Wang Xiaoming

    2004-01-01

    Based on a level set model,a topology optimization method has been suggested recently.It uses a level set to express the moving structural boundary,which can flexibly handle complex topological changes.By combining vector level set models with gradient projection technology,the level set method for topological optimization is extended to a topological optimization problem with multi-constraints,multi-materials and multi-load cases.Meanwhile,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints for a fast convergence.Then the method is applied to structure designs,mechanism and material designs by a number of benchmark examples.Finally,in order to further improve computational efficiency and overcome the difficulty that the level set method cannot generate new material interfaces during the optimization process,the topological derivative analysis is incorporated into the level set method for topological optimization,and a topological derivative and level set algorithm for topological optimization is proposed.

  15. A new three-dimensional topology optimization method based on moving morphable components (MMCs)

    Science.gov (United States)

    Zhang, Weisheng; Li, Dong; Yuan, Jie; Song, Junfu; Guo, Xu

    2017-04-01

    In the present paper, a new method for solving three-dimensional topology optimization problem is proposed. This method is constructed under the so-called moving morphable components based solution framework. The novel aspect of the proposed method is that a set of structural components is introduced to describe the topology of a three-dimensional structure and the optimal structural topology is found by optimizing the layout of the components explicitly. The standard finite element method with ersatz material is adopted for structural response analysis and the shape sensitivity analysis only need to be carried out along the structural boundary. Compared to the existing methods, the description of structural topology is totally independent of the finite element/finite difference resolution in the proposed solution framework and therefore the number of design variables can be reduced substantially. Some widely investigated benchmark examples, in the three-dimensional topology optimization designs, are presented to demonstrate the effectiveness of the proposed approach.

  16. Topology optimization using bi-directional evolutionary structural optimization based on the element-free Galerkin method

    Science.gov (United States)

    Shobeiri, Vahid

    2016-03-01

    In this article, the bi-directional evolutionary structural optimization (BESO) method based on the element-free Galerkin (EFG) method is presented for topology optimization of continuum structures. The mathematical formulation of the topology optimization is developed considering the nodal strain energy as the design variable and the minimization of compliance as the objective function. The EFG method is used to derive the shape functions using the moving least squares approximation. The essential boundary conditions are enforced by the method of Lagrange multipliers. Several topology optimization problems are presented to show the effectiveness of the proposed method. Many issues related to topology optimization of continuum structures, such as chequerboard patterns and mesh dependency, are studied in the examples.

  17. SEQUENTIAL CONVEX PROGRAMMING METHODS FOR SOLVING LARGE TOPOLOGY OPTIMIZATION PROBLEMS: IMPLEMENTATION AND COMPUTATIONAL RESULTS

    Institute of Scientific and Technical Information of China (English)

    Qin Ni; Ch. Zillober; K. Schittkowski

    2005-01-01

    In this paper, we describe a method to solve large-scale structural optimization problems by sequential convex programming (SCP). A predictor-corrector interior point method is applied to solve the strictly convex subproblems. The SCP algorithm and the topology optimization approach are introduced. Especially, different strategies to solve certain linear systems of equations are analyzed. Numerical results are presented to show the efficiency of the proposed method for solving topology optimization problems and to compare different variants.

  18. Topology optimization for reduction of thermo-elastic dissipation in MEMS resonators

    DEFF Research Database (Denmark)

    Gerrard, Dustin D.; Chen, Yunhan; Chandorkar, Saurabh A.

    2017-01-01

    This paper presents a topology optimization approach for reducing thermo-elastic dissipation (TED) in MEMS resonators. This algorithm is applied to a clamped-clamped resonant beam to maximize the quality factor (Q). Optimal designs have a Q ten times higher than a solid beam and are 75% higher than...... previously optimized devices. Furthermore, new designs have intuitive topologies. Beams are fabricated in silicon wafers and experimental measurements of Q agree well with simulation....

  19. Spring-joint method for topology optimization of planar passive compliant mechanisms

    Science.gov (United States)

    Jin, Mohui; Zhang, Xianmin; Zhu, Benliang; Wang, Nianfeng

    2013-11-01

    There is seldom approach developed for the initial topology design of flexure-based compliant mechanisms. The most commonly-used approaches, which start with an existing rigid-body mechanism, do not consider the performances between different topologies. Moreover, they rely heavily on the rigid-body topology, therefore limit the diversity of compliant mechanisms topology. To obtain the optimal initial topology of such mechanisms directly from problem specifications without referencing to the existing mechanism topologies, a spring-joint method is presented for a restricted class of the serial passive flexure-based compliant mechanisms, which are the building blocks of parallel compliant mechanisms. The topology of the compliant mechanisms is represented by a serial spring-joint mechanism(SSJM) that is a traditional rigid-body mechanism with a torsional spring acting on each joint, and is described by position vectors of the spring-joints. A simplified compliance matrix, determined by the position vectors, is used to characterize the tip of the SSJM kinematically, and is optimized to ensure the desired freedoms of the compliant mechanisms during optimization. The topology optimization problem is formulated as finding out the optimal position of the spring-joints in a blank design domain with an objective function derived from the simplified compliance matrix. In design examples, syntheses of the compliant mechanisms with both single freedom and two decoupled freedoms are presented to illustrate the proposed method. The proposed method provides a new way for the initial design of flexure-based compliant mechanisms.

  20. Optimal PMU placement using topology transformation method in power systems.

    Science.gov (United States)

    Rahman, Nadia H A; Zobaa, Ahmed F

    2016-09-01

    Optimal phasor measurement units (PMUs) placement involves the process of minimizing the number of PMUs needed while ensuring the entire power system completely observable. A power system is identified observable when the voltages of all buses in the power system are known. This paper proposes selection rules for topology transformation method that involves a merging process of zero-injection bus with one of its neighbors. The result from the merging process is influenced by the selection of bus selected to merge with the zero-injection bus. The proposed method will determine the best candidate bus to merge with zero-injection bus according to the three rules created in order to determine the minimum number of PMUs required for full observability of the power system. In addition, this paper also considered the case of power flow measurements. The problem is formulated as integer linear programming (ILP). The simulation for the proposed method is tested by using MATLAB for different IEEE bus systems. The explanation of the proposed method is demonstrated by using IEEE 14-bus system. The results obtained in this paper proved the effectiveness of the proposed method since the number of PMUs obtained is comparable with other available techniques.

  1. Combined shape and topology optimization for minimization of maximal von Mises stress

    DEFF Research Database (Denmark)

    Lian, Haojie; Christiansen, Asger Nyman; Tortorelli, Daniel A.

    2017-01-01

    This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology....... By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy....

  2. Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems

    DEFF Research Database (Denmark)

    Wang, Fengwen; Lazarov, Boyan Stefanov; Sigmund, Ole

    2014-01-01

    The focus of this paper is on interpolation schemes for fictitious domain and topology optimization approaches with structures undergoing large displacements. Numerical instability in the finite element simulations can often be observed, due to excessive distortion in low stiffness regions. A new...... for a challenging test geometry as well as for topology optimization of minimum compliance and compliant mechanisms. The effect of combining the proposed interpolation scheme with different hyperelastic material models is investigated as well. Numerical results show that the proposed approach alleviates...... the problems in the low stiffness regions and for the simulated cases, results in stable topology optimization of structures undergoing large displacements. © 2014 Elsevier B.V....

  3. Simulation and experimental validation of powertrain mounting bracket design obtained from multi-objective topology optimization

    Directory of Open Access Journals (Sweden)

    Qinghai Zhao

    2015-06-01

    Full Text Available A framework of multi-objective topology optimization for vehicle powertrain mounting bracket design with consideration of multiple static and dynamic loading conditions is developed in this article. Incorporating into the simplified isotropic material with penalization model, compromise programming method is employed to describe the multi-objective and multi-stiffness topology optimization under static loading conditions, whereas mean eigenvalue formulation is proposed to analyze vibration optimization. To yield well-behaved optimal topologies, minimum member size and draw constraint are settled for meeting manufacturing feasibility requirements. The ultimate mounting bracket is reconstructed based on the optimum results. Numerical analyses of the bracket are performed, followed by physical tests. It is proven that topology optimization methodology is promising and effective for vehicle component design.

  4. Optimal placement of piezoelectric active bars in vibration control by topological optimization

    Institute of Scientific and Technical Information of China (English)

    Guozhong Zhao; Jian Wang; Yuanxian Gu

    2008-01-01

    A continuous variable optimization method and a topological optimization method are proposed for the vibra-tion control of piezoelectric truss structures by means of the optimal placements of active bars. In this optimization model, a zero-one discrete variable is defined in order to solve the optimal placement of piezoelectric active bars. At the same time, the feedback gains are also optimized as conti-nuous design variables. A two-phase procedure is proposed to solve the optimization problem. The sequential linear pro-gramming algorithm is used to solve optimization problem and the sensitivity analysis is carried out for objective and constraint functions to make linear approximations. On the basis of the Newmark time integration of structural tran-sient dynamic responses, a new sensitivity analysis method is developed in this paper for the vibration control problem of piezoelectric truss structures with respect to various kinds of design variables. Numerical examples are given in the paper to demonstrate the effectiveness of the methods.

  5. On reducing computational effort in topology optimization: how far can we go?

    DEFF Research Database (Denmark)

    Amir, Oded; Sigmund, Ole

    2011-01-01

    An approximate approach to solving the nested analysis equations in topology optimization is proposed. The procedure consists of only one matrix factorization for the whole design process and a small number of iterative corrections for each design cycle. The approach is tested on 3D topology opti...

  6. Optimization and comparison of superconducting generator topologies for a 10 MW wind turbine application

    DEFF Research Database (Denmark)

    Liu, Dong; Polinder, Henk; Abrahamsen, Asger Bech

    2017-01-01

    -linear finite element models. By implementing this method, three typical superconducting generator topologies are compared in terms of the active material cost and mass, the synchronous reactance and the phase resistance. The optimization method and the comparison results provide the DDSCG designers...... with a guideline for selecting a suitable machine topology....

  7. Topology

    CERN Document Server

    Manetti, Marco

    2015-01-01

    This is an introductory textbook on general and algebraic topology, aimed at anyone with a basic knowledge of calculus and linear algebra. It provides full proofs and includes many examples and exercises. The covered topics include: set theory and cardinal arithmetic; axiom of choice and Zorn's lemma; topological spaces and continuous functions; connectedness and compactness; Alexandrov compactification; quotient topologies; countability and separation axioms; prebasis and Alexander's theorem; the Tychonoff theorem and paracompactness; complete metric spaces and function spaces; Baire spaces; homotopy of maps; the fundamental group; the van Kampen theorem; covering spaces; Brouwer and Borsuk's theorems; free groups and free product of groups; and basic category theory. While it is very concrete at the beginning, abstract concepts are gradually introduced. It is suitable for anyone needing a basic, comprehensive introduction to general and algebraic topology and its applications.

  8. On the usefulness of non-gradient approaches in topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole

    2011-01-01

    Topology optimization is a highly developed tool for structural design and is by now being extensively used in mechanical, automotive and aerospace industries throughout the world. Gradient-based topology optimization algorithms may efficiently solve fine-resolution problems with thousands and up...... appearing in the literature. This forum article discusses the practical and scientific relevance of publishing papers that use immense computational resources for solving simple problems for which there already exist efficient solution techniques.......Topology optimization is a highly developed tool for structural design and is by now being extensively used in mechanical, automotive and aerospace industries throughout the world. Gradient-based topology optimization algorithms may efficiently solve fine-resolution problems with thousands and up...

  9. Tailoring Macroscale Response of Mechanical and Heat Transfer Systems by Topology Optimization of Microstructural Details

    DEFF Research Database (Denmark)

    Alexandersen, Joe; Lazarov, Boyan Stefanov

    2015-01-01

    -contrast material parameters is proposed to alleviate the high computational cost associated with solving the discrete systems arising during the topology optimization process. Problems within important engineering areas, heat transfer and linear elasticity, are considered for exemplifying the approach...

  10. Effects of finite element formulation on optimal plate and shell structural topologies

    CSIR Research Space (South Africa)

    Long, CS

    2009-09-01

    Full Text Available The effects of selected membrane, plate and flat shell finite element formulations on optimal topologies are numerically investigated. Two different membrane components are considered. The first is a standard 4-node bilinear quadrilateral...

  11. A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

    Institute of Scientific and Technical Information of China (English)

    MEI Yulin; WANG Xiaoming

    2004-01-01

    Combining the vector level set model, the shape sensitivity analysis theory with the gradient projection technique, a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper. The method implicitly describes structural material interfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure. In order to increase computational efficiency for a fast convergence, an appropriate nonlinear speed mapping is established in the tangential space of the active constraints. Meanwhile, in order to overcome the numerical instability of general topology optimization problems, the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process. The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity, compared with other methods based on explicit boundary variations in the literature.

  12. Dynamic design of stiffeners for a typical panel using topology optimization and finite element analysis

    National Research Council Canada - National Science Library

    Zhou, Yadong; Fei, Qingguo

    2015-01-01

    .... In order to improve the stiffness–mass efficiency, this article presents a combined use of topology optimization and finite element analysis to the dynamic design of stiffeners for a typical panel...

  13. Topology optimization of bounded acoustic problems using the hybrid finite element-wave based method

    DEFF Research Database (Denmark)

    Goo, Seongyeol; Wang, Semyung; Kook, Junghwan

    2017-01-01

    This paper presents an alternative topology optimization method for bounded acoustic problems that uses the hybrid finite element-wave based method (FE-WBM). The conventional method for the topology optimization of bounded acoustic problems is based on the finite element method (FEM), which...... is limited to low frequency applications due to considerable computational efforts. To this end, we propose a gradient-based topology optimization method that uses the hybrid FE-WBM whereby the entire domain of a problem is partitioned into design and non-design domains. In this respect, the FEM is used...... as a design domain of topology optimization, and the WBM is used as a non-design domain to increase computational efficiency. The adjoint variable method based on the hybrid FE-WBM is also proposed as a means of computing design sensitivities. Numerical examples are presented to demonstrate the effectiveness...

  14. Topology optimization for enhancing the acoustical and thermal characteristics of acoustic devices simultaneously

    Science.gov (United States)

    Oh, Kee Seung; Lee, Jin Woo

    2017-08-01

    In this study, an optimal design method was developed using topology optimization for an acoustic device in the presence of temperature gradient. Although acoustic properties were strongly affected by temperature distribution, many topology optimization problems for optimal acoustic devices were formulated under the assumption that temperature was uniformly distributed in the design domain or that heat transfer through boundaries was negligible. An acoustically optimized topology could negatively influence the heat transfer characteristics of a mechanical device. To figure out this issue, thermo-acoustical topology optimization problems were formulated for an optimal design of the acoustic device. A general form of a finite element equation was developed for acoustical and thermal analyses, and interpolation functions were carefully selected to obtain a black-and-white topology in the final step. Optimal design examples were solved for various acoustical and thermal design requirements, and the physical characteristics of an optimal muffler obtained using the proposed approach in the present study were compared with those of a well-known existing design.

  15. Design of materials with extreme thermal expansion using a three-phase topology optimization method

    DEFF Research Database (Denmark)

    Sigmund, Ole; Torquato, S.

    1997-01-01

    Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases...... materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion...

  16. Simulation and experimental validation of powertrain mounting bracket design obtained from multi-objective topology optimization

    OpenAIRE

    Qinghai Zhao; Xiaokai Chen; Lu Wang; Jianfeng Zhu; Zheng-Dong Ma; Yi Lin

    2015-01-01

    A framework of multi-objective topology optimization for vehicle powertrain mounting bracket design with consideration of multiple static and dynamic loading conditions is developed in this article. Incorporating into the simplified isotropic material with penalization model, compromise programming method is employed to describe the multi-objective and multi-stiffness topology optimization under static loading conditions, whereas mean eigenvalue formulation is proposed to analyze vibration op...

  17. Topology optimization based on moving deformable components: A new computational framework

    OpenAIRE

    2014-01-01

    In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the proposed solution paradigm can incorporate more geometry and mechanical information into topology optimization directly and therefore render the solution process more flexible. It also has the great potential to reduce the computational burden associated with top...

  18. An explicit parameterization for casting constraints in gradient driven topology optimization

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund; Andreasen, Casper Schousboe

    2011-01-01

    From a practical point of view it is often desirable to limit the complexity of a topology optimization design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained by ...... by use of a Heaviside design parameterization in a specified casting direction. This reduces the number of design variables considerably and the approach is simple to implement....

  19. Benefits and Challenges when Performing Robust Topology Optimization for Interior Acoustic Problems

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Jensen, Jakob Søndergaard; Lazarov, Boyan Stefanov

    The objective of this work is to present benets and challenges of using robust topology optimization techniques for minimizing the sound pressure in interior acoustic problems. The focus is on creating designs which maintain high performance under uniform spatial variations. This work takes offset...... in previous work considering topology optimization for interior acoustic problems, [1]. However in the previous work the robustness of the designs was not considered....

  20. Topology Optimization Using Multiscale Finite Element Method for High-Contrast Media

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov

    2014-01-01

    The focus of this paper is on the applicability of multiscale finite element coarse spaces for reducing the computational burden in topology optimization. The coarse spaces are obtained by solving a set of local eigenvalue problems on overlapping patches covering the computational domain....... The approach is relatively easy for parallelization, due to the complete independence of the subproblems, and ensures contrast independent convergence of the iterative state problem solvers. Several modifications for reducing the computational cost in connection to topology optimization are discussed...

  1. The impact of migration topology on the runtime of island models in dynamic optimization

    DEFF Research Database (Denmark)

    Lissovoi, Andrei; Witt, Carsten

    2016-01-01

    We introduce a simplified island model with behavior similar to the λ (1+1) islands optimizing the Maze fitness function, and investigate the effects of the migration topology on the ability of the simplified island model to track the optimum of a dynamic fitness function. More specifically, we...... prove that there exist choices of model parameters for which using a unidirectional ring as the migration topology allows the model to track the oscillating optimum through n Mazelike phases with high probability, while using a complete graph as the migration topology results in the island model losing...... track of the optimum with overwhelming probability. Additionally, we prove that if migration occurs only rarely, denser migration topologies may be advantageous. This serves to illustrate that while a less-dense migration topology may be useful when optimizing dynamic functions with oscillating behavior...

  2. Topology optimization: An effective method for designing front metallization patterns of solar cells

    NARCIS (Netherlands)

    Gupta, D.K.; Langelaar, M.; Barink, M.; Keulen, F. van

    2014-01-01

    Optimal front electrode design is one of the approaches to improve the performance of solar cells. This work introduces the application of topology optimization (TO) to design complex front metallization patterns for solar cells. TO optimizes the distribution of electrode material on the front surfa

  3. Topology optimization: An effective method for designing front metallization patterns of solar cells

    NARCIS (Netherlands)

    Gupta, D.K.; Langelaar, M.; Barink, M.; Keulen, F. van

    2014-01-01

    Optimal front electrode design is one of the approaches to improve the performance of solar cells. This work introduces the application of topology optimization (TO) to design complex front metallization patterns for solar cells. TO optimizes the distribution of electrode material on the front surfa

  4. Design of one-dimensional optical pulse-shaping filters by time-domain topology optimization

    DEFF Research Database (Denmark)

    Yang, Lirong; Lavrinenko, Andrei; Hvam, Jørn Märcher

    2009-01-01

    Time-domain topology optimization is used here to design optical pulse-shaping filters in Si/SiO2 thin-film systems. A novel envelope objective function as well as explicit penalization are used to adapt the optimization method to this unique class of design problems.......Time-domain topology optimization is used here to design optical pulse-shaping filters in Si/SiO2 thin-film systems. A novel envelope objective function as well as explicit penalization are used to adapt the optimization method to this unique class of design problems....

  5. Topology Optimization of Shape Memory Alloy Actuators using Element Connectivity Parameterization

    DEFF Research Database (Denmark)

    Langelaar, Matthijs; Yoon, Gil Ho; Kim, Yoon Young

    2005-01-01

    This paper presents the first application of topology optimization to the design of shape memory alloy actuators. Shape memory alloys (SMA’s) exhibit strongly nonlinear, temperature-dependent material behavior. The complexity in the constitutive behavior makes the topology design of SMA structures...... intractable by the conventional element density-based topology optimization. Therefore, in the present study, the recently developed element connectivity parameterization (ECP) formulation is applied, which offers important advantages for complex nonlinear topology optimization problems. A history......) stiffness matrix of continuum finite elements. Therefore, any finite element code, including commercial codes, can be readily used for the ECP implementation. The key ideas and characteristics of these methods will be presented in this paper....

  6. THE SATELLITE STRUCTURE TOPOLOGY OPTIMIZATION BASED ON HOMOGENIZATION METHOD AND ITS SIZE SENSITIVITY ANALYSIS

    Institute of Scientific and Technical Information of China (English)

    ChenChangya; PanJin; WangDeyu

    2005-01-01

    With the development of satellite structure technology, more and more design parameters will affect its structural performance. It is desirable to obtain an optimal structure design with a minimum weight, including optimal configuration and sizes. The present paper aims to describe an optimization analysis for a satellite structure, including topology optimization and size optimization. Based on the homogenization method, the topology optimization is carried out for the main supporting frame of service module under given constraints and load conditions, and then the sensitivity analysis is made of 15 structural size parameters of the whole satellite and the optimal sizes are obtained. The numerical result shows that the present optimization design method is very effective.

  7. Computational study of Wolff's law with trabecular architecture in the human proximal femur using topology optimization.

    Science.gov (United States)

    Jang, In Gwun; Kim, Il Yong

    2008-08-07

    In the field of bone adaptation, it is believed that the morphology of bone is affected by its mechanical loads, and bone has self-optimizing capability; this phenomenon is well known as Wolff's law of the transformation of bone. In this paper, we simulated trabecular bone adaptation in the human proximal femur using topology optimization and quantitatively investigated the validity of Wolff's law. Topology optimization iteratively distributes material in a design domain producing optimal layout or configuration, and it has been widely and successfully used in many engineering fields. We used a two-dimensional micro-FE model with 50 microm pixel resolution to represent the full trabecular architecture in the proximal femur, and performed topology optimization to study the trabecular morphological changes under three loading cases in daily activities. The simulation results were compared to the actual trabecular architecture in previous experimental studies. We discovered that there are strong similarities in trabecular patterns between the computational results and observed data in the literature. The results showed that the strain energy distribution of the trabecular architecture became more uniform during the optimization; from the viewpoint of structural topology optimization, this bone morphology may be considered as an optimal structure. We also showed that the non-orthogonal intersections were constructed to support daily activity loadings in the sense of optimization, as opposed to Wolff's drawing.

  8. Design, Analysis And Realization Of Topology Optimized Concrete Structures

    DEFF Research Database (Denmark)

    Søndergaard, Asbjørn; Dombernowsky, Per

    2012-01-01

    This paper proposes the application of topology optimisation as a constitutive design tool for design and form-finding of architectural concrete structures, and realisation of these designs using large scale CNCmilling of polystyrene form-work for in situ casting....

  9. Optimizing Fiber Topologies for WDM Optical Networks Based on Multi-Granularity Optical Switching Technology

    Institute of Scientific and Technical Information of China (English)

    LI Junjie; ZHOU Bingkun; ZHANG Hanyi; LI Yanhe

    2006-01-01

    For the quality of service (QoS) and fairness considerations, the hop counts of various lightpaths in a wavelength division multiplexing (WDM) optical network should be short and compact. The development of multi-granularity optical switching technology has made it possible to construct various fiber topologies over a fixed physical topology. This paper describes a fiber topology design (FTD) problem, which minimizes the maximum number of required fibers in the physical links for a maximum lightpath hop count in the fiber topology. After the formular description for the FTD problem, a method was given to obtain the lower bound on the maximum number of required fibers. For large or moderate scale networks, three heuristic algorithms are given to efficiently solve the FTD problem. This study gives a new way to optimize the resource configuration performance in WDM optical networks at the topology level and proves its effectiveness via both analyses and numerical experiments.

  10. Topological Susceptibility in Two Flavors Lattice QCD with the Optimal Domain-Wall Fermion

    CERN Document Server

    Chiu, Ting-Wai; Mao, Yao-Yuan

    2011-01-01

    We determine the topological susceptibility of the gauge configurations generated by lattice simulations using two flavors of optimal domain-wall fermion on the $ 16^3 \\times 32 $ lattice with length 16 in the fifth dimension, at the lattice spacing $ a \\simeq 0.1 $ fm. Using the adaptive thick-restart Lanczos algorithm, we project the low-lying eigenmodes of the overlap Dirac operator, and obtain the topological charge of each configuration, for eight ensembles with pion masses in the range $ 220-550 $ MeV. From the topological charge, we compute the topological susceptibility and the second normalized cumulant. Our result of the topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory and provides a determination of the chiral condensate, $\\Sigma^{\\bar{MS}}(2 GeV)=[259(6)(7) MeV]^3 $, and the pion decay constant $F_\\pi = 92(12)(2)$ MeV.

  11. Topology Optimization using the Level Set and eXtended Finite Element Methods: Theory and Applications

    Science.gov (United States)

    Villanueva Perez, Carlos Hernan

    Computational design optimization provides designers with automated techniques to develop novel and non-intuitive optimal designs. Topology optimization is a design optimization technique that allows for the evolution of a broad variety of geometries in the optimization process. Traditional density-based topology optimization methods often lack a sufficient resolution of the geometry and physical response, which prevents direct use of the optimized design in manufacturing and the accurate modeling of the physical response of boundary conditions. The goal of this thesis is to introduce a unified topology optimization framework that uses the Level Set Method (LSM) to describe the design geometry and the eXtended Finite Element Method (XFEM) to solve the governing equations and measure the performance of the design. The methodology is presented as an alternative to density-based optimization approaches, and is able to accommodate a broad range of engineering design problems. The framework presents state-of-the-art methods for immersed boundary techniques to stabilize the systems of equations and enforce the boundary conditions, and is studied with applications in 2D and 3D linear elastic structures, incompressible flow, and energy and species transport problems to test the robustness and the characteristics of the method. A comparison of the framework against density-based topology optimization approaches is studied with regards to convergence, performance, and the capability to manufacture the designs. Furthermore, the ability to control the shape of the design to operate within manufacturing constraints is developed and studied. The analysis capability of the framework is validated quantitatively through comparison against previous benchmark studies, and qualitatively through its application to topology optimization problems. The design optimization problems converge to intuitive designs and resembled well the results from previous 2D or density-based studies.

  12. Industrial Application of Topology Optimization for Combined Conductive and Convective Heat Transfer Problems

    DEFF Research Database (Denmark)

    Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole

    2016-01-01

    This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady......-state heat transfer under convection is simulated using SIMULIA-Abaqus. A corresponding topology optimization feature is provided by SIMULIA-Tosca. By following a standard workflow of design optimization, the proposed solution is able to accommodate practical design scenarios and results in efficient...

  13. Minimum scale controlled topology optimization and experimental test of a micro thermal actuator

    DEFF Research Database (Denmark)

    Heo, S.; Yoon, Gil Ho; Kim, Y.Y.

    2008-01-01

    This paper is concerned with the optimal topology design, fabrication and test of a micro thermal actuator. Because the minimum scale was controlled during the design optimization process, the production yield rate of the actuator was improved considerably; alternatively, the optimization design...... without scale control resulted in a very low yield rate. Using the minimum scale controlling topology design method developed earlier by the authors, micro thermal actuators were designed and fabricated through a MEMS process. Moreover, both their performance and production yield were experimentally...

  14. Element stacking method for topology optimization with material-dependent boundary and loading conditions

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Park, Y.K.; Kim, Y.Y.

    2007-01-01

    A new topology optimization scheme, called the element stacking method, is developed to better handle design optimization involving material-dependent boundary conditions and selection of elements of different types. If these problems are solved by existing standard approaches, complicated finite...... element models or topology optimization reformulation may be necessary. The key idea of the proposed method is to stack multiple elements on the same discretization pixel and select a single or no element. In this method, stacked elements on the same pixel have the same coordinates but may have...

  15. A Method for treating Damage Related Criteria in Optimal Topology Design of Continuum Structures

    DEFF Research Database (Denmark)

    Bendsøe, Martin P; Diaz, Alejandro

    1997-01-01

    In this paper we present a formulation of the well-known structural topology optimization problem that accounts for the presence of loads capable of causing permanent damage to the structure. Damage is represented in the form of an internal variable model which is standard in continuum damage...... mechanics. Here we employ an interpretation of this model as an optimum remodeling problem for maximal compliance over all damage distributions, making also the analysis of the damage model a study in structural optimization. The damage criterion can be included in the optimal design model in a number...... of ways. We present results for finding the optimal topology of the reinforcement of an existing design with the goal of minimizing damage. Also, we treat a problem of finding the topology of a structure were we seek maximal stiffness under service loads with a constraint on the amount of damage which...

  16. A Method for treating Damage Related Criteria in Optimal Topology Design of Continuum Structures

    DEFF Research Database (Denmark)

    Bendsøe, Martin P; Diaz, A.R.

    1998-01-01

    In this paper we present a formulation of the well-known structural topology optimization problem that accounts for the presence of loads capable of causing permanent damage to the structure. Damage is represented in the form of an internal variable model which is standard in continuum damage...... mechanics. Here we employ an interpretation of this model as an optimum remodeling problem for maximal compliance over all damage distributions, making also the analysis of the damage model a study in structural optimization. The damage criterion can be included in the optimal design model in a number...... of ways. We present results for finding the optimal topology of the reinforcement of an existing design with the goal of minimizing damage. Also, we treat the problem of finding the topology of a structure where we seek maximal stiffness under service loads with a constraint on the amount of damage which...

  17. An efficient selectivity estimation method for spatial query optimization with topological relationships

    Institute of Scientific and Technical Information of China (English)

    CHUNG Warn-ill; CHOI Jun-ho; BAE Hae-young

    2004-01-01

    Many commercial database systems maintain histograms to summarize the contents of relations and permit the efficient estimation of query result sizes and the access plan cost. In spatial database systems, most spatial query predicates are consisted of topological relationships between spatial objects, and it is very important to estimate the selectivity of those predicates for spatial query optimizer. In this paper, we propose a selectivity estimation scheme for spatial topological predicates based on the multidimensional histogram and the transformation scheme. Proposed scheme applies twopartition strategy on transformed object space to generate spatial histogram and estimates the selectivity of topological predicates based on the topological characteristics of the transformed space. Proposed scheme provides a way for estimating the selectivity without too much memory space usage and additional I/Os in most spatial query optimizers.

  18. Space-time topology optimization for one-dimensional wave propagation

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2009-01-01

    A space-time extension of the topology optimization method is presented. The formulation, with design variables in both the spatial and temporal domains, is used to create structures with an optimized distribution of material properties that can vary in time. The method is outlined for one...

  19. Topology optimization of unsteady flow problems using the lattice Boltzmann method

    DEFF Research Database (Denmark)

    Nørgaard, Sebastian Arlund; Sigmund, Ole; Lazarov, Boyan Stefanov

    2016-01-01

    This article demonstrates and discusses topology optimization for unsteady incompressible fluid flows. The fluid flows are simulated using the lattice Boltzmann method, and a partial bounceback model is implemented to model the transition between fluid and solid phases in the optimization problems...

  20. Pushing the Boundaries: Level-set Methods and Geometrical Nonlinearities in Structural Topology Optimization

    NARCIS (Netherlands)

    Van Dijk, N.P.

    2012-01-01

    This thesis aims at understanding and improving topology optimization techniques focusing on density-based level-set methods and geometrical nonlinearities. Central in this work are the numerical modeling of the mechanical response of a design and the consistency of the optimization process itself.

  1. Damage approach: A new method for topology optimization with local stress constraints

    DEFF Research Database (Denmark)

    Verbart, Alexander; Langelaar, Matthijs; van Keulen, Fred

    2016-01-01

    In this paper, we propose a new method for topology optimization with local stress constraints. In this method, material in which a stress constraint is violated is considered as damaged. Since damaged material will contribute less to the overall performance of the structure, the optimizer will p...

  2. Topology Optimization of Distributed Mass Dampers for Low-frequency Vibration Suppression

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Lazarov, Boyan Stefanov

    2007-01-01

    In this paper the method of topology optimization is used to find optimized parameter distributions for a multiple mass damper system with the purpose of minimizing the low-frequency steady-state response of a carrier structure. An effective density model that describes the steady-state effect...

  3. A parametric level-set approach for topology optimization of flow domains

    DEFF Research Database (Denmark)

    Pingen, Georg; Waidmann, Matthias; Evgrafov, Anton

    2010-01-01

    Traditional methods based on an element-wise parameterization of the material distribution applied to the topology optimization of fluidic systems often suffer from slow convergence of the optimization process, as well as robustness issues at increased Reynolds numbers. The local influence...

  4. On the design of 1-3 piezo-composites using topology optimization

    DEFF Research Database (Denmark)

    Sigmund, Ole; Torquato, S.; Aksay, I.A.

    1998-01-01

    We use a topology optimization method to design 1-3 piezocomposites with optimal performance characteristics for hydrophone applications. The performance characteristics we focus on are the hydrostatic charge coefficient d(h)((*)), the hydrophone figure of merit d(h)((*))g(h)((*)), and the electr...

  5. System Topology Optimization - An Approach to System Design of Electro-Hydraulic-Mechanical Systems

    DEFF Research Database (Denmark)

    Andersen, T. O.; Hansen, M. R.; Conrad, Finn

    2003-01-01

    design the procedure attempts to find the optimal topology and the related parameters. The topology considerations comprise the type of hydraulic pump, the employment of knee linkages or not as well as the type of hydraulic actuators. The design variables also include the signals to the proportional......The current paper presents an approach to system design of combined electro-hydraulic-mechanical systems. The approach is based on the concurrent handling of the topology as well as the design parameters of the mechanical, hydraulic and controller sub- systems, respectively. Based on an initial...... valve in a number of predefined load cases as well as the hydraulic and mechanical parameters....

  6. An explicit parametrization for casting constraints in gradient driven topology optimization

    DEFF Research Database (Denmark)

    Gersborg, Allan Roulund; Andreasen, Casper Schousboe

    From a practical point of view it is often desirable to limit the complexity of a topology design such that casting/milling type manufacturing techniques can be applied. In the context of gradient driven topology optimization this work studies how castable designs can be obtained by use of a Heav...... of a Heaviside design parametrization in a specific casint direction. This reduces the number of design variables considerably and the approach is simple to implement....

  7. Topology Optimization Design of 3D Continuum Structure with Reserved Hole Based on Variable Density Method

    Directory of Open Access Journals (Sweden)

    Bai Shiye

    2016-05-01

    Full Text Available An objective function defined by minimum compliance of topology optimization for 3D continuum structure was established to search optimal material distribution constrained by the predetermined volume restriction. Based on the improved SIMP (solid isotropic microstructures with penalization model and the new sensitivity filtering technique, basic iteration equations of 3D finite element analysis were deduced and solved by optimization criterion method. All the above procedures were written in MATLAB programming language, and the topology optimization design examples of 3D continuum structure with reserved hole were examined repeatedly by observing various indexes, including compliance, maximum displacement, and density index. The influence of mesh, penalty factors, and filter radius on the topology results was analyzed. Computational results showed that the finer or coarser the mesh number was, the larger the compliance, maximum displacement, and density index would be. When the filtering radius was larger than 1.0, the topology shape no longer appeared as a chessboard problem, thus suggesting that the presented sensitivity filtering method was valid. The penalty factor should be an integer because iteration steps increased greatly when it is a noninteger. The above modified variable density method could provide technical routes for topology optimization design of more complex 3D continuum structures in the future.

  8. Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA Approach

    Directory of Open Access Journals (Sweden)

    Zheng Ling

    2011-01-01

    Full Text Available Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an

  9. On the similarities between micro/nano lithography and topology optimization projection methods

    DEFF Research Database (Denmark)

    Jansen, Miche; Lazarov, Boyan Stefanov; Schevenels, Mattias;

    2013-01-01

    The aim of this paper is to incorporate a model for micro/nano lithography production processes in topology optimization. The production process turns out to provide a physical analogy for projection filters in topology optimization. Blueprints supplied by the designers cannot be directly used...... projection filter can be used to account for uncertainties due to lithographic production processes which results in manufacturable blueprint designs and eliminates the need for subsequent corrections....... as inputs to lithographic processes due to the proximity effect which causes rounding of sharp corners and geometric interaction of closely spaced design elements. Therefore, topology optimization is applied as a tool for proximity effect correction. Furthermore, it is demonstrated that the robust...

  10. Buckling of Bucket Foundations

    DEFF Research Database (Denmark)

    Madsen, Søren; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo

    2012-01-01

    In this paper, the risk of structural buckling during installation of large-diameter bucket foundations is addressed using numerical methods. Imperfect geometries are introduced based on the pre-buckling mode shapes from a linear Eigenvalue buckling analysis. Various imperfect geometries...... are introduced to reveal how sensitive the buckling load is to the mentioned imperfections. Including the first 21 mode shapes as imperfect geometries reduces the buckling pressure compared to only considering mode 1....

  11. Modelling of Active Semiconductor Photonic Crystal Waveguides and Robust Designs based on Topology Optimization

    DEFF Research Database (Denmark)

    Chen, Yaohui; Wang, Fengwen; Ek, Sara;

    2011-01-01

    In this paper, we present a theoretical analysis of slow-light enhanced light amplification in an active semiconductor photonic crystal line defect waveguide. The impact of enhanced light-matter interactions on propagation effects and local carrier dynamics are investigated in the framework...... of the Lorentz reciprocity theorem. We highlight topology optimization as a systematic and robust design methodology considering manufacturing imperfections in optimizing active photonic crystal device performances, and compare the performance of standard photonic crystal waveguides with optimized structures....

  12. 三种增强复合材料层合板抗屈曲优化分析%Optimal Analyses of Three Types for Reinforced Composite Panels against Buckling

    Institute of Scientific and Technical Information of China (English)

    庞华华; Guo Shijun

    2013-01-01

    Topological analyses of isotropic panels have been carried out to investigate the stiffener patterns and orientations under specified three loading types:unidirectional compressive,compound and pure shear loads,while obtaining the load paths which can be termed as material distributions as well.By creating optimization codes in terms of employing MSC.Nastran package language,a large number of finite element optimization cases have been simulated,and optimal structure efficiencies against buckling of above reinforced composite panels have been achieved.The best strengthened patterns of the composite panels according to the four loading conditions have been proposed based on comparative analyses of the results,which can be utilized as references when designing the wing panels of aircrafts.%基于单向轴压、压剪复合以及纯剪三种栽荷形式,对各向同性均质板进行拓扑优化分析,得到了相应的传力路径,即对应载荷条件下的材料分布;针对三种增强复合材料层合板:常规夹芯板、单向加筋板和非常规网格加筋板,运用MSC.Nastran语言,编写抗屈曲优化代码,采用大量有限元优化算例,求解了上述增强复合材料层合板在给定载荷条件下最优的抗屈曲结构效率,对比分析得出四种载荷形式下的最优增强形式,为飞机壁板类结构选型设计提供参考.

  13. Optimality criteria-based topology optimization of a bi-material model for acoustic-structural coupled systems

    Science.gov (United States)

    Shang, Linyuan; Zhao, Guozhong

    2016-06-01

    This article investigates topology optimization of a bi-material model for acoustic-structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic-structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic-structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC.

  14. From a quasi-static fluid-based evolutionary topology optimization to a generalization of BESO

    Science.gov (United States)

    Daróczy, László; Jármai, Károly

    2015-05-01

    A new algorithm is proposed for topology optimization based on a fluid dynamics analogy. It possesses characteristics similar to most well-known methods, such as the Evolutionary Structural Optimization (ESO)/Bidirectional Evolutionary Structural Optimization (BESO) method due to Xie and Steven (1993, "A Simple Evolutionary Procedure for Structural Optimisation." Computers and Structures 49 (5): 885-896.), which works with discrete values, and the Solid Isotropic Material with Penalization (SIMP) method due to Bendsøe (1989, "Optimal Shape Design as aMaterial Distribution Problem." Structural Optimization 1 (4): 193-202.) and Zhou and Rozvany (1991, "The COCAlgorithm-Part II: Topological, Geometry and Generalized Shape Optimization." Computer Methods in Applied Mechanics and Engineering 89 (1-3): 309-336.) (using Optimality Criterion (OC) or Method of Moving Asymptotes (MMA)), which works with intermediate values, as it is able to work both with discrete and intermediate densities, but always yields a solution with discrete densities. It can be proven mathematically that the new method is a generalization of the BESO method and using appropriate parameters it will operate exactly as the BESO method. The new method is less sensitive to rounding errors of the matrix solver as compared to the BESO method and is able to give alternative topologies to well-known problems. The article presents the basic idea and the optimization algorithm, and compares the results of three cantilever optimizations to the results of the SIMP and BESO methods.

  15. Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Sigmund, Ole

    2013-01-01

    This article presents a new procedure for the layout design of reinforcement in concrete structures. Concrete is represented by a gradient-enhanced continuum damage model with strain-softening and reinforcement is modeled as elastic bars that are embedded into the concrete domain. Adjoint...... sensitivity analysis is derived in complete consistency with respect to path-dependency and the nonlocal model. Classical truss topology optimization based on the ground structure approach is applied to determine the optimal topology and cross-sections of the reinforcement bars. This approach facilitates...

  16. Experimental Validation of Topology Optimization for RF MEMS Capacitive Switch Design

    DEFF Research Database (Denmark)

    Philippine, Mandy Axelle; Zareie, Hosein; Sigmund, Ole

    2013-01-01

    In this paper, we present 30 distinct RF MEMS capacitive switch designs that are the product of topology optimizations that control key mechanical properties such as stiffness, response to intrinsic stress gradients, and temperature sensitivity. The designs were evaluated with high-accuracy simul......In this paper, we present 30 distinct RF MEMS capacitive switch designs that are the product of topology optimizations that control key mechanical properties such as stiffness, response to intrinsic stress gradients, and temperature sensitivity. The designs were evaluated with high...

  17. An efficient second-order SQP method for structural topology optimization

    DEFF Research Database (Denmark)

    Rojas Labanda, Susana; Stolpe, Mathias

    2016-01-01

    This article presents a Sequential Quadratic Programming (SQP) solver for structural topology optimization problems named TopSQP. The implementation is based on the general SQP method proposed in Morales et al. J Numer Anal 32(2):553–579 (2010) called SQP+. The topology optimization problem...... nonlinear solvers IPOPT and SNOPT. Numerical experiments on a large set of benchmark problems show good performance of TopSQP in terms of number of function evaluations. In addition, the use of second-order information helps to decrease the objective function value....

  18. On the Selection of Physical Layer Optimized Network Topologies for the Zigbee Network

    Directory of Open Access Journals (Sweden)

    Manpreet

    2016-01-01

    Full Text Available Zigbee standard has been designed for low data rate, low cost and limited power applications for short-range wireless communication. The successful implementation of Zigbee based network depends on the suitable selection of physical (PHY layer and medium access control (MAC layer parameters. In this work the PHY layer parameters have been optimized for star, tree and mesh topologies. The performance investigations have been carried out for different frequency band and data rate and different bandwidth (BW in each of standard topologies. Through extensive simulations, QoS parameters like throughput, network load and delay have been evaluated to achieve optimal performance of physical layer.

  19. Topology-optimized slow-light couplers for ring-shaped photonic crystal waveguide

    DEFF Research Database (Denmark)

    Pu, Minhao; Yang, Lirong; Frandsen, L. H.;

    2010-01-01

    We demonstrate a topology-optimized coupler for a ring-shaped photonic crystal waveguide to improve the coupling of light located in the slow-light regime. An enhancement of the coupling efficiency of up to 2.5 dB is experimentally demonstrated.......We demonstrate a topology-optimized coupler for a ring-shaped photonic crystal waveguide to improve the coupling of light located in the slow-light regime. An enhancement of the coupling efficiency of up to 2.5 dB is experimentally demonstrated....

  20. Feasibility of using Hybrid Wavelet Collocation - Brinkman Penalization Method for Shape and Topology Optimization

    Science.gov (United States)

    Vasilyev, Oleg V.; Gazzola, Mattia; Koumoutsakos, Petros

    2009-11-01

    In this talk we discuss preliminary results for the use of hybrid wavelet collocation - Brinkman penalization approach for shape and topology optimization of fluid flows. Adaptive wavelet collocation method tackles the problem of efficiently resolving a fluid flow on a dynamically adaptive computational grid in complex geometries (where grid resolution varies both in space and time time), while Brinkman volume penalization allows easy variation of flow geometry without using body-fitted meshes by simply changing the shape of the penalization region. The use of Brinkman volume penalization approach allow seamless transition from shape to topology optimization by combining it with level set approach and increasing the size of the optimization space. The approach is demonstrated for shape optimization of a variety of fluid flows by optimizing single cost function (time averaged Drag coefficient) using covariance matrix adaptation (CMA) evolutionary algorithm.

  1. Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials

    Science.gov (United States)

    Huang, X.; Xie, Y. M.

    2009-02-01

    There are several well-established techniques for the generation of solid-void optimal topologies such as solid isotropic material with penalization (SIMP) method and evolutionary structural optimization (ESO) and its later version bi-directional ESO (BESO) methods. Utilizing the material interpolation scheme, a new BESO method with a penalization parameter is developed in this paper. A number of examples are presented to demonstrate the capabilities of the proposed method for achieving convergent optimal solutions for structures with one or multiple materials. The results show that the optimal designs from the present BESO method are independent on the degree of penalization. The resulted optimal topologies and values of the objective function compare well with those of SIMP method.

  2. Topology Optimization and Robotic Fabrication of Advanced Timber Space-frame Structures

    DEFF Research Database (Denmark)

    Søndergaard, Asbjørn; Amir, Oded; Eversmann, Phillip

    2016-01-01

    This paper presents a novel method for integrated topology optimization and fabrication of advanced timber space-frame structures. The method, developed in research collaboration between ETH Zürich, Aarhus School of Architecture and Israel Institute of Technology, entails the coupling of truss......-based topology optimization with digital procedures for rationalization and robotic assembly of bespoke timber members, through a procedural, cross-application workflow. Through this, a direct chaining of optimization and robotic fabrication is established, in which optimization data is driving subsequent...... processes solving timber joint intersections, robotically controlling member prefabrication, and spatial robotic assembly of the optimized timber structures. The implication of this concept is studied through pilot fabrication and load-testing of a full scale prototype structure....

  3. Phase field model for optimization of multi-material structural topology in two and three dimensions

    Science.gov (United States)

    Zhou, Shiwei

    The Optimization of Structural Topology (OST) is a breakthrough in product design because it can optimize size, shape and topology synchronously under different physical constraints. It has promising applications in industry ranging from automobile and aerospace engineering to micro electromechanical system. This dissertation first substitutes the nonlinear diffusion method for filter process in the optimization of structural topology. Filtering has been a major technique used in a homogenization-based method for topology optimization of structures. It plays a key role in regularizing the basic problem into a well-behaved setting. But it has a drawback of smoothing effect around the boundary of material domain. A diffusion technique is presented here as a variational approach to the regularization of the topology optimization problem. A nonlinear or anisotropic diffusion process not only leads to a suitable problem regularization but also exhibits strong "edge"-preserving characteristics. Thus, it shows that the use of the nonlinear diffusions brings desirable effects of boundary preservation and even enhancement of lower-dimensional features such as flow-like structures. The proposed diffusion techniques have a close relationship with the diffusion methods and the phase-field methods of the fields of materials and digital image processing. Then this dissertation introduces a gradient flow in the norm of H-1 for the problem of multi-material structural topology optimization in 2/3D with a generalized Cahn-Hilliard (C-H) model with elasticity. Unlike the traditional C-H model applied to spinodal separation which only has bulk energy and interface energy, the generalized model couples the macroscopic elastic energy (mean compliance) into the total free energy. As a result, the grain morphology is not random islands or zigzag web-like objects but regular truss or bar structure. Although disturbed by elastic energy, the C-H system still keeps its two most important

  4. Biomechanical analysis and design of a dynamic spinal fixator using topology optimization: a finite element analysis.

    Science.gov (United States)

    Lin, Hung-Ming; Liu, Chien-Lin; Pan, Yung-Ning; Huang, Chang-Hung; Shih, Shih-Liang; Wei, Shun-Hwa; Chen, Chen-Sheng

    2014-05-01

    Surgeons often use spinal fixators to manage spinal instability. Dynesys (DY) is a type of dynamic fixator that is designed to restore spinal stability and to provide flexibility. The aim of this study was to design a new spinal fixator using topology optimization [the topology design (TD) system]. Here, we constructed finite element (FE) models of degenerative disc disease, DY, and the TD system. A hybrid-controlled analysis was applied to each of the three FE models. The rod structure of the topology optimization was modelled at a 39 % reduced volume compared with the rigid rod. The TD system was similar to the DY system in terms of stiffness. In contrast, the TD system reduced the cranial adjacent disc stress and facet contact force at the adjacent level. The TD system also reduced pedicle screw stresses in flexion, extension, and lateral bending.

  5. Topology optimized and 3D printed polymer-bonded permanent magnets for a predefined external field

    Science.gov (United States)

    Huber, C.; Abert, C.; Bruckner, F.; Pfaff, C.; Kriwet, J.; Groenefeld, M.; Teliban, I.; Vogler, C.; Suess, D.

    2017-08-01

    Topology optimization offers great opportunities to design permanent magnetic systems that have specific external field characteristics. Additive manufacturing of polymer-bonded magnets with an end-user 3D printer can be used to manufacture permanent magnets with structures that had been difficult or impossible to manufacture previously. This work combines these two powerful methods to design and manufacture permanent magnetic systems with specific properties. The topology optimization framework is simple, fast, and accurate. It can also be used for the reverse engineering of permanent magnets in order to find the topology from field measurements. Furthermore, a magnetic system that generates a linear external field above the magnet is presented. With a volume constraint, the amount of magnetic material can be minimized without losing performance. Simulations and measurements of the printed systems show very good agreement.

  6. Topology Optimization for Minimizing the Resonant Response of Plates with Constrained Layer Damping Treatment

    Directory of Open Access Journals (Sweden)

    Zhanpeng Fang

    2015-01-01

    Full Text Available A topology optimization method is proposed to minimize the resonant response of plates with constrained layer damping (CLD treatment under specified broadband harmonic excitations. The topology optimization problem is formulated and the square of displacement resonant response in frequency domain at the specified point is considered as the objective function. Two sensitivity analysis methods are investigated and discussed. The derivative of modal damp ratio is not considered in the conventional sensitivity analysis method. An improved sensitivity analysis method considering the derivative of modal damp ratio is developed to improve the computational accuracy of the sensitivity. The evolutionary structural optimization (ESO method is used to search the optimal layout of CLD material on plates. Numerical examples and experimental results show that the optimal layout of CLD treatment on the plate from the proposed topology optimization using the conventional sensitivity analysis or the improved sensitivity analysis can reduce the displacement resonant response. However, the optimization method using the improved sensitivity analysis can produce a higher modal damping ratio than that using the conventional sensitivity analysis and develop a smaller displacement resonant response.

  7. A level-set based topology optimization using the element connectivity parameterization method

    NARCIS (Netherlands)

    Van Dijk, N.P.; Yoon, G.H.; Van Keulen, F.; Langelaar, M.

    2010-01-01

    This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element connectivity parameterization method or ECP. The combined advantages of both methods open up the possibility to treat a wide range of optimiza

  8. Direct gradient projection method with transformation of variables technique for structural topology optimization

    NARCIS (Netherlands)

    Chang, C.; Borgart, A.; Chen, A.; Hendriks, M.A.N.

    2014-01-01

    This paper proposes an efficient and reliable topology optimization method that can obtain a black and white solution with a low objective function value within a few tens of iterations. First of all, a transformation of variables technique is adopted to eliminate the constraints on the design varia

  9. Topology optimization of grating couplers for the efficient excitation of surface plasmons

    DEFF Research Database (Denmark)

    Andkjær, Jacob Anders; Sigmund, Ole; Nishiwaki, Shinji

    2010-01-01

    We propose a methodology for a systematic design of grating couplers for efficient excitation of surface plasmons at metal-dielectric interfaces. The methodology is based on a two-dimensional topology optimization formulation based on the H-polarized scalar Helmholtz equation and finite-element m...

  10. Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2004-01-01

    Topology optimization is a promising method for systematic design of optical devices. As an example, we demonstrate how the method can be used to design a 90degrees bend in a two-dimensional photonic crystal waveguide with a transmission loss of less than 0.3% in almost the entire frequency range...

  11. Design of Electric Vehicle Racing Car Chassis using Topology Optimization Method

    Directory of Open Access Journals (Sweden)

    bin Ab Razak Mohd Suffian

    2017-01-01

    Full Text Available The goal of this project is to improve the design of space frame chassis of electric vehicle which meet the rules and regulations of Formula Varsity (FV Malaysia. The chassis was designed using topology optimization method and analyzed for its structural performance using various loading analyses and RULA assessment.

  12. Industrial Application of Topology Optimization for Combined Conductive and Convective Heat Transfer Problems

    DEFF Research Database (Denmark)

    Zhou, Mingdong; Alexandersen, Joe; Sigmund, Ole;

    2016-01-01

    This paper presents an industrial application of topology optimization for combined conductive and convective heat transfer problems. The solution is based on a synergy of computer aided design and engineering software tools from Dassault Systemes. The considered physical problem of steady...

  13. TOPOLOGY OPTIMIZATION OF OPTICAL BAND GAP EFFECTS IN SLAB STRUCTURES MODULATED BY PERIODIC RAYLEIGHWAVES

    DEFF Research Database (Denmark)

    This paper is concerned with topology optimization of a coupled optical and mechanical wave propagation problem in photonic crystals. It is motivated by the potential gain in functionality of optical devices where mechanical Rayleigh waves (travelling in the surface of the material) play a leadin...

  14. Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials

    DEFF Research Database (Denmark)

    Andreassen, Erik; Jensen, Jakob Søndergaard

    2014-01-01

    We present a topology optimization method for the design of periodic composites with dissipative materials for maximizing the loss/attenuation of propagating waves. The computational model is based on a finite element discretization of the periodic unit cell and a complex eigenvalue problem...

  15. Topology optimization: a systematic method to improve the performance of photonic crystal structures

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2004-01-01

    The method of topology optimization has previously been used to design exotic materials, MEMS and thermo-elastic mechanisms, as well as several other devices in mechanics and multi-physics applications [1]. Recently, the method was applied to design photonic and phononic crystals with maximum siz...... band gaps [2,3]. In [3] the optimization of phononic crystal structures was considered also, with examples demonstrating the possibility for designing wave-reflecting and wave-guiding structures with optimized performance.......The method of topology optimization has previously been used to design exotic materials, MEMS and thermo-elastic mechanisms, as well as several other devices in mechanics and multi-physics applications [1]. Recently, the method was applied to design photonic and phononic crystals with maximum size...

  16. Parallel framework for topology optimization using the method of moving asymptotes

    DEFF Research Database (Denmark)

    Aage, Niels; Lazarov, Boyan Stefanov

    2013-01-01

    The complexity of problems attacked in topology optimization has increased dramatically during the past decade. Examples include fully coupled multiphysics problems in thermo-elasticity, fluid-structure interaction, Micro-Electro Mechanical System (MEMS) design and large-scale three dimensional...... and simple to implement linear solvers and optimization algorithms. However, to ensure generality, the code is developed to be easily extendable in terms of physical models as well as in terms of solution methods, without compromising the parallel scalability. The widely used Method of Moving Asymptotes...... optimization algorithm is parallelized and included as a fundamental part of the code. The capabilities of the presented approaches are demonstrated on topology optimization of a Stokes flow problem with target outflow constraints as well as the minimum compliance problem with a volume constraint from linear...

  17. Topology optimization of double- and triple-layer grids using a hybrid methodology

    Science.gov (United States)

    Dehghani, M.; Mashayekhi, M.; Salajegheh, E.

    2016-08-01

    In this article, a hybrid methodology combining evolutionary structural optimization (ESO) and gravitational particle swarm (GPS) methods is proposed for topology optimization of double- and triple-layer grids. In the present methodology, which is called the ESO-GPS method, the size optimization of double- and triple-layer grids is first performed by ESO. Then, the outcomes of the ESO are used to improve the GPS through four modifications. Structural weight is minimized against constraints on the displacements of nodes, internal stresses and element slenderness ratio. The GPS is used to investigate the optimum topology of large-scale skeletal structures with discrete variables whose agents update their respective positions by the particle swarm optimization velocity and the acceleration of the gravitational search algorithm. The numerical results show that the proposed algorithm, the ESO-GPS, performs better than the GPS and the other methods presented in the literature.

  18. Topology Optimal Design of Material Microstructures Using Strain Energy-based Method

    Institute of Scientific and Technical Information of China (English)

    Zhang Weihong; Wang Fengwen; Dai Gaoming; Sun Shiping

    2007-01-01

    Sensitivity analysis and topology optimization of microstructures using strain energy-based method is presented. Compared with homogenization method, the strain energy-based method has advantages of higher computing efficiency and simplified programming.Both the dual convex programming method and perimeter constraint scheme are used to optimize the 2D and 3D microstructures. Numerical results indicate that the strain energy-based method has the same effectiveness as that of homogenization method for orthotropic materials.

  19. Design of materials with extreme thermal expansion using a three-phase topology optimization method

    DEFF Research Database (Denmark)

    Sigmund, Ole; Torquato, S.

    1997-01-01

    We show how composites with extremal or unusual thermal expansion coefficients can be designed using a numerical topology optimization method. The composites are composed of two different material phases and void. The optimization method is illustrated by designing materials having maximum thermal...... expansion, zero thermal expansion, and negative thermal expansion. Assuming linear elasticity, it is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void. We also show...

  20. Optimizing Network Topology to Reduce Aggregate Traffic in Systems of Mobile Robots

    CERN Document Server

    Navaravong, Leenhapat; Pasiliao, Eduardo L; Barnette, Gregory L; Dixon, Warren E

    2011-01-01

    Systems of networked mobile robots, such as unmanned aerial or ground vehicles, will play important roles in future military and commercial applications. The communications for such systems will typically be over wireless links and may require that the robots form an ad hoc network and communicate on a peer-to-peer basis. In this paper, we consider the problem of optimizing the network topology to minimize the total traffic in a network required to support a given set of data flows under constraints on the amount of movement possible at each mobile robot. In this paper, we consider a subclass of this problem in which the initial and final topologies are trees, and the movement restrictions are given in terms of the number of edges in the graph that must be traversed. We develop algorithms to optimize the network topology while maintaining network connectivity during the topology reconfiguration process. Our topology reconfiguration algorithm uses the concept of prefix labelling and routing to move nodes throu...

  1. Topology and shape optimization of induced-charge electro-osmotic micropumps

    Energy Technology Data Exchange (ETDEWEB)

    Gregersen, M M; Okkels, F; Bruus, H [Department of Micro- and Nanotechnology, Technical University of Denmark, DTU Nanotech, Building 345 East, DK-2800 Kongens Lyngby (Denmark); Bazant, M Z [Departments of Chemical Engineering and Mathematics, MIT, Cambridge, MA 02139 (United States)], E-mail: Henrik.Bruus@nanotech.dtu.dk

    2009-07-15

    For a dielectric solid surrounded by an electrolyte and positioned inside an externally biased parallel-plate capacitor, we study numerically how the resulting induced-charge electro-osmotic (ICEO) flow depends on the topology and shape of the dielectric solid. In particular, we extend existing conventional electrokinetic models with an artificial design field to describe the transition from the liquid electrolyte to the solid dielectric. Using this design field, we have succeeded in applying the method of topology optimization to find system geometries with non-trivial topologies that maximize the net induced electro-osmotic flow rate through the electrolytic capacitor in the direction parallel to the capacitor plates. Once found, the performance of the topology-optimized geometries has been validated by transferring them to conventional electrokinetic models not relying on the artificial design field. Our results show the importance of the topology and shape of the dielectric solid in ICEO systems and point to new designs of ICEO micropumps with significantly improved performance.

  2. Topology Optimization of a High-Temperature Superconducting Field Winding of a Synchronous Machine

    DEFF Research Database (Denmark)

    Pozzi, Matias; Mijatovic, Nenad; Jensen, Bogi Bech

    2013-01-01

    genetic algorithm with local optimization search based on on/off sensitivity analysis. The results show an optimal HTS coil distribution, achieving compact designs with a maximum of approximately 22% of the available space for the field winding occupied with HTS tape. In addition, this paper describes......This paper presents topology optimization (TO) of the high-temperature superconductor (HTS) field winding of an HTS synchronous machine. The TO problem is defined in order to find the minimum HTS material usage for a given HTS synchronous machine design. Optimization is performed using a modified...

  3. Inverse design of dielectric materials by topology optimization

    DEFF Research Database (Denmark)

    Otomori, M.; Andkjær, Jacob Anders; Sigmund, Ole

    2012-01-01

    the effective permittivity and a prescribed value. The optimization algorithm uses the adjoint variable method (AVM) for the sensitivity analysis and the finite element method (FEM) for solving the equilibrium and adjoint equations, respectively. A Heaviside projection filter is used to obtain clear optimized...... con¯gurations. Several design problems show that clear optimized unit cell configurations that provide the prescribed electric permittivity can be obtained for all the presented cases. These include the design of isotropic material, anisotropic material, anisotropic material with a non-zero off......The capabilities and operation of electromagnetic devices can be dramatically enhanced if artificial materials that provide certain prescribed properties can be designed and fabricated. This paper presents a systematic methodology for the design of dielectric materials with prescribed electric...

  4. Multiscale modeling and topology optimization of poroelastic actuators

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe; Sigmund, Ole

    2012-01-01

    This paper presents a method for design of optimized poroelastic materials which under internal pressurization turn into actuators for application in, for example, linear motors. The actuators are modeled in a two-scale fluid–structure interaction approach. The fluid saturated material microstruc......This paper presents a method for design of optimized poroelastic materials which under internal pressurization turn into actuators for application in, for example, linear motors. The actuators are modeled in a two-scale fluid–structure interaction approach. The fluid saturated material...

  5. Efficient use of iterative solvers in nested topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Stolpe, Mathias; Sigmund, Ole

    2010-01-01

    In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov...... subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures...

  6. On some fundamental properties of structural topology optimization problems

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2009-01-01

    --1. We show, by examples which can be solved by hand calculations, that the optimal solutions in general are not unique and possibly do not have an active volume constraint. These observations have immediate consequences on the theoretical convergence properties of penalization approaches. Furthermore...

  7. On Topology Optimization of Inertia Driven Dosing Units

    DEFF Research Database (Denmark)

    Andreasen, Casper Schousboe

    2016-01-01

    are modeled using the steady state incompressible Navier-Stokes equations and the two fluids are considered havingthe same properties. A Brinkman penalization term is added to the governing equations such that a control problem of the flow topologyis obtained. Optimized component geometries for a range...

  8. On some fundamental properties of structural topology optimization problems

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2010-01-01

    convergence properties of penalization approaches based on material interpolation models. Furthermore, we illustrate that the optimal solutions to the considered problems in general are not symmetric even if the design domain, the external loads, and the boundary conditions are symmetric around an axis...

  9. Efficient use of iterative solvers in nested topology optimization

    DEFF Research Database (Denmark)

    Amir, Oded; Stolpe, Mathias; Sigmund, Ole

    2009-01-01

    by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence...

  10. Topology optimization of magnetic source distributions for diamagnetic and superconducting levitation

    Science.gov (United States)

    Kuznetsov, Sergey; Guest, James K.

    2017-09-01

    Topology optimization is used to obtain a magnetic source distribution providing levitation of a diamagnetic body or type I superconductor with maximized thrust force. We show that this technique identifies non-trivial source distributions and may be useful to design devices based on non-contact magnetic suspension and other magnetic devices, such as micro-magneto-mechanical devices, high field magnets etc. Diamagnetic and superconducting suspensions are often used in physical experiments and thus we believe this approach will be interesting to physics community as it may generate non-trivial and often unexpected topologies and may be useful to create new experiments and devices.

  11. Topology Optimization of Shape Memory Alloy Actuators using Element Connectivity Parameterization

    DEFF Research Database (Denmark)

    Langelaar, Matthijs; Yoon, Gil Ho; Kim, Yoon Young

    2005-01-01

    This paper presents the first application of topology optimization to the design of shape memory alloy actuators. Shape memory alloys (SMA’s) exhibit strongly nonlinear, temperature-dependent material behavior. The complexity in the constitutive behavior makes the topology design of SMA structures......-independent constitutive model of SMA’s is employed which allows efficient adjoint sensitivity analysis. The effectiveness of the proposed technique is illustrated by several numerical examples.In terms of computation time, the I-ECP method, a newly-developed version of ECP, is much more efficient because the degrees...

  12. Optimal Topology of Aircraft Rib and Spar Structures under Aeroelastic Loads

    Science.gov (United States)

    Stanford, Bret K.; Dunning, Peter D.

    2014-01-01

    Several topology optimization problems are conducted within the ribs and spars of a wing box. It is desired to locate the best position of lightening holes, truss/cross-bracing, etc. A variety of aeroelastic metrics are isolated for each of these problems: elastic wing compliance under trim loads and taxi loads, stress distribution, and crushing loads. Aileron effectiveness under a constant roll rate is considered, as are dynamic metrics: natural vibration frequency and flutter. This approach helps uncover the relationship between topology and aeroelasticity in subsonic transport wings, and can therefore aid in understanding the complex aircraft design process which must eventually consider all these metrics and load cases simultaneously.

  13. Filters in topology optimization based on Helmholtz‐type differential equations

    DEFF Research Database (Denmark)

    Lazarov, Boyan Stefanov; Sigmund, Ole

    2011-01-01

    The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology optimizat......The aim of this paper is to apply a Helmholtz‐type partial differential equation as an alternative to standard density filtering in topology optimization problems. Previously, this approach has been successfully applied as a sensitivity filter. The usual filtering techniques in topology...... optimization require information about the neighbor cells, which is difficult to obtain for fine meshes or complex domains and geometries. The complexity of the problem increases further in parallel computing, when the design domain is decomposed into multiple non‐overlapping partitions. Obtaining information...... from the neighbor subdomains is an expensive operation. The proposed filter technique requires only mesh information necessary for the finite element discretization of the problem. The main idea is to define the filtered variable implicitly as a solution of a Helmholtz‐type differential equation...

  14. Topology optimization of compliant adaptive wing leading edge with composite materials

    Directory of Open Access Journals (Sweden)

    Tong Xinxing

    2014-12-01

    Full Text Available An approach for designing the compliant adaptive wing leading edge with composite material is proposed based on the topology optimization. Firstly, an equivalent constitutive relationship of laminated glass fiber reinforced epoxy composite plates has been built based on the symmetric laminated plate theory. Then, an optimization objective function of compliant adaptive wing leading edge was used to minimize the least square error (LSE between deformed curve and desired aerodynamics shape. After that, the topology structures of wing leading edge of different glass fiber ply-orientations were obtained by using the solid isotropic material with penalization (SIMP model and sensitivity filtering technique. The desired aerodynamics shape of compliant adaptive wing leading edge was obtained based on the proposed approach. The topology structures of wing leading edge depend on the glass fiber ply-orientation. Finally, the corresponding morphing experiment of compliant wing leading edge with composite materials was implemented, which verified the morphing capability of topology structure and illustrated the feasibility for designing compliant wing leading edge. The present paper lays the basis of ply-orientation optimization for compliant adaptive wing leading edge in unmanned aerial vehicle (UAV field.

  15. Robust topology optimization of three-dimensional photonic-crystal band-gap structures.

    Science.gov (United States)

    Men, H; Lee, K Y K; Freund, R M; Peraire, J; Johnson, S G

    2014-09-22

    We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniques such as a simple approach to impose symmetry constraints. We also demonstrate a technique for robust topology optimization, in which some uncertainty is included in each voxel and we optimize the worst-case gap, and we show that the resulting band gaps have increased robustness to systematic fabrication errors.

  16. Robust topology optimization of three-dimensional photonic-crystal band-gap structures

    CERN Document Server

    Men, Han; Freund, Robert M; Peraire, Jaime; Johnson, Steven G

    2014-01-01

    We perform full 3D topology optimization (in which "every voxel" of the unit cell is a degree of freedom) of photonic-crystal structures in order to find optimal omnidirectional band gaps for various symmetry groups, including fcc (including diamond), bcc, and simple-cubic lattices. Even without imposing the constraints of any fabrication process, the resulting optimal gaps are only slightly larger than previous hand designs, suggesting that current photonic crystals are nearly optimal in this respect. However, optimization can discover new structures, e.g. a new fcc structure with the same symmetry but slightly larger gap than the well known inverse opal, which may offer new degrees of freedom to future fabrication technologies. Furthermore, our band-gap optimization is an illustration of a computational approach to 3D dispersion engineering which is applicable to many other problems in optics, based on a novel semidefinite-program formulation for nonconvex eigenvalue optimization combined with other techniq...

  17. Topology Optimization and Design Guidelines of Sub-Stiffened Panels in Aerospace Applications

    Directory of Open Access Journals (Sweden)

    Layachi Hemza

    2017-01-01

    Full Text Available The present work is a proposed optimization model of grid sub-stiffened panels for aerospace applications, having a better knowledge about the stability analysis of conventional grid sub-stiffened panels against loading and different mode of failure occurring lead us thinking about the topology optimization. In a first stage, we will analyse the stability performance of such structures against specific mechanical loading and conclude some techniques to introduce a topology optimization through PSO algorithm of some design variables. The aim is the better exploitation of the sub-stiffened panel along the plan so that the area less stressed due the charging will be extruded in mass for the enhancement of the concept of looking for better performance with a structure already saved in weight.

  18. Topology optimization applied to room acoustic problems and surface acoustic wave devices

    DEFF Research Database (Denmark)

    Dühring, Maria Bayard; Sigmund, Ole; Jensen, Jakob Søndergaard

    The work of this PhD-project is concerned with the method of topology optimization1, which has been developed and used since the late eighties to optimize the material distribution of structures in order to minimize static compliance. Since then it has successfully been applied to a range...... of engineering fields such as mechanism design, fluid problems and photonic and phononic band-gap materials and structures [1,2]. In this project topology optimization is first applied to control acoustic properties in a room [3]. It is shown how the squared sound pressure amplitude in a certain part of a room...... can be minimized either by distribution of reflecting material in a design domain along the ceiling or by distribution of absorbing and reflecting material along all the walls for both 2D and 3D problems. It is also shown how the method can be used to design sound barriers. The main part...

  19. Topology optimization of acoustic-structure interaction problems using a mixed finite element formulation

    DEFF Research Database (Denmark)

    Yoon, Gil Ho; Jensen, Jens Stissing; Sigmund, Ole

    2007-01-01

    The paper presents a gradient-based topology optimization formulation that allows to solve acoustic-structure (vibro-acoustic) interaction problems without explicit boundary interface representation. In acoustic-structure interaction problems, the pressure and displacement fields are governed...... by Helmholtz equation and the elasticity equation, respectively. Normally, the two separate fields are coupled by surface-coupling integrals, however, such a formulation does not allow for free material re-distribution in connection with topology optimization schemes since the boundaries are not explicitly...... given during the optimization process. In this paper we circumvent the explicit boundary representation by using a mixed finite element formulation with displacements and pressure as primary variables (a u/p-formulation). The Helmholtz equation is obtained as a special case of the mixed formulation...

  20. Buckling of Bucket Foundations

    DEFF Research Database (Denmark)

    Madsen, Søren; Andersen, Lars Vabbersgaard; Ibsen, Lars Bo

    2012-01-01

    In this paper, the risk of structural buckling during installation of large-diameter bucket foundations is addressed using numerical methods. Imperfect geometries are introduced based on the pre-buckling mode shapes from a linear Eigenvalue buckling analysis. Various imperfect geometries are intr...

  1. 3D Topology optimization of Stokes flow problems

    DEFF Research Database (Denmark)

    Gersborg-Hansen, Allan; Dammann, Bernd

    for the fluid behavior in a micro fluidic device. Such a device has finite size and a large degree of freedom for the design of geometry. Physically Stokes flow is an exotic inertia free flow. This, however, complicates mixing by passive devices. Passive devices, that is, devices without moving parts, are often......, the optimizer suggests a design that stretches the hot-cold interface, which is encouraging since "stretching and folding" is known to be key ingredients in efficient mixing. The modelling is performed using a finite element based solver, with analytically derived sensitivities that drives a gradient based...... Program Interface, http://www.openmp.org/...

  2. Simultaneous Optimization of Topology and Component Sizes for Double Planetary Gear Hybrid Powertrains

    Directory of Open Access Journals (Sweden)

    Weichao Zhuang

    2016-05-01

    Full Text Available Hybrid powertrain technologies are successful in the passenger car market and have been actively developed in recent years. Optimal topology selection, component sizing, and controls are required for competitive hybrid vehicles, as multiple goals must be considered simultaneously: fuel efficiency, emissions, performance, and cost. Most of the previous studies explored these three design dimensions separately. In this paper, two novel frameworks combining these three design dimensions together are presented and compared. One approach is nested optimization which searches through the whole design space exhaustively. The second approach is called enhanced iterative optimization, which executes the topology optimization and component sizing alternately. A case study shows that the later method can converge to the global optimal design generated from the nested optimization, and is much more computationally efficient. In addition, we also address a known issue of optimal designs: their sensitivity to parameters, such as varying vehicle weight, which is a concern especially for the design of hybrid buses. Therefore, the iterative optimization process is applied to design a robust multi-mode hybrid electric bus under different loading scenarios as the final design challenge of this paper.

  3. Phase-Field Relaxation of Topology Optimization with Local Stress Constraints

    DEFF Research Database (Denmark)

    Stainko, Roman; Burger, Martin

    2006-01-01

    We introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase-field method. In the basic formulation we have a PDE-constrained optimization problem, where the finite element and design analysis are solved simultaneously...... parameter decreases to zero. A major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter. The relaxation scheme yields a large-scale optimization problem with a high number of linear...

  4. Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization

    Institute of Scientific and Technical Information of China (English)

    Zhe-Qi Lin; Hae Chang Gea; Shu-Tian Liu

    2011-01-01

    Converting ambient vibration energy into electrical energy by using piezoelectric energy harvester has attracted a lot of interest in the past few years.In this paper,a topology optimization based method is applied to simultaneously determine the optimal layout of the piezoelectric energy harvesting devices and the optimal position of the mass loading.The objective function is to maximize the energy harvesting performance over a range of vibration frequencies.Pseudo excitation method (PEM) is adopted to analyze structural stationary random responses,and sensitivity analysis is then performed by using the adjoint method.Numerical examples are presented to demonstrate the validity of the proposed approach.

  5. Topology optimization of fail-safe structures using a simplified local damage model

    DEFF Research Database (Denmark)

    Jansen, Miche; Lombaert, Geert; Schevenels, Mattias;

    2014-01-01

    Topology optimization of mechanical structures often leads to efficient designs which resemble statically determinate structures. These economical structures are especially vulnerable to local loss of stiffness due to material failure. This paper therefore addresses local failure of continuum...... with a fixed shape. The damage scenarios are taken into account by means of a minimax formulation of the optimization problem which minimizes the worst case performance.The detrimental influence of local failure on the nominal design is demonstrated in two representative examples: a cantilever beam optimized...

  6. A Fully Developed Flow Thermofluid Model for Topology Optimization of 3D-Printed Air-Cooled Heat Exchangers

    DEFF Research Database (Denmark)

    Haertel, Jan Hendrik Klaas; Nellis, Gregory F.

    2017-01-01

    . The conductance of the heat exchanger is maximized for a prescribed pressure drop and prescribed air-side temperature change across the heat exchanger. Polymer with infilled thermally conducting metal filaments is considered as the heat exchanger material which allows cost effective additive manufacturing...... optimized slot channel model in order to demonstrate the superior performance of the topology optimized designs. Thus, this work demonstrates the usefulness of topology optimization to fully exploit the design freedom afforded by additive manufacturing technologies....

  7. Topology optimization of reinforced concrete beams by a spread-over reinforcement model with fixed grid mesh

    OpenAIRE

    Benjapon Wethyavivorn; Siradech Surit

    2011-01-01

    For this investigation, topology optimization was used as a tool to determine the optimal reinforcement for reinforcedconcrete beam. The topology optimization process was based on a unit finite element cell with layers of concrete and steel.The thickness of the reinforced steel layer of this unit cell was then adjusted when the concrete layer could not carry thetensile or compressive stress. At the same time, unit cells which carried very low stress were eliminated. The process wasperformed i...

  8. An integrated approach of topology optimized design and selective laser melting process for titanium implants materials.

    Science.gov (United States)

    Xiao, Dongming; Yang, Yongqiang; Su, Xubin; Wang, Di; Sun, Jianfeng

    2013-01-01

    The load-bearing bone implants materials should have sufficient stiffness and large porosity, which are interacted since larger porosity causes lower mechanical properties. This paper is to seek the maximum stiffness architecture with the constraint of specific volume fraction by topology optimization approach, that is, maximum porosity can be achieved with predefine stiffness properties. The effective elastic modulus of conventional cubic and topology optimized scaffolds were calculated using finite element analysis (FEA) method; also, some specimens with different porosities of 41.1%, 50.3%, 60.2% and 70.7% respectively were fabricated by Selective Laser Melting (SLM) process and were tested by compression test. Results showed that the computational effective elastic modulus of optimized scaffolds was approximately 13% higher than cubic scaffolds, the experimental stiffness values were reduced by 76% than the computational ones. The combination of topology optimization approach and SLM process would be available for development of titanium implants materials in consideration of both porosity and mechanical stiffness.

  9. Using Pareto optimality to explore the topology and dynamics of the human connectome.

    Science.gov (United States)

    Avena-Koenigsberger, Andrea; Goñi, Joaquín; Betzel, Richard F; van den Heuvel, Martijn P; Griffa, Alessandra; Hagmann, Patric; Thiran, Jean-Philippe; Sporns, Olaf

    2014-10-05

    Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain's topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an 'economical' small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.

  10. Topology optimization of reinforced concrete beams by a spread-over reinforcement model with fixed grid mesh

    Directory of Open Access Journals (Sweden)

    Benjapon Wethyavivorn

    2011-02-01

    Full Text Available For this investigation, topology optimization was used as a tool to determine the optimal reinforcement for reinforcedconcrete beam. The topology optimization process was based on a unit finite element cell with layers of concrete and steel.The thickness of the reinforced steel layer of this unit cell was then adjusted when the concrete layer could not carry thetensile or compressive stress. At the same time, unit cells which carried very low stress were eliminated. The process wasperformed iteratively to create a topology of reinforced concrete beam which satisfied design conditions.

  11. An Optimized Parallel FDTD Topology for Challenging Electromagnetic Simulations on Supercomputers

    Directory of Open Access Journals (Sweden)

    Shugang Jiang

    2015-01-01

    Full Text Available It may not be a challenge to run a Finite-Difference Time-Domain (FDTD code for electromagnetic simulations on a supercomputer with more than 10 thousands of CPU cores; however, to make FDTD code work with the highest efficiency is a challenge. In this paper, the performance of parallel FDTD is optimized through MPI (message passing interface virtual topology, based on which a communication model is established. The general rules of optimal topology are presented according to the model. The performance of the method is tested and analyzed on three high performance computing platforms with different architectures in China. Simulations including an airplane with a 700-wavelength wingspan, and a complex microstrip antenna array with nearly 2000 elements are performed very efficiently using a maximum of 10240 CPU cores.

  12. Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides

    DEFF Research Database (Denmark)

    Frellsen, Louise Floor; Ding, Yunhong; Sigmund, Ole;

    2016-01-01

    We design and experimentally verify a topology optimized low-loss and broadband two-mode (de-)multiplexer, which is (de-)multiplexing the fundamental and the first-order transverse-electric modes in a silicon photonic wire. The device has a footprint of 2.6 μm x 4.22 μm and exhibits a loss 14 dB ...

  13. Topology optimization of truss-like structures: from theory to practice

    OpenAIRE

    Richardson, James

    2013-01-01

    The goal of this thesis is the development of theoretical methods targeting the implementation of topology optimization in structural engineering applications. In civil engineering applications, structures are typically assemblies of many standardized components, such as bars, where the largest gains in efficiency can be made during the preliminary design of the overall structure. The work is aimed mainly at truss-like structures in civil engineering applications, however several of the devel...

  14. Broadband topology-optimized photonic crystal components for both TE and TM polarizations

    DEFF Research Database (Denmark)

    Têtu, A.; Kristensen, M.; Frandsen, Lars Hagedorn

    2005-01-01

    Several planar photonic crystal components topology-optimized for TE-polarized light, including 60º bends, Y-splitters, and 90º bends, have been characterized for the TM polarization. The experimental results are confirmed by finite-difference time-domain calculations. The surprising efficiency...... for TM-polarized light is found and paves the way for photonic crystal components suitable for both polarizations....

  15. Flat-top Drop Filter based on a Single Topology Optimized Photonic Crystal Cavity

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Elesin, Yuriy; Guan, Xiaowei

    2015-01-01

    Outperforming conventional design concepts, a flat-top drop filter has been designed byapplying 3D topology optimization to a single waveguide-coupled L3 photonic crystal cavity.Measurements on the design fabricated in silicon-on-insulator material reveal that the pass-band ofthe drop channel...... is flat within 0.44 dB over a wavelength range of 9.7 nm with an insertion losslower than 0.85 dB....

  16. Broadband photonic crystal waveguide 60° bend obtained utilizing topology optimization

    DEFF Research Database (Denmark)

    Frandsen, Lars Hagedorn; Harpøth, Anders; Borel, Peter Ingo

    2004-01-01

    Topology optimization has been used to design a 60° bend in a single-mode planar photonic crystal waveguide. The design has been realized in a silicon-on-insulator material and we demonstrate a record-breaking 200-nm transmission bandwidth with an average bend loss of 0.43±0.27 dB for the TE...... polarization. The experimental results agree well with 3D finite-difference-time-domain simulations....

  17. Topology Optimization of Passive Constrained Layer Damping with Partial Coverage on Plate

    Directory of Open Access Journals (Sweden)

    Weiguang Zheng

    2013-01-01

    Full Text Available The potential of using topology optimization as a tool to optimize the passive constrained layer damping (PCLD layouts with partial coverage on flat plates is investigated. The objective function is defined as a combination of several modal loss factors solved by finite element-modal strain energy (FE-MSE method. An interface finite element is introduced to modeling the viscoelastic core of PCLD patch to save the computational space and time in the optimization procedure. Solid isotropic material with penalization (SIMP method is used as the material interpolation scheme and the parameters are well selected to avoid local pseudo modes. Then, the method of moving asymptote (MMA is employed as an optimizer to search the optimal topologies of PCLD patch on plates. Applications of two flat plates with different shapes have been applied to demonstrate the validation of the proposed approach. The results show that the objective function is in a steady convergence process and the damping effect of the plates can be enhanced by the optimized PCLD layouts.

  18. Level Set-Based Topology Optimization for the Design of an Electromagnetic Cloak With Ferrite Material

    DEFF Research Database (Denmark)

    Otomori, Masaki; Yamada, Takayuki; Andkjær, Jacob Anders;

    2013-01-01

    This paper presents a structural optimization method for the design of an electromagnetic cloak made of ferrite material. Ferrite materials exhibit a frequency-dependent degree of permeability, due to a magnetic resonance phenomenon that can be altered by changing the magnitude of an externally...... applied dc magnetic field. Thus, such ferrite cloaks have the potential to provide novel functions, such as on-off operation in response to on-off application of an external magnetic field. The optimization problems are formulated to minimize the norm of the scattering field from a cylindrical obstacle....... A level set-based topology optimization method incorporating a fictitious interface energy is used to find optimized configurations of the ferrite material. The numerical results demonstrate that the optimization successfully found an appropriate ferrite configuration that functions as an electromagnetic...

  19. Optimal rectangular plate and shallow shell topologies using thickness distribution or homogenization

    Science.gov (United States)

    Tenek, Lazarus H.; Hagiwara, Ichiro

    1994-05-01

    Topological optimization of plates, as well as shallow cylindrical and curved (spherical) shells, are attempted in the present study. For all structures examined, our objective is the minimization of the strain energy function under a volume constraint. An optimum distribution of thickness or microstructural density is sought under the hypothesis that the design variables can only be assigned their extreme allowable bounds, or values very near them, so that material can be removed from low density areas and thus, an optimum topology can be determined. The structural response is computed via a finite element analysis. The analytical formulation is based on a form of linear shallow shell theory with the effects of transverse shear deformation and bending-extensional coupling included. The method of feasible directions is used to perform the optimization task. Numerical examples for various boundary conditions showing similarities or differences of the two methods are presented and discussed. For all structures examined, it is found that the assumption of a repetitious microstructure based on homogenization theory resulted in stronger optima. For clamped plates and shells, both methods converged to nearly identical topologies, an indication of possible global optimal layouts.

  20. A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials

    DEFF Research Database (Denmark)

    Otomori, Masaki; Yamada, Takayuki; Izui, Kazuhiro;

    2012-01-01

    are highly impractical from an engineering and manufacturing point of view. Therefore, a topology optimization method that can obtain clear optimized configurations is desirable. Here, a level set-based topology optimization method incorporating a fictitious interface energy is applied to a negative......This paper presents a level set-based topology optimization method for the design of negative permeability dielectric metamaterials. Metamaterials are artificial materials that display extraordinary physical properties that are unavailable with natural materials. The aim of the formulated...... optimization problem is to find optimized layouts of a dielectric material that achieve negative permeability. The presence of grayscale areas in the optimized configurations critically affects the performance of metamaterials, positively as well as negatively, but configurations that contain grayscale areas...

  1. TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURE WITH FUNDAMENTAL FREQUENCY AND FREQUENCY DOMAIN DYNAMIC RESPONSE CONSTRAINTS

    Institute of Scientific and Technical Information of China (English)

    Pan Jin; Wang De-yu

    2006-01-01

    In this paper, adaptive genetic algorithm (AGA) is applied to topology optimization of truss structure with frequency domain excitations. The optimization constraints include fundamental frequency, displacement responses under force excitations and acceleration responses under foundation acceleration excitations. The roulette wheel selection operator, adaptive crossover and mutation operators are used as genetic operators. Some heuristic strategies are put forward to direct the deletion of the extra bars and nodes on truss structures. Three examples demonstrate that the proposed method can yield the optimum structure form and the lightest weight of the given ground structure while satisfying dynamic response constraints.

  2. High-Level Topology-Oblivious Optimization of MPI Broadcast Algorithms on Extreme-Scale Platforms

    KAUST Repository

    Hasanov, Khalid

    2014-01-01

    There has been a significant research in collective communication operations, in particular in MPI broadcast, on distributed memory platforms. Most of the research works are done to optimize the collective operations for particular architectures by taking into account either their topology or platform parameters. In this work we propose a very simple and at the same time general approach to optimize legacy MPI broadcast algorithms, which are widely used in MPICH and OpenMPI. Theoretical analysis and experimental results on IBM BlueGene/P and a cluster of Grid’5000 platform are presented.

  3. Hinge-free topology optimization with embedded translation-invariant differentiable wavelet shrinkage

    DEFF Research Database (Denmark)

    Yoon, G. H.; Kim, Y. Y.; Bendsøe, Martin P.;

    2004-01-01

    In topology optimization applications for the design of compliant mechanisms, the formation of hinges is typically encountered. Often such hinges are unphysical artifacts that appear due to the choice of discretization spaces for design and analysis. The objective of this work is to present a new...... in the multiscale design space. To imbed the shrinkage method implicitly in the optimization formulation and thus facilitate sensitivity analysis, the shrinkage method is made differentiable by means of differentiable versions of logical operators. The validity of the present method is confirmed by solving typical...... two-dimensional compliant mechanism design problems....

  4. Topology optimization design of crushed 2D-frames for desired energy absorption history

    DEFF Research Database (Denmark)

    Pedersen, Claus B. Wittendorf

    2004-01-01

    The present work deals with topology optimization for obtaining a desired energy absorption history of a crushed structure. The optimized energy absorbing structures are used to improve the crashworthiness of transportation vehicles. The ground structure consists of rectangular 2D-beam elements...... with plastic hinges. The elements can undergo large rotations, so the analysis accommodates geometric nonlinearities. A quasi-static nonlinear finite element solution is obtained with an implicit backward Euler algorithm, and the analytical sensitivities are computed by the direct differentiation method....

  5. Topology optimization for the design of folding liquid crystal elastomer actuators.

    Science.gov (United States)

    Fuchi, Kazuko; Ware, Taylor H; Buskohl, Philip R; Reich, Gregory W; Vaia, Richard A; White, Timothy J; Joo, James J

    2015-10-01

    Aligned liquid crystal elastomers (LCEs) are capable of undergoing large reversible shape change in response to thermal stimuli and may act as actuators for many potential applications such as self-assembly and deployment of micro devices. Recent advances in LCE patterning tools have demonstrated sub-millimetre control of director orientation, enabling the preparation of materials with arbitrarily complex director fields. However, without design tools to connect the 2D director pattern with the activated 3D shape, LCE design relies on intuition and trial and error. Here we present a design methodology to generate reliable folding in monolithic LCEs designed with topology optimization. The distributions of order/disorder and director orientations are optimized so that the remotely actuated deformation closely matches a target deformation for origami folding. The optimal design exhibits a strategy to counteract the mechanical frustration that may lead to an undesirable deformation, such as anti-clastic bending. Multi-hinge networks were developed using insights from the optimal hinge designs and were demonstrated through the fabrication and reversible actuation of a self-folding box. Topology optimization provides an important step towards leveraging the opportunities afforded by LCE patterning into functional designs.

  6. Structure Topology Optimization of Brake Pad in Large- megawatt Wind Turbine Brake Considering Thermal- structural Coupling

    Science.gov (United States)

    Zhang, S. F.; Yin, J.; Liu, Y.; Sha, Z. H.; Ma, F. J.

    2016-11-01

    There always exists severe non-uniform wear of brake pad in large-megawatt wind turbine brake during the braking process, which has the brake pad worn out in advance and even threats the safety production of wind turbine. The root cause of this phenomenon is the non-uniform deformation caused by thermal-structural coupling effect between brake pad and disc while braking under the conditions of both high speed and heavy load. For this problem, mathematical model of thermal-structural coupling analysis is built. Based on the topology optimization method of Solid Isotropic Microstructures with Penalization, SIMP, structure topology optimization of brake pad is developed considering the deformation caused by thermal-structural coupling effect. The objective function is the minimum flexibility, and the structure topology optimization model of brake pad is established after indirect thermal- structural coupling analysis. Compared with the optimization result considering non-thermal- structural coupling, the conspicuous influence of thermal effect on brake pad wear and deformation is proven as well as the rationality of taking thermal-structural coupling effect as optimization condition. Reconstructed model is built according to the result, meanwhile analysis for verification is carried out with the same working condition. This study provides theoretical foundation for the design of high-speed and heavy-load brake pad. The new structure may provide design reference for improving the stress condition between brake pad and disc, enhancing the use ratio of friction material and increasing the working performance of large-megawatt wind turbine brake.

  7. Analogy of strain energy density based bone-remodeling algorithm and structural topology optimization.

    Science.gov (United States)

    Jang, In Gwun; Kim, Il Yong; Kwak, Byung Ban

    2009-01-01

    In bone-remodeling studies, it is believed that the morphology of bone is affected by its internal mechanical loads. From the 1970s, high computing power enabled quantitative studies in the simulation of bone remodeling or bone adaptation. Among them, Huiskes et al. (1987, "Adaptive Bone Remodeling Theory Applied to Prosthetic Design Analysis," J. Biomech. Eng., 20, pp. 1135-1150) proposed a strain energy density based approach to bone remodeling and used the apparent density for the characterization of internal bone morphology. The fundamental idea was that bone density would increase when strain (or strain energy density) is higher than a certain value and bone resorption would occur when the strain (or strain energy density) quantities are lower than the threshold. Several advanced algorithms were developed based on these studies in an attempt to more accurately simulate physiological bone-remodeling processes. As another approach, topology optimization originally devised in structural optimization has been also used in the computational simulation of the bone-remodeling process. The topology optimization method systematically and iteratively distributes material in a design domain, determining an optimal structure that minimizes an objective function. In this paper, we compared two seemingly different approaches in different fields-the strain energy density based bone-remodeling algorithm (biomechanical approach) and the compliance based structural topology optimization method (mechanical approach)-in terms of mathematical formulations, numerical difficulties, and behavior of their numerical solutions. Two numerical case studies were conducted to demonstrate their similarity and difference, and then the solution convergences were discussed quantitatively.

  8. Acoustical topology optimization for Zwicker's loudness model - Application to noise barriers

    DEFF Research Database (Denmark)

    Kook, Junghwan; Koo, Kunmo; Hyun, Jaeyub

    2012-01-01

    Traditionally, the objective of design optimization of an acoustic system is to reduce physical acoustic properties, i.e., sound pressure and power. However, since these parameters are not sufficient to present the relation of physical sound stimulus with human perceptual judgment, physical...... acoustic properties may not represent adequate parameters for optimizing acoustic devices. In this paper, we first present a design method for acoustical topology optimization by considering human's subjective conception of sound. To consider human hearing characteristics. Zwicker's loudness is calculated...... according to DIN45631 (ISO 532B). The main objective of this work is to minimize the main specific loudness of a target critical band rate by optimizing the distribution of the reflecting material in a design domain. The Helmholtz equation is used to model acoustic wave propagation and, it is solved using...

  9. Aerostructural Level Set Topology Optimization for a Common Research Model Wing

    Science.gov (United States)

    Dunning, Peter D.; Stanford, Bret K.; Kim, H. Alicia

    2014-01-01

    The purpose of this work is to use level set topology optimization to improve the design of a representative wing box structure for the NASA common research model. The objective is to minimize the total compliance of the structure under aerodynamic and body force loading, where the aerodynamic loading is coupled to the structural deformation. A taxi bump case was also considered, where only body force loads were applied. The trim condition that aerodynamic lift must balance the total weight of the aircraft is enforced by allowing the root angle of attack to change. The level set optimization method is implemented on an unstructured three-dimensional grid, so that the method can optimize a wing box with arbitrary geometry. Fast matching and upwind schemes are developed for an unstructured grid, which make the level set method robust and efficient. The adjoint method is used to obtain the coupled shape sensitivities required to perform aerostructural optimization of the wing box structure.

  10. Topology Optimization of Turbulent Fluid Flow with a Sensitive Porosity Adjoint Method (SPAM)

    CERN Document Server

    Philippi, B

    2015-01-01

    A sensitive porosity adjoint method (SPAM) for optimizing the topology of fluid machines has been proposed. A sensitivity function with respect to the porosity has been developed. In the first step of the optimization process, porous media are introduced into the flow regime according to the sensitivity function. Then the optimized porous media are transformed to solid walls. The turbulent flow in porous media is accounted for by a modified eddy-viscosity based turbulence model. Its influence on the adjoint equations is nevertheless neglected, which refers to the so called frozen turbulence assumption. A test case of application in terms of the turbulent rough wall channel flow shows that a considerable reduction of the objective function can be obtained by this method. The transformation from porous media to solid walls may have important effect on the optimization results.

  11. Multi-objective optimization of aerostructures inspired by nature

    Science.gov (United States)

    Kearney, Adam C.

    The focus of this doctoral work is on the optimization of aircraft wing structures. The optimization was performed against the shape, size and topology of simple aircraft wing designs. A simple morphing wing actuator optimization is performed as well as a wing panel buckling topology optimization. This is done with biologically-inspired mathematical systems including a map L-system, a multi-objective genetic algorithm, and cellular structures represented by Voronoi diagrams. As with most aircraft optimizations, both studies aim to minimize the total weight of a wing while simultaneously meeting stiffness and strength requirements. Optimization is performed with the scripts developed in MATLAB as well as through the use of finite element codes, NASTRAN and LS-Dyna. The intent of this methodology is to develop unique designs inspired by nature and optimized through natural selection. The optimal designs are those with minimal weight as well as additional requirements specific to the problems. The designs and methodology have the potential to be of use in determining minimum weight designs in aircraft structures. A literature review of optimization techniques, methodology and method validation, and optimization comparisons is presented. The buckling panel optimization considered here also includes composite buckling failure and manufacturing assumptions for composite panels. The panels are optimized for mass and strength by controlling the laminate stacking sequence, stiffener size, and topology. The morphing wing is optimized for actuator loading and redundancy.

  12. Buckling optimisation of sandwich cylindrical panels

    Science.gov (United States)

    Abouhamzeh, M.; Sadighi, M.

    2016-06-01

    In this paper, the buckling load optimisation is performed on sandwich cylindrical panels. A finite element program is developed in MATLAB to solve the governing differential equations of the global buckling of the structure. In order to find the optimal solution, the genetic algorithm Toolbox in MATLAB is implemented. Verifications are made for both the buckling finite element code and also the results from the genetic algorithm by comparisons to the results available in literature. Sandwich cylindrical panels are optimised for the buckling strength with isotropic or orthotropic cores with different boundary conditions. Results are presented in terms of stacking sequence of fibers in the face sheets and core to face sheet thickness ratio.

  13. Integrated Topology Optimization of Structure/Vibration Control for Piezoelectric Cylindrical Shell Based on the Genetic Algorithm

    Directory of Open Access Journals (Sweden)

    Jianjun He

    2015-01-01

    Full Text Available A hybrid optimization strategy for integrated topological optimization design of piezoelectric cylindrical flat shell structure is proposed. The method combines the genetic algorithm (GA and linear-quadratic-regulator (LQR theory to optimize the performance of coupling structure/control system. The GA is used to choose the optimal structure topology and number and placements of actuators and control parameters; meanwhile, the LQR is used to design control system to suppress vibration of optimal structure under sinusoidal excitation, which is based on the couple-mode space control. In addition, the mathematical morphology operators are used for repairs of disconnected structure topology. The results of numerical simulation and computations show that the proposed method is effective and feasible, with good performance for the optimal and coupling piezoelectric cylindrical shell structure/control system.

  14. Spectral Quantitative Analysis Model with Combining Wavelength Selection and Topology Structure Optimization

    Directory of Open Access Journals (Sweden)

    Qian Wang

    2016-01-01

    Full Text Available Spectroscopy is an efficient and widely used quantitative analysis method. In this paper, a spectral quantitative analysis model with combining wavelength selection and topology structure optimization is proposed. For the proposed method, backpropagation neural network is adopted for building the component prediction model, and the simultaneousness optimization of the wavelength selection and the topology structure of neural network is realized by nonlinear adaptive evolutionary programming (NAEP. The hybrid chromosome in binary scheme of NAEP has three parts. The first part represents the topology structure of neural network, the second part represents the selection of wavelengths in the spectral data, and the third part represents the parameters of mutation of NAEP. Two real flue gas datasets are used in the experiments. In order to present the effectiveness of the methods, the partial least squares with full spectrum, the partial least squares combined with genetic algorithm, the uninformative variable elimination method, the backpropagation neural network with full spectrum, the backpropagation neural network combined with genetic algorithm, and the proposed method are performed for building the component prediction model. Experimental results verify that the proposed method has the ability to predict more accurately and robustly as a practical spectral analysis tool.

  15. Topology Optimization

    DEFF Research Database (Denmark)

    A. Kristensen, Anders Schmidt; Damkilde, Lars

    2007-01-01

    The technological competition has demanded an ever increasing technological development, and in e.g. design of airplanes and cars engineers use very sophisticated Finite Element models to simulate the real behaviour of the structures. The Finite Element models often uses highly sophisticated...

  16. A sequential, multi-complexity topology optimization process for aeroelastic wing structure design

    Science.gov (United States)

    Guiles, Mark A.

    The design of structures is motivated by the requirement that performance goals must be met at the lowest possible cost. In the realm of aircraft design, the least-weight structure typically leads to the lowest cost vehicle. Therefore, the goal becomes that of supporting all flight loads at the minimum achievable weight. This study outlines a method to identify the optimal layout or topology of a wing structure that minimizes the wing's weight under multiple loads, subject to strength and aeroelastic constraints. The procedure was developed with the goal of using available, well-defined tools for structural sizing optimization to simplify the layout selection process. This approach uses a sequence of sizing optimization problems to identify and remove non-essential elements from an overpopulated structure. The optimization and deletion processes produce a series of improving feasible topologies for the set of flight loads imposed on the wing. These candidate structures are compared and the least-weight design is chosen as the optimum. The procedure was first applied to a plane truss problem and was able to reproduce the well-established Michell truss solution, providing validation of the approach. Then, the process was applied to wing models representing several different types of aircraft to illustrate its applicability across a wide range of wing design problems.

  17. Effective mass density based topology optimization of locally resonant acoustic metamaterials for bandgap maximization

    Science.gov (United States)

    Yang, Xiong Wei; Lee, Joong Seok; Kim, Yoon Young

    2016-11-01

    Because effective material properties are essential concepts in the analyses of wave phenomena in metamaterials, they may also be utilized in the optimal design of metamaterials. In this work, we propose a topology optimization method directly using the Effective Mass Density (EMD) concept to maximize the first bandgaps of two-dimensional solid Locally Resonant Acoustic Metamaterials (LRAMs). When the first bandgap is characterized by the negative EMD, the bandgap maximization can be formulated efficiently as a topology optimization problem to broaden the frequency zone of the negative EMD values. In this work, EMD is calculated by considering the macroscopic isotropy of LRAMs in the long wavelength limit. To facilitate the analytical sensitivity analysis, we propose an elaborate calculation scheme of EMD. A sensitivity averaging technique is also suggested to guarantee the macroscopically isotropic behavior of the LRAMs. In the present study, the coating layer interfacing the core and the matrix of a ternary LRAM is chosen as the design region because it significantly influences the bandgap. By considering several numerical examples, the validity of this method is verified, and the effects of the mass constraint ratios on the optimized results are also investigated.

  18. Topology optimization of adaptive fluid-actuated cellular structures with arbitrary polygonal motor cells

    Science.gov (United States)

    Lv, Jun; Tang, Liang; Li, Wenbo; Liu, Lei; Zhang, Hongwu

    2016-05-01

    This paper mainly focuses on the fast and efficient design method for plant bioinspired fluidic cellular materials and structures composed of polygonal motor cells. Here we developed a novel structural optimization method with arbitrary polygonal coarse-grid elements based on multiscale finite element frameworks. The fluidic cellular structures are meshed with irregular polygonal coarse-grid elements according to their natural size and the shape of the imbedded motor cells. The multiscale base functions of solid displacement and hydraulic pressure are then constructed to bring the small-scale information of the irregular motor cells to the large-scale simulations on the polygonal coarse-grid elements. On this basis, a new topology optimization method based on the resulting polygonal coarse-grid elements is proposed to determine the optimal distributions or number of motor cells in the smart cellular structures. Three types of optimization problems are solved according to the usages of the fluidic cellular structures. Firstly, the proposed optimization method is utilized to minimize the system compliance of the load-bearing fluidic cellular structures. Second, the method is further extended to design biomimetic compliant actuators of the fluidic cellular materials due to the fact that non-uniform volume expansions of fluid in the cells can induce elastic action. Third, the optimization problem focuses on the weight minimization of the cellular structure under the constraints for the compliance of the whole system. Several representative examples are investigated to validate the effectiveness of the proposed polygon-based topology optimization method of the smart materials.

  19. Acoustical topology optimization of Zwicker's loudness with Padé approximation

    DEFF Research Database (Denmark)

    Kook, Junghwan; Jensen, Jakob Søndergaard; Wang, Semyung

    2013-01-01

    Zwicker's loudness is a conventional standard index for measuring human hearing annoyance and has been widely considered in many industrial fields for noise evaluations. The calculation of Zwicker's loudness, which is needed for a wide range of frequency responses with a fine frequency resolution......, using the finite element procedure usually requires significant computation time, since a numerical solution must be obtained for each considered frequency. Furthermore, if the analysis is the basis for an iterative optimization procedure such as a gradient-based acoustical topology optimization......, this approach imposes prohibitively high computational costs. In this research, we propose a computationally-efficient approach to resolve the computational issue in the computation and optimization of Zwicker's loudness. We present an efficient approach which combines the finite element method (FEM...

  20. Design of passive directional acoustic devices using Topology Optimization - from method to experimental validation

    DEFF Research Database (Denmark)

    Christiansen, Rasmus Ellebæk; Fernandez Grande, Efren

    2016-01-01

    The paper presents a topology optimization based method for designing acoustic focusing devices, capable of tailoring the sound emission pattern of one or several sources, across a chosen frequency band. The method is demonstrated numerically considering devices optimized for directional sound...... emission in two dimensions and is experimentally validated using three dimensional prints of the optimized designs. The emitted fields exhibit a level difference of at least 15 dB on axis relative to the off-axis directions, over frequency bands of approximately an octave. It is demonstrated to be possible...... to outperform the latter in terms of directivity and maximum side-lobe level over nearly an octave band. A set of frequencies are considered simultaneously in the design formulation and performance robustness toward uniform spatial production errors in the designed devices is assured by including perturbations...

  1. On the use of topology optimization for improving heat transfer in molding process

    Science.gov (United States)

    Agazzi, A.; LeGoff, R.; Truc-Vu, C.

    2016-10-01

    In the plastic industry, one of the key factor is to control heat transfer. One way to achieve that goal is to design an effective cooling system. But in some area of the mold, where it is not possible to design cooling system, the use of a highly conductive material, such as copper pin, is often used. Most of the time, the location, the size and the quantity of the copper pin are made by empirical considerations, without using optimization procedures. In this article, it is proposed to use topology optimization, in order to improve transient conductive heat transfer in an injection/blowing mold. Two methodologies are applied and compared. Finally, the optimal distribution of cooper pin in the mold is given.

  2. Three-Dimensional Dynamic Topology Optimization with Frequency Constraints Using Composite Exponential Function and ICM Method

    Directory of Open Access Journals (Sweden)

    Hongling Ye

    2015-01-01

    Full Text Available The dynamic topology optimization of three-dimensional continuum structures subject to frequency constraints is investigated using Independent Continuous Mapping (ICM design variable fields. The composite exponential function (CEF is selected to be a filter function which recognizes the design variables and to implement the changing process of design variables from “discrete” to “continuous” and back to “discrete.” Explicit formulations of frequency constraints are given based on filter functions, first-order Taylor series expansion. And an improved optimal model is formulated using CEF and the explicit frequency constraints. Dual sequential quadratic programming (DSQP algorithm is used to solve the optimal model. The program is developed on the platform of MSC Patran & Nastran. Finally, numerical examples are given to demonstrate the validity and applicability of the proposed method.

  3. Topology-oblivious optimization of MPI broadcast algorithms on extreme-scale platforms

    KAUST Repository

    Hasanov, Khalid

    2015-11-01

    © 2015 Elsevier B.V. All rights reserved. Significant research has been conducted in collective communication operations, in particular in MPI broadcast, on distributed memory platforms. Most of the research efforts aim to optimize the collective operations for particular architectures by taking into account either their topology or platform parameters. In this work we propose a simple but general approach to optimization of the legacy MPI broadcast algorithms, which are widely used in MPICH and Open MPI. The proposed optimization technique is designed to address the challenge of extreme scale of future HPC platforms. It is based on hierarchical transformation of the traditionally flat logical arrangement of communicating processors. Theoretical analysis and experimental results on IBM BlueGene/P and a cluster of the Grid\\'5000 platform are presented.

  4. A unified aggregation and relaxation approach for stress-constrained topology optimization

    DEFF Research Database (Denmark)

    Verbart, Alexander; Langelaar, Matthijs; Keulen, Fred van

    2017-01-01

    optima accessible. The main advantage is that no separate constraint relaxation techniques are necessary, which reduces the parameter dependence of the problem. Furthermore, there is a clear relationship between the original feasible domain and the perturbed feasible domain via this aggregation parameter.......In this paper, we propose a unified aggregation and relaxation approach for topology optimization with stress constraints. Following this approach, we first reformulate the original optimization problem with a design-dependent set of constraints into an equivalent optimization problem with a fixed...... design-independent set of constraints. The next step is to perform constraint aggregation over the reformulated local constraints using a lower bound aggregation function. We demonstrate that this approach concurrently aggregates the constraints and relaxes the feasible domain, thereby making singular...

  5. Research into topology optimization and the FDM method for a space cracked membrane

    Science.gov (United States)

    Hu, Qingxi; Li, Wanyuan; Zhang, Haiguang; Liu, Dali; Peng, Fujun; Duan, Yongchao

    2017-07-01

    The problem that the space membranes are easily torn open is the main focus in this paper, and a bionic strengthening-ribs structure is proposed for a space membrane based on interdisciplinary strengths, such as topology optimization, composite materials, and rapid prototyping. The optimization method and modeling method of membranes with bionic strengthening-ribs was studied. The PEEK and SCF/PEEK composite material which are applied to the space environment are chosen, and FDM technology is used. Through topology optimization, bionic strengthening-ribs with good tensile and tear capacities were obtained. Cracked membranes, cracked membranes with PEEK strengthening-ribs and SCF/PEEK strengthening-ribs were tested and test data were obtained. An extension situation and tension fracture were compared for three cases. The experimental results showed that membranes with the bionic strengthening-ribs structure have better mechanical properties, and the strength of the membranes with PEEK and SCF/PEEK strengthening-ribs were raised, respectively, up to 266.9% and 185.9%. The strengthening-ribs structure greatly improves the capacity to halt membrane crack-growth, which has an important significance to avoid membrane tear, and to ensure the spacecraft orbital lifetime.

  6. Designing patient-specific 3D printed craniofacial implants using a novel topology optimization method.

    Science.gov (United States)

    Sutradhar, Alok; Park, Jaejong; Carrau, Diana; Nguyen, Tam H; Miller, Michael J; Paulino, Glaucio H

    2016-07-01

    Large craniofacial defects require efficient bone replacements which should not only provide good aesthetics but also possess stable structural function. The proposed work uses a novel multiresolution topology optimization method to achieve the task. Using a compliance minimization objective, patient-specific bone replacement shapes can be designed for different clinical cases that ensure revival of efficient load transfer mechanisms in the mid-face. In this work, four clinical cases are introduced and their respective patient-specific designs are obtained using the proposed method. The optimized designs are then virtually inserted into the defect to visually inspect the viability of the design . Further, once the design is verified by the reconstructive surgeon, prototypes are fabricated using a 3D printer for validation. The robustness of the designs are mechanically tested by subjecting them to a physiological loading condition which mimics the masticatory activity. The full-field strain result through 3D image correlation and the finite element analysis implies that the solution can survive the maximum mastication of 120 lb. Also, the designs have the potential to restore the buttress system and provide the structural integrity. Using the topology optimization framework in designing the bone replacement shapes would deliver surgeons new alternatives for rather complicated mid-face reconstruction.

  7. Computational multiobjective topology optimization of silicon anode structures for lithium-ion batteries

    Science.gov (United States)

    Mitchell, Sarah L.; Ortiz, Michael

    2016-09-01

    This study utilizes computational topology optimization methods for the systematic design of optimal multifunctional silicon anode structures for lithium-ion batteries. In order to develop next generation high performance lithium-ion batteries, key design challenges relating to the silicon anode structure must be addressed, namely the lithiation-induced mechanical degradation and the low intrinsic electrical conductivity of silicon. As such this work considers two design objectives, the first being minimum compliance under design dependent volume expansion, and the second maximum electrical conduction through the structure, both of which are subject to a constraint on material volume. Density-based topology optimization methods are employed in conjunction with regularization techniques, a continuation scheme, and mathematical programming methods. The objectives are first considered individually, during which the influence of the minimum structural feature size and prescribed volume fraction are investigated. The methodology is subsequently extended to a bi-objective formulation to simultaneously address both the structural and conduction design criteria. The weighted sum method is used to derive the Pareto fronts, which demonstrate a clear trade-off between the competing design objectives. A rigid frame structure was found to be an excellent compromise between the structural and conduction design criteria, providing both the required structural rigidity and direct conduction pathways. The developments and results presented in this work provide a foundation for the informed design and development of silicon anode structures for high performance lithium-ion batteries.

  8. Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

    Directory of Open Access Journals (Sweden)

    Qinghai Zhao

    2015-01-01

    Full Text Available A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA and the sequential optimization and reliability assessment (SORA. To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

  9. A MAC based excitation frequency increasing method for structural topology optimization under harmonic excitations

    Directory of Open Access Journals (Sweden)

    Liu Tao

    2017-01-01

    Full Text Available This work is focused on the topology optimization of structures that are subjected to harmonic force excitation with prescribed frequency and amplitude. As an important objective of such a design problem, the natural resonance frequency of the structure is driven far away from the prescribed excitation frequency for the purpose of avoiding resonance and reducing the vibration level. Therefore when the excitation frequency is higher than the natural resonance frequency of the structure, the natural resonance frequency will decrease, then the optimum topology configuration will be distorted with large amount of gray elements. A MAC (Modal Assurance Criteria based excitation frequency increasing method is proposed to obtain a desired configuration. MAC is adopted here to track the natural resonance frequency which can provide the baseline reference for the current excitation frequency during the optimum iterative procedure. Then the excitation frequency increases progressively up to its originally prescribed value. By means of numerical examples, the proposed formulation can generate effective topology configurations which can avoid resonance.

  10. Rapid prototyping of nanotube-based devices using topology-optimized microgrippers

    DEFF Research Database (Denmark)

    Sardan, Özlem; Eichhorn, Volkmar; Petersen, D.H.

    2008-01-01

    Nanorobotic handling of carbon nanotubes (CNTs) using microgrippers is one of the most promising approaches for the rapid characterization of the CNTs and also for the assembly of prototypic nanotube-based devices. In this paper, we present pick-and-place nanomanipulation of multi-walled CNTs...... as well as close. Topology optimization leads to a 10-100 times improvement of the gripping force compared to conventional designs of similar size. Furthermore, we improved our nanorobotic system to offer more degrees of freedom. TEM investigation of the CNTs shows that the multi-walled tubes are coated...

  11. Global optimization of discrete truss topology design problems using a parallel cut-and-branch method

    DEFF Research Database (Denmark)

    Rasmussen, Marie-Louise Højlund; Stolpe, Mathias

    2008-01-01

    the physics, and the cuts (Combinatorial Benders’ and projected Chvátal–Gomory) come from an understanding of the particular mathematical structure of the reformulation. The impact of a stronger representation is investigated on several truss topology optimization problems in two and three dimensions....... to a mixed-integer linear program, which is solved with a parallel implementation of branch-and-bound. Additional valid inequalities and cuts are introduced to give a stronger representation of the problem, which improves convergence and speed up of the parallel method. The valid inequalities represent...

  12. Buckling of Ship Structures

    CERN Document Server

    Shama, Mohamed

    2013-01-01

    Buckling of Ship Structures presents a comprehensive analysis of the buckling problem of ship structural members. A full analysis of the various types of loadings and stresses imposed on ship plating and primary and secondary structural members is given. The main causes and consequences of the buckling mode of failure of ship structure and the methods commonly used to control buckling failure are clarified. This book contains the main equations required to determine the critical buckling stresses for both ship plating and the primary and secondary stiffening structural members. The critical buckling stresses are given for ship plating subjected to the induced various types of loadings and having the most common boundary conditions encountered in ship structures.  The text bridges the gap existing in most books covering the subject of buckling of ship structures in the classical analytical format, by putting the emphasis on the practical methods required to ensure safety against buckling of ship structur...

  13. On the reformulation of topology optimization problems as linear or convex quadratic mixed 0–1 programs

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2007-01-01

    We consider equivalent reformulations of nonlinear mixed 0–1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. We show that the considered problems can equivalently be cast as either...... linear or convex quadratic mixed 0–1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...

  14. On the reformulation of topology optimization problems as linear or convex quadratic mixed 0-1 programs

    DEFF Research Database (Denmark)

    Stolpe, Mathias

    2004-01-01

    We consider equivalent reformulations of nonlinear mixed 0-1 optimization problems arising from a broad range of recent applications of topology optimization for the design of continuum structures and composite materials. It is shown that the considered problems may equivalently be cast as either...... linear or as convex quadratic mixed 0-1 programs. The reformulations provide new insight into the structure of the problems and may provide a foundation for the development of new methods and heuristics for solving topology optimization problems. The applications considered are maximum stiffness design...

  15. A Dynamic Programming Algorithm for Finding the Optimal Placement of a Secondary Structure Topology in Cryo-EM Data.

    Science.gov (United States)

    Biswas, Abhishek; Ranjan, Desh; Zubair, Mohammad; He, Jing

    2015-09-01

    The determination of secondary structure topology is a critical step in deriving the atomic structures from the protein density maps obtained from electron cryomicroscopy technique. This step often relies on matching the secondary structure traces detected from the protein density map to the secondary structure sequence segments predicted from the amino acid sequence. Due to inaccuracies in both sources of information, a pool of possible secondary structure positions needs to be sampled. One way to approach the problem is to first derive a small number of possible topologies using existing matching algorithms, and then find the optimal placement for each possible topology. We present a dynamic programming method of Θ(Nq(2)h) to find the optimal placement for a secondary structure topology. We show that our algorithm requires significantly less computational time than the brute force method that is in the order of Θ(q(N) h).

  16. Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard; Sigmund, Ole

    2005-01-01

    A T junction in a photonic crystal waveguide is designed with the topology-optimization method. The gradientbased optimization tool is used to modify the material distribution in the junction area so that the power transmission in the output ports is maximized. To obtain high transmission...

  17. Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

    Science.gov (United States)

    Deng, Yongbo; Korvink, Jan G.

    2016-05-01

    This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

  18. Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.

    Science.gov (United States)

    Deng, Yongbo; Korvink, Jan G

    2016-05-01

    This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.

  19. Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method

    Science.gov (United States)

    Korvink, Jan G.

    2016-01-01

    This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766

  20. Maximizing phononic band gaps in piezocomposite materials by means of topology optimization.

    Science.gov (United States)

    Vatanabe, Sandro L; Paulino, Glaucio H; Silva, Emílio C N

    2014-08-01

    Phononic crystals (PCs) can exhibit phononic band gaps within which sound and vibrations at certain frequencies do not propagate. In fact, PCs with large band gaps are of great interest for many applications, such as transducers, elastic/acoustic filters, noise control, and vibration shields. Previous work in the field concentrated on PCs made of elastic isotropic materials; however, band gaps can be enlarged by using non-isotropic materials, such as piezoelectric materials. Because the main property of PCs is the presence of band gaps, one possible way to design microstructures that have a desired band gap is through topology optimization. Thus in this work, the main objective is to maximize the width of absolute elastic wave band gaps in piezocomposite materials designed by means of topology optimization. For band gap calculation, the finite element analysis is implemented with Bloch-Floquet theory to solve the dynamic behavior of two-dimensional piezocomposite unit cells. Higher order frequency branches are investigated. The results demonstrate that tunable phononic band gaps in piezocomposite materials can be designed by means of the present methodology.

  1. Experimental Observation of the Skeletal Adaptive Repair Mechanism and Bionic Topology Optimization Method

    Directory of Open Access Journals (Sweden)

    Kaysar Rahman

    2014-01-01

    Full Text Available Bone adaptive repair theory considers that the external load is the direct source of bone remodeling; bone achieves its maintenance by remodeling some microscopic damages due to external load during the process. This paper firstly observes CT data from the whole self-repairing process in bone defects in rabbit femur. Experimental result shows that during self-repairing process there exists an interaction relationship between spongy bone and enamel bone volume changes of bone defect, that is when volume of spongy bone increases, enamel bone decreases, and when volume of spongy bone decreases, enamel bone increases. Secondly according to this feature a bone remodeling model based on cross-type reaction-diffusion system influenced by mechanical stress is proposed. Finally, this model coupled with finite element method by using the element adding and removing process is used to simulate the self-repairing process and engineering optimization problems by considering the idea of bionic topology optimization.

  2. Optimizing topological cascade resilience based on the structure of terrorist networks.

    Directory of Open Access Journals (Sweden)

    Alexander Gutfraind

    Full Text Available Complex socioeconomic networks such as information, finance and even terrorist networks need resilience to cascades--to prevent the failure of a single node from causing a far-reaching domino effect. We show that terrorist and guerrilla networks are uniquely cascade-resilient while maintaining high efficiency, but they become more vulnerable beyond a certain threshold. We also introduce an optimization method for constructing networks with high passive cascade resilience. The optimal networks are found to be based on cells, where each cell has a star topology. Counterintuitively, we find that there are conditions where networks should not be modified to stop cascades because doing so would come at a disproportionate loss of efficiency. Implementation of these findings can lead to more cascade-resilient networks in many diverse areas.

  3. Optimizing Topological Cascade Resilience Based on the Structure of Terrorist Networks

    Science.gov (United States)

    Gutfraind, Alexander

    2010-01-01

    Complex socioeconomic networks such as information, finance and even terrorist networks need resilience to cascades - to prevent the failure of a single node from causing a far-reaching domino effect. We show that terrorist and guerrilla networks are uniquely cascade-resilient while maintaining high efficiency, but they become more vulnerable beyond a certain threshold. We also introduce an optimization method for constructing networks with high passive cascade resilience. The optimal networks are found to be based on cells, where each cell has a star topology. Counterintuitively, we find that there are conditions where networks should not be modified to stop cascades because doing so would come at a disproportionate loss of efficiency. Implementation of these findings can lead to more cascade-resilient networks in many diverse areas. PMID:21085710

  4. Shape and Topology Optimization in Stokes Flow with a Phase Field Approach

    Energy Technology Data Exchange (ETDEWEB)

    Garcke, Harald, E-mail: harald.garcke@mathematik.uni-regensburg.de; Hecht, Claudia, E-mail: claudia.hecht@mathematik.uni-regensburg.de [Universität Regensburg, Fakultät für Mathematik (Germany)

    2016-02-15

    In this paper we introduce a new formulation for shape optimization problems in fluids in a diffuse interface setting that can in particular handle topological changes. By adding the Ginzburg–Landau energy as a regularization to the objective functional and relaxing the non-permeability outside the fluid region by introducing a porous medium approach we hence obtain a phase field problem where the existence of a minimizer can be guaranteed. This problem is additionally related to a sharp interface problem, where the permeability of the non-fluid region is zero. In both the sharp and the diffuse interface setting we can derive necessary optimality conditions using only the natural regularity of the minimizers. We also pass to the limit in the first order conditions.

  5. CONTINUUM TOPOLOGY OPTIMIZATION FOR MONOLITHIC COMPLIANT MECHANISMS OF MICRO-ACTUATORS

    Institute of Scientific and Technical Information of China (English)

    Luo Zhen; Du Yixian; Chen Liping; Yang Jingzhou; Karim Abdel-Malek

    2006-01-01

    A multi-objective scheme for structural topology optimization of distributed compliant mechanisms of micro-actuators in MEMS condition is presented in this work, in which mechanical flexibility and structural stiffness are both considered as objective functions. The compliant micro-mechanism developed in this way can not only provide sufficient output work but also have sufficient rigidity to resist reaction forces and maintain its shape when holding the work-piece. A density filtering approach is also proposed to eliminate numerical instabilities such as checkerboards, mesh-dependency and one-node connected hinges occurring in resulting mechanisms. SIMP is used as the interpolation scheme to indicate the dependence of material modulus on element-regularized densities. The sequential convex programming method, such as the methodof moving asymptotes (MMA), is used to solve the optimization problem. The validation of the presented methodologies is demonstrated by a typical numerical example.

  6. Reliability based topology optimization for continuum structures with local failure constraints

    DEFF Research Database (Denmark)

    Luo, Yangjun; Zhou, Mingdong; Wang, Michael Yu

    2014-01-01

    -related) target performance constraints. In order to overcome the stress singularity phenomenon caused by the combined stress and reliability constraints, a reduction strategy on target reliability index is proposed and utilized together with the ε-relaxation approach. Meanwhile, an enhanced aggregation method......This paper presents an effective method for stress constrained topology optimization problems under load and material uncertainties. Based on the Performance Measure Approach (PMA), the optimization problem is formulated as to minimize the objective function under a large number of (stress...... is employed to aggregate the selected active constraints using a general K–S function, which avoids expensive computational cost from the large-scale nature of local failure constraints. Several numerical examples are given to demonstrate the validity of the present method....

  7. Optimal Channel Width Adaptation, Logical Topology Design, and Routing in Wireless Mesh Networks

    Directory of Open Access Journals (Sweden)

    Li Li

    2009-01-01

    Full Text Available Radio frequency spectrum is a finite and scarce resource. How to efficiently use the spectrum resource is one of the fundamental issues for multi-radio multi-channel wireless mesh networks. However, past research efforts that attempt to exploit multiple channels always assume channels of fixed predetermined width, which prohibits the further effective use of the spectrum resource. In this paper, we address how to optimally adapt channel width to more efficiently utilize the spectrum in IEEE802.11-based multi-radio multi-channel mesh networks. We mathematically formulate the channel width adaptation, logical topology design, and routing as a joint mixed 0-1 integer linear optimization problem, and we also propose our heuristic assignment algorithm. Simulation results show that our method can significantly improve spectrum use efficiency and network performance.

  8. Buckling analysis of planar compression micro-springs

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Jing; Sui, Li; Shi, Gengchen [School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081 (China); Science and Technology on Electromechanical Dynamic Control Laboratory, 5 South Street Zhongguancun, Haidian 100081, Beijing (China)

    2015-04-15

    Large compression deformation causes micro-springs buckling and loss of load capacity. We analyzed the impact of structural parameters and boundary conditions for planar micro-springs, and obtained the change rules for the two factors that affect buckling. A formula for critical buckling deformation of micro-springs under compressive load was derived based on elastic thin plate theory. Results from this formula were compared with finite element analysis results but these did not always correlate. Therefore, finite element analysis is necessary for micro-spring buckling analysis. We studied the variation of micro-spring critical buckling deformation caused by four structural parameters using ANSYS software under two constraint conditions. The simulation results show that when an x-direction constraint is added, the critical buckling deformation increases by 32.3-297.9%. The critical buckling deformation decreases with increase in micro-spring arc radius or section width and increases with increase in micro-spring thickness or straight beam width. We conducted experiments to confirm the simulation results, and the experimental and simulation trends were found to agree. Buckling analysis of the micro-spring establishes a theoretical foundation for optimizing micro-spring structural parameters and constraint conditions to maximize the critical buckling load.

  9. Finite element analysis of the dental implant using a topology optimization method.

    Science.gov (United States)

    Chang, Chih-Ling; Chen, Chen-Sheng; Huang, Chang-Hung; Hsu, Ming-Lun

    2012-09-01

    In recent years, many attempts have been made to optimize the shape of dental implants. The purpose of this study took advantage of the topology optimization in the finite element (FE) method to look for redundant material distribution on a dental threaded implant and redesigned a new implant macrogeometry with the evaluation of its biomechanical functions. Three-dimensional FE models were created of a first molar section of the maxilla and embedded with an implant, abutment and a superstructure by using the commercial software ANSYS 11.0. The final design of a new implant was shaped by topology optimization, and four FE models namely traditional implants with bonded (TB) and contact (TC) interfaces, and new implants with bonded (NB) and contact (NC) interfaces, were established. Material properties of compact and cancellous bone were modeled as fully orthotropy and transversely isotropy respectively. Oblique (200-N vertical and 40-N horizontal) occlusal loading was applied on the central and distal fossa of the crown. The FE model estimated that the volume of the new implant could be reduced by 17.9% of the traditional one and the biomechanical performances were similar, such as the stress of the implant, stress of the implant-bone complex, lower displacement, and greater stiffness than the traditional implant. The advantages of the new implant increased the space to allow more new bone ingrowth or assist in fusing more bone graft into the bone sustaining the implant stability and saved material. Its disadvantage was higher stress level compared with that of the traditional implant.

  10. Numerical study and topology optimization of 1D periodic bimaterial phononic crystal plates for bandgaps of low order Lamb waves.

    Science.gov (United States)

    Hedayatrasa, Saeid; Abhary, Kazem; Uddin, Mohammad

    2015-03-01

    The optimum topology of bimaterial phononic crystal (PhCr) plates with one-dimensional (1D) periodicity to attain maximum relative bandgap width of low order Lamb waves is computationally investigated. The evolution of optimized topology with respect to filling fraction of constituents, alternatively stiff scattering inclusion, is explored. The underlying idea is to develop PhCr plate structures with high specific bandgap efficiency at particular filling fraction, or further with multiscale functionality through gradient of optimized PhCr unitcell all over the lattice array. Multiobjective genetic algorithm (GA) is employed in this research in conjunction with finite element method (FEM) for topology optimization of silicon-tungsten PhCr plate unitcells. A specialized FEM model is developed and verified for dispersion analysis of plate waves and calculation of modal response. Modal band structure of regular PhCr plate unitcells with centric scattering layer is studied as a function of aspect ratio and filling fraction. Topology optimization is then carried out for a few aspect ratios, with and without prescribed symmetry, over various filling fractions. The efficiency of obtained solutions is verified as compared to corresponding regular centric PhCr plate unitcells. Moreover, being inspired by the obtained optimum topologies, definite and easy to produce topologies are proposed with enhanced bandgap efficiency as compared to centric unitcells. Finally a few cases are introduced to evaluate the frequency response of finite PhCr plate structures produced by achieved topologies and also to confirm the reliability of calculated modal band structures. Cases made by consecutive unitcells of different filling fraction are examined in order to attest the bandgap efficiency and multiscale functionality of such graded PhCr plate structures. Crown Copyright © 2014. Published by Elsevier B.V. All rights reserved.

  11. Preform design optimization for forging process based on the topological approach

    Science.gov (United States)

    Shao, Yong; Lu, Bin; Ou, Hengan; Cui, Zhenshan

    2013-05-01

    Preform design plays an important role in forging design especially for parts with complex shapes. In this paper, an attempt was made to develop a topological approach in the preform design of bulk metal forming processes based on the Bi-direction evolutionary structural optimization (BESO) strategy. In this approach, a new element addition and removal criteria based on the equivalent strain have been proposed for evaluating and optimizing the material flow in the forging process. To obtain a smooth preform boundary, a closed B-spline curve based on the least square approximation algorithm is employed to approximate the uneven surface of updated preform. An inhouse developed C♯ program has been employed to integrate the FE simluation, shape optimsation and surface approximation process. A 2D blade forging perform design problem are evaluate using the developed method. The results suggest that the optimized preform has shown better performance in improving the material flow and deformation uniformity during the forging. The results also demonstrate the robustness and efficiency of the developed preform design optimization method.

  12. A novel design for passive misscromixers based on topology optimization method.

    Science.gov (United States)

    Chen, Xueye; Li, Tiechuan

    2016-08-01

    In this paper, a series of novel passive micromixers, called topological micromixers with reversed flow (TMRFX), are proposed. The reversed flow in the microchannels can enhance chaotic advection and produce better mixing performance. Therefore the maximum of reversed flow is chosen as the objective function of the topology optimization problem. Because the square-wave unit is easier to fabricate and have better mixing performance than many other serpentine micromixers, square-wave structure becomes the original geometry structure. By simulating analysis, the series of TMRFX, namely TMRF, TMRF0.75, TMRF0.5, TMRF0.25, mix better than the square-wave micromixer at various Reynolds numbers (Re), but pressure drops of TMRFX are much higher. Lots of intensive numerical simulations are conducted to prove that TMRF and TMRF0.75 have remarkable advantages on mixing over other micromixers at various Re. The mixing performance of TMRF0.75 is similar to TMRF's. What's more, TMRF have a larger pressure drop than TMRF0.75, which means that TMRF have taken more energy than TMRF0.75. For a wide range of Re (Re ≤ 0.1 and Re ≥ 10), TMRF0.75 delivers a great performance and the mixing efficiency is greater than 95 %. Even in the range of 0.1-10 for the Re, the mixing efficiency of TMRF0.75 is higher than 85 %.

  13. High-performance slow light photonic crystal waveguides with topology optimized or circular-hole based material layouts

    DEFF Research Database (Denmark)

    Wang, Fengwen; Jensen, Jakob Søndergaard; Sigmund, Ole

    2012-01-01

    Photonic crystal waveguides are optimized for modal confinement and loss related to slow light with high group index. A detailed comparison between optimized circular-hole based waveguides and optimized waveguides with free topology is performed. Design robustness with respect to manufacturing...... imperfections is enforced by considering different design realizations generated from under-, standard- and over-etching processes in the optimization procedure. A constraint ensures a certain modal confinement, and loss related to slow light with high group index is indirectly treated by penalizing field...... of 0.48 or above. The comparisons between circular-hole based designs and topology optimized designs illustrate that the former can be efficient for dispersion engineering but that larger improvements are possible if irregular geometries are allowed....

  14. Network Lifetime Global Optimization for Multi-Source and Single-Sink Topology in Wireless Sensor Networks

    Institute of Scientific and Technical Information of China (English)

    WANG Hui; WU Di; AGOULMINE Nazim; MA Mao-de

    2009-01-01

    The multi-source and single-sink (MSSS) topology in wireless sensor networks (WSNs) is defined as a network topology, where all of nodes can gather, receive and transmit data to the sink. In energy-constrained WSNs with such a topology, the joint optimal design in the physical, medium access control (MAC) and network layers is considered for network lifetime maximization (NLM). The problem of integrating multi-layer information to compute NLM, which involves routing flow, link schedule and transmission power, is formulated as a non-linear optimization problem. Specially under time division multiple access (TDMA) scheme, this problem can be transformed into a convex optimization problem. To solve it analytically we make use of the property that local optimization is global optimization in convex problem. This allows us to exploit the Karush-Kuhn-Tucker (KKT) optimality conditions to solve it and obtain analytical solution expression, i.e., the globally optimal network lifetime (NL). NL is derived as a function of number of nodes, their initial energy and data rate arrived at them.Based on the analysis of analytical approach, it takes the influence of data rates, link access and routing method over NLM into account. Moreover, the globally optimal transmission schemes are achieved by solution set during analytical approach and applied to algorithms in TDMA-based WSNs aiming at NLM on OMNeT to compare with other suboptimal schemes.

  15. Development of a new concrete pipe molding machine using topology optimization

    Energy Technology Data Exchange (ETDEWEB)

    Park, Hong Seok; Dahal, Prakash [School of Mechanical and Automotive Engineering, University of Ulsan, Ulsan (Korea, Republic of); Nguyen, Trung Thanh [Faculty of Mechanical Engineering, Le Quy Don Technical University, Hanoi (Viet Nam)

    2016-08-15

    Sulfur polymer concrete (SPC) is a relatively new material used to replace Portland cement for manufacturing sewer pipes. The objective of this work is to develop an efficient molding machine with an inner rotating die to mix, compress and shape the SPC pipe. First, the alternative concepts were generated based on the TRIZ principles to overcome the drawbacks of existing machines. Then, the concept scoring technique was used to identify the best design in terms of machine structure and product quality. Finally, topology optimization was applied with the support of the density method to reduce mass and to displace the inner die. Results showed that the die volume can be reduced by approximately 9% and the displacement can be decreased by approximately 3% when compared with the initial design. This work is expected to improve the manufacturing efficiency of the concrete pipe molding machine.

  16. Buckling analysis of a ring stiffened hybrid composite cylinder

    Science.gov (United States)

    Potluri, Rakesh; Eswara Kumar, A.; Navuri, Karteek; Nagaraju, M.; Mojeswara Rao, Duduku

    2016-09-01

    This study aims to understand the response of the ring stiffened cylinders made up of hybrid composites subjected to buckling loads by using the concepts of Design of Experiments (DOE) and optimization by using Finite Element Method (FEM) simulation software Ansys workbench V15. Carbon epoxy and E-glass epoxy composites were used in the hybrid composite. This hybrid composite was analyzed by using different layup angles. Central composite design (CCD) was used to perform design of experiments (D.O.E) and kriging method was used to generate a response surface. The response surface optimization (RSO) was performed by using the method of the multi-objective genetic algorithm (MOGA). After optimization, the best candidate was chosen and applied to the ring stiffened cylinder and eigenvalue buckling analysis was performed to understand the buckling behavior. Best laminate candidates with high buckling strength have been identified. A generalized procedure of the laminate optimization and analysis have been shown.

  17. ILP Model and Relaxation-Based Decomposition Approach for Incremental Topology Optimization in p-Cycle Networks

    Directory of Open Access Journals (Sweden)

    Md. Noor-E-Alam

    2012-01-01

    Full Text Available p-cycle networks have attracted a considerable interest in the network survivability literature in recent years. However, most of the existing work assumes a known network topology upon which to apply p-cycle restoration. In the present work, we develop an incremental topology optimization ILP for p-cycle network design, where a known topology can be amended with new fibre links selected from a set of eligible spans. The ILP proves to be relatively easy to solve for small test case instances but becomes computationally intensive on larger networks. We then follow with a relaxation-based decomposition approach to overcome this challenge. The decomposition approach significantly reduces computational complexity of the problem, allowing the ILP to be solved in reasonable time with no statistically significant impact on solution optimality.

  18. An Algorithm for the Design of a Cost-Optimized Topology for the Fixed Part of a GSM Network

    Institute of Scientific and Technical Information of China (English)

    2002-01-01

    This paper proposes an algorithm to design a cost optimized topology for the fixed part of a mobile network. For the given locations of base stations and mobile switching centers, the algorithm decides the number and position of the base station controllers as well as the way the base stations are connected to the base stations controllers.

  19. Topology Optimization of Nano-Mechanical Cantilever Sensors Using a C0 Discontinuous Galerkin-Type Approach

    DEFF Research Database (Denmark)

    Marhadi, Kun Saptohartyadi; Evgrafov, Anton; Sørensen, Mads Peter

    2011-01-01

    We demonstrate the use of a C0 discontinuous Galerkin method for topology optimization of nano-mechanical sensors, namely temperature, surface stress, and mass sensors. The sensors are modeled using classical thin plate theory, which requires C1 basis functions in the standard finite element method...

  20. Critical phenomena in communication/computation networks with various topologies and suboptimal to optimal resource allocation

    Science.gov (United States)

    Cogoni, Marco; Busonera, Giovanni; Anedda, Paolo; Zanetti, Gianluigi

    2015-01-01

    We generalize previous studies on critical phenomena in communication networks [1,2] by adding computational capabilities to the nodes. In our model, a set of tasks with random origin, destination and computational structure is distributed on a computational network, modeled as a graph. By varying the temperature of a Metropolis Montecarlo, we explore the global latency for an optimal to suboptimal resource assignment at a given time instant. By computing the two-point correlation function for the local overload, we study the behavior of the correlation distance (both for links and nodes) while approaching the congested phase: a transition from peaked to spread g(r) is seen above a critical (Montecarlo) temperature Tc. The average latency trend of the system is predicted by averaging over several network traffic realizations while maintaining a spatially detailed information for each node: a sharp decrease of performance is found over Tc independently of the workload. The globally optimized computational resource allocation and network routing defines a baseline for a future comparison of the transition behavior with respect to existing routing strategies [3,4] for different network topologies.

  1. Passive Vibration Isolation by Compliant Mechanism Using Topology Optimization with Building Blocks

    Directory of Open Access Journals (Sweden)

    V. Vijayan

    2014-10-01

    Full Text Available Compliant Mechanism has been designed for various types of application to transmit desired force and motion. In this study, we have explored an application of Compliant Mechanism for passive vibration isolation systems, for which compliant isolator is used to cancel undesired disturbance, which results in attenuated output amplitude. The Compliant Mechanism is equipped with isolator, which acts as a transmission of force, in order to control the amount of displacement transmitted from it. Compliant Mechanism also used as passive vibration isolator. Here, introducing compliance into the connection, the transmission of applied forces is reduced at some frequencies, at the expense of increasing transmission at other frequencies. The force transmissibility is numerically identical to the motion transmissibility. In order to find the flexible building blocks for force transmissibility, structural optimization approach is applied. The Structural optimization approach focuses on the determination of the topology, shape and size of the mechanism. Thus approach is used to establish the actuator model of the block and it is validated by commercial Finite Element software. A library of compliant elements is proposed in FlexIn. These blocks are in limited number and the basis is composed of 36 elements. The force transmitted to the rigid foundation through the isolator is reduced to avoid transmission of vibration to other machines. Thus the preliminary results of FEA from ANSYS demonstrate that the compliant mechanism can be effectively used to reduce the amount of force transmitted to the surface.

  2. Topology optimization of support structure of telescope skin based on bit-matrix representation NSGA-II

    Institute of Scientific and Technical Information of China (English)

    Liu Weidong; Zhu Hua; Wang Yiping; Zhou Shengqiang; Bai Yalei; Zhao Chunsheng

    2013-01-01

    Non-dominated sorting genetic algorithm II (NSGA-II) with multiple constraints han-dling is employed for multi-objective optimization of the topological structure of telescope skin, in which a bit-matrix is used as the representation of a chromosome, and genetic algorithm (GA) operators are introduced based on the matrix. Objectives including mass, in-plane performance, and out-of-plane load-bearing ability of the individuals are obtained by finite element analysis (FEA) using ANSYS, and the matrix-based optimization algorithm is realized in MATLAB by han-dling multiple constraints such as structural connectivity and in-plane strain requirements. Feasible configurations of the support structure are achieved. The results confirm that the matrix-based NSGA-II with multiple constraints handling provides an effective method for two-dimensional multi-objective topology optimization.

  3. Experimental and Numerical Study of Buckling of Vacuum Chambers for Fast-Cycling Synchrotrons

    DEFF Research Database (Denmark)

    Bräuner, Lars Erik

    The optimal functioning of the long span thin walled elliptical cross section shells used as vacuum chambers for fast-cycling synchrotrons is provided by their buckling capacity. Also it is often necessary to design inter-stiffener panels of elliptical shells used as vacuum chambers to resist any...... tendency towards pressure induced buckling due to some combination of excessive out-gassing, fragility, radiation damage, magnetic field distortion,. The analysis for design is complicated because elliptical shell chambers display a complex form of nonlinear snap buckling behavior under the external...... pressure. Buckling analysis for shells is further complicated by the observation that geometric imperfections have an important influence on the buckling mode as well as on the buckling load-carrying capacity. Buckling loads are, in general, considerably lower than the lowest critical loads predicted from...

  4. Scleral Buckling with Chandelier Illumination.

    Science.gov (United States)

    Seider, Michael I; Nomides, Riikka E K; Hahn, Paul; Mruthyunjaya, Prithvi; Mahmoud, Tamer H

    2016-01-01

    Scleral buckling is a highly successful technique for the repair of rhegmatogenous retinal detachment that requires intra-operative examination of the retina and treatment of retinal breaks via indirect ophthalmoscopy. Data suggest that scleral buckling likely results in improved outcomes for many patients but is declining in popularity, perhaps because of significant advances in vitrectomy instrumentation and visualization systems. Emerging data suggest that chandelier-assisted scleral buckling is safe and has many potential advantages over traditional buckling techniques. By combining traditional scleral buckling with contemporary vitreoretinal visualization techniques, chandelier-assistance may increase the popularity of scleral buckling to treat primary rhegmatogenous retinal detachment for surgeons of the next generation, maintaining buckling as an option for appropriate patients in the future.

  5. Scleral buckling with chandelier illumination

    Directory of Open Access Journals (Sweden)

    Michael I Seider

    2016-01-01

    Full Text Available Scleral buckling is a highly successful technique for the repair of rhegmatogenous retinal detachment that requires intra-operative examination of the retina and treatment of retinal breaks via indirect ophthalmoscopy. Data suggest that scleral buckling likely results in improved outcomes for many patients but is declining in popularity, perhaps because of significant advances in vitrectomy instrumentation and visualization systems. Emerging data suggest that chandelier-assisted scleral buckling is safe and has many potential advantages over traditional buckling techniques. By combining traditional scleral buckling with contemporary vitreoretinal visualization techniques, chandelier-assistance may increase the popularity of scleral buckling to treat primary rhegmatogenous retinal detachment for surgeons of the next generation, maintaining buckling as an option for appropriate patients in the future.

  6. Communication Characterization and Optimization of Applications Using Topology-Aware Task Mapping on Large Supercomputers

    Energy Technology Data Exchange (ETDEWEB)

    Sreepathi, Sarat [ORNL; D' Azevedo, Eduardo [ORNL; Philip, Bobby [ORNL; Worley, Patrick H [ORNL

    2016-01-01

    On large supercomputers, the job scheduling systems may assign a non-contiguous node allocation for user applications depending on available resources. With parallel applications using MPI (Message Passing Interface), the default process ordering does not take into account the actual physical node layout available to the application. This contributes to non-locality in terms of physical network topology and impacts communication performance of the application. In order to mitigate such performance penalties, this work describes techniques to identify suitable task mapping that takes the layout of the allocated nodes as well as the application's communication behavior into account. During the first phase of this research, we instrumented and collected performance data to characterize communication behavior of critical US DOE (United States - Department of Energy) applications using an augmented version of the mpiP tool. Subsequently, we developed several reordering methods (spectral bisection, neighbor join tree etc.) to combine node layout and application communication data for optimized task placement. We developed a tool called mpiAproxy to facilitate detailed evaluation of the various reordering algorithms without requiring full application executions. This work presents a comprehensive performance evaluation (14,000 experiments) of the various task mapping techniques in lowering communication costs on Titan, the leadership class supercomputer at Oak Ridge National Laboratory.

  7. Porous biodegradable lumbar interbody fusion cage design and fabrication using integrated global-local topology optimization with laser sintering.

    Science.gov (United States)

    Kang, Heesuk; Hollister, Scott J; La Marca, Frank; Park, Paul; Lin, Chia-Ying

    2013-10-01

    Biodegradable cages have received increasing attention for their use in spinal procedures involving interbody fusion to resolve complications associated with the use of nondegradable cages, such as stress shielding and long-term foreign body reaction. However, the relatively weak initial material strength compared to permanent materials and subsequent reduction due to degradation may be problematic. To design a porous biodegradable interbody fusion cage for a preclinical large animal study that can withstand physiological loads while possessing sufficient interconnected porosity for bony bridging and fusion, we developed a multiscale topology optimization technique. Topology optimization at the macroscopic scale provides optimal structural layout that ensures mechanical strength, while optimally designed microstructures, which replace the macroscopic material layout, ensure maximum permeability. Optimally designed cages were fabricated using solid, freeform fabrication of poly(ε-caprolactone) mixed with hydroxyapatite. Compression tests revealed that the yield strength of optimized fusion cages was two times that of typical human lumbar spine loads. Computational analysis further confirmed the mechanical integrity within the human lumbar spine, although the pore structure locally underwent higher stress than yield stress. This optimization technique may be utilized to balance the complex requirements of load-bearing, stress shielding, and interconnected porosity when using biodegradable materials for fusion cages.

  8. Preliminary Structural Design Using Topology Optimization with a Comparison of Results from Gradient and Genetic Algorithm Methods

    Science.gov (United States)

    Burt, Adam O.; Tinker, Michael L.

    2014-01-01

    In this paper, genetic algorithm based and gradient-based topology optimization is presented in application to a real hardware design problem. Preliminary design of a planetary lander mockup structure is accomplished using these methods that prove to provide major weight savings by addressing the structural efficiency during the design cycle. This paper presents two alternative formulations of the topology optimization problem. The first is the widely-used gradient-based implementation using commercially available algorithms. The second is formulated using genetic algorithms and internally developed capabilities. These two approaches are applied to a practical design problem for hardware that has been built, tested and proven to be functional. Both formulations converged on similar solutions and therefore were proven to be equally valid implementations of the process. This paper discusses both of these formulations at a high level.

  9. Topology and sizing optimization of discrete structures using a cooperative coevolutionary genetic algorithm with independent ground structures

    Science.gov (United States)

    Zhong, Wei; Su, Ruiyi; Gui, Liangjin; Fan, Zijie

    2016-06-01

    This article proposes a method called the cooperative coevolutionary genetic algorithm with independent ground structures (CCGA-IGS) for the simultaneous topology and sizing optimization of discrete structures. An IGS strategy is proposed to enhance the flexibility of the optimization by offering two separate design spaces and to improve the efficiency of the algorithm by reducing the search space. The CCGA is introduced to divide a complex problem into two smaller subspaces: the topological and sizing variables are assigned into two subpopulations which evolve in isolation but collaborate in fitness evaluations. Five different methods were implemented on 2D and 3D numeric examples to test the performance of the algorithms. The results demonstrate that the performance of the algorithms is improved in terms of accuracy and convergence speed with the IGS strategy, and the CCGA converges faster than the traditional GA without loss of accuracy.

  10. A Novel Optimization Method for the Electric Topology of Thermoelectric Modules Used in an Automobile Exhaust Thermoelectric Generator

    Science.gov (United States)

    Quan, Rui; Tang, Xinfeng; Quan, Shuhai; Huang, Liang

    2013-07-01

    Based on Bi2Te3 thermoelectric modules, a kind of automobile exhaust thermoelectric generator (AETEG) with a single-column cold-source structure was designed. To enhance its net power and efficiency, the output performance of all the thermoelectric modules was tested with a temperature monitoring unit and voltage monitoring unit, and modeled using a back-propagation (BP) neural network based on various hot-source temperatures, cold-source temperatures, load currents, and contact pressures according to the temperature distribution of the designed heat exchanger and cooling system. Then, their electric topology (series or parallel hybrid) was optimized using a genetic algorithm to achieve the maximum peak power of the AETEG. From the experimental results, compared with when all the thermoelectric modules were connected only in series or parallel at random, it is concluded that the AETEG performance is evidently affected by the electric topology of all the single thermoelectric modules. The optimized AETEG output power is greatly superior to the other two investigated designs, validating the proposed optimized electric topology as both feasible and practical.

  11. Topology Optimization for Photonic Crystal Waveguide Intersection with Wide and Flat Bandwidths in Ultra-Fast All-Optical Switch (PC-SMZ)

    DEFF Research Database (Denmark)

    Sugimoto, Y; Watanabe, Y; Ikeda, N

    2006-01-01

    Numerical and experimental studies on the photonic crystal waveguide intersection based on the topology optimization design method are reported and the effectiveness is shown by achieving high transmission spectra with low crosstalk for the straightforward beam-propagation line....

  12. Scleral buckling biomaterials and implants for retinal detachment surgery.

    Science.gov (United States)

    Baino, Francesco

    2010-11-01

    Scleral buckling is a widely used surgical procedure that aims at repairing retinal detachments. Many materials and procedural techniques have been variously proposed and tested in an attempt to find the best combination for providing optimal results to the patient. This review highlights the evolution of scleral buckling implants and chronicles the main advances that have been made in such a context. Specifically, the limitations of the materials and implants fallen in disuse, as well as the advantages of currently adopted devices are critically examined and discussed. Future directions for the research are considered, underlining in particular the great potential carried by the development of accurate mathematical models for describing the postoperative evolution of buckled eye. These analytical models, supported by a comprehensive data set provided by advanced techniques of medical investigations, may become useful tools for helping surgeons to choose, and to design if necessary, the best buckling material and configuration to be used in each specific clinical case.

  13. Scleral Buckling with Chandelier Illumination

    OpenAIRE

    Michael I Seider; Riikka E.K Nomides; Paul Hahn; Prithvi Mruthyunjaya; Mahmoud, Tamer H

    2016-01-01

    Scleral buckling is a highly successful technique for the repair of rhegmatogenous retinal detachment that requires intra-operative examination of the retina and treatment of retinal breaks via indirect ophthalmoscopy. Data suggest that scleral buckling likely results in improved outcomes for many patients but is declining in popularity, perhaps because of significant advances in vitrectomy instrumentation and visualization systems. Emerging data suggest that chandelier-assisted scleral buckl...

  14. Buckling of dislocation in graphene

    Science.gov (United States)

    Yao, Yin; Wang, Shaofeng; Bai, Jianhui; Wang, Rui

    2016-10-01

    The buckling of dislocation in graphene is discussed through the lattice theory of dislocation and elastic theory. The approximate solution of the buckling is obtained based on the inner stress distribution caused by different structure of dislocations and is proved to be suitable by the simulation. The position of the highest buckling is predicted to be at the vertex of the pentagon far away from the heptagon. The buckling is strongly influenced by the internal stress and the distance between the extrusive area and stretching area, as well as the critical stress σc. The SW defect is proved to be unbuckled due to its strong interaction between extrusion and stretching.

  15. Using the Hypergeometric Model to analyze the buckling of drillstrings in curved boreholes

    Energy Technology Data Exchange (ETDEWEB)

    Sampaio, J.H.B. Jr. [PETROBRAS, Rio de Janeiro (Brazil); Eustes, A.W. III [Colorado School of Mines, Golden, CO (United States). Petroleum Engineering Dept.

    1998-12-31

    Current methodologies for analytically determining the onset of buckling of drillstrings within curved boreholes are limited. In this paper, the Hypergeometric Model is shown to be an effective model to determine drillstring buckling within curved boreholes. With the Hypergeometric Model, the analysis of drillstring buckling results in curves expressing the local buckling force versus the angle of inclination. The local buckling force alone, however, does not contain all the information required for a practical analysis. From the local buckling force curve, the positional buckling force is derived. The positional buckling force considers the distributed weight of the drillstring and the friction between the drillstring and the borehole wall. From this curve, the point of minimum resistance to buckling of the drillstring is determined. Using the local and positional buckling force curves, experimental results and simulations are presented. When multiple configurations exist (for example tapered drillstrings, tapered boreholes, multi-curved boreholes, or any combination of these), the analysis procedure uses superposition of two or more single configuration curves and a graphical algorithm. The Hypergeometric Model permits the optimization of the position of the crossing points (cross-over positioning, casing-shoe positioning, and change of curvature) to achieve extended reach with less risk and cost. The procedure for this model and examples are presented in this paper.

  16. Topology optimization design of a lightweight ultra-broadband wide-angle resistance frequency selective surface absorber

    Science.gov (United States)

    Sui, Sai; Ma, Hua; Wang, Jiafu; Pang, Yongqiang; Qu, Shaobo

    2015-06-01

    In this paper, the topology design of a lightweight ultra-broadband polarization-independent frequency selective surface absorber is proposed. The absorption over a wide frequency range of 6.68-26.08 GHz with reflection below -10 dB can be achieved by optimizing the topology and dimensions of the resistive frequency selective surface by virtue of genetic algorithm. This ultra-broadband absorption can be kept when the incident angle is less than 55 degrees and is independent of the incident wave polarization. The experimental results agree well with the numerical simulations. The density of our ultra-broadband absorber is only 0.35 g cm  -  3 and thus may find potential applications in microwave engineering, such as electromagnetic interference and stealth technology.

  17. The secondary buckling transition: wrinkling of buckled spherical shells.

    Science.gov (United States)

    Knoche, Sebastian; Kierfeld, Jan

    2014-07-01

    We theoretically explain the complete sequence of shapes of deflated spherical shells. Decreasing the volume, the shell remains spherical initially, then undergoes the classical buckling instability, where an axisymmetric dimple appears, and, finally, loses its axisymmetry by wrinkles developing in the vicinity of the dimple edge in a secondary buckling transition. We describe the first axisymmetric buckling transition by numerical integration of the complete set of shape equations and an approximate analytic model due to Pogorelov. In the buckled shape, both approaches exhibit a locally compressive hoop stress in a region where experiments and simulations show the development of polygonal wrinkles, along the dimple edge. In a simplified model based on the stability equations of shallow shells, a critical value for the compressive hoop stress is derived, for which the compressed circumferential fibres will buckle out of their circular shape in order to release the compression. By applying this wrinkling criterion to the solutions of the axisymmetric models, we can calculate the critical volume for the secondary buckling transition. Using the Pogorelov approach, we also obtain an analytical expression for the critical volume at the secondary buckling transition: The critical volume difference scales linearly with the bending stiffness, whereas the critical volume reduction at the classical axisymmetric buckling transition scales with the square root of the bending stiffness. These results are confirmed by another stability analysis in the framework of Donnel, Mushtari and Vlasov (DMV) shell theory, and by numerical simulations available in the literature.

  18. Finding Quasi-Optimal Network Topologies for Information Transmission in Active Networks

    Science.gov (United States)

    Baptista, Murilo S.; de Carvalho, Josué X.; Hussein, Mahir S.

    2008-01-01

    This work clarifies the relation between network circuit (topology) and behaviour (information transmission and synchronization) in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements) whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons. PMID:18941516

  19. Finding quasi-optimal network topologies for information transmission in active networks.

    Directory of Open Access Journals (Sweden)

    Murilo S Baptista

    Full Text Available This work clarifies the relation between network circuit (topology and behaviour (information transmission and synchronization in active networks, e.g. neural networks. As an application, we show how one can find network topologies that are able to transmit a large amount of information, possess a large number of communication channels, and are robust under large variations of the network coupling configuration. This theoretical approach is general and does not depend on the particular dynamic of the elements forming the network, since the network topology can be determined by finding a Laplacian matrix (the matrix that describes the connections and the coupling strengths among the elements whose eigenvalues satisfy some special conditions. To illustrate our ideas and theoretical approaches, we use neural networks of electrically connected chaotic Hindmarsh-Rose neurons.

  20. Buckling of polymerized monomolecular films

    Science.gov (United States)

    Bourdieu, L.; Daillant, J.; Chatenay, D.; Braslau, A.; Colson, D.

    1994-03-01

    The buckling of a two-dimensional polymer network at the air-water interface has been evidenced by grazing incidence x-ray scattering. A comprehensive description of the inhomogeneous octadecyltrichlorosilane polymerized film was obtained by atomic force microscopy and x-ray scattering measurements. The buckling occurs with a characteristic wavelength ~=10 μm.