Calculation of elastic-plastic strain ranges for fatigue analysis based on linear elastic stresses
Sauer, G.
1998-01-01
Fatigue analysis requires that the maximum strain ranges be known. These strain ranges are generally computed from linear elastic analysis. The elastic strain ranges are enhanced by a factor K e to obtain the total elastic-plastic strain range. The reliability of the fatigue analysis depends on the quality of this factor. Formulae for calculating the K e factor are proposed. A beam is introduced as a computational model for determining the elastic-plastic strains. The beam is loaded by the elastic stresses of the real structure. The elastic-plastic strains of the beam are compared with the beam's elastic strains. This comparison furnishes explicit expressions for the K e factor. The K e factor is tested by means of seven examples. (orig.)
On the use of elastic-plastic material characteristics for linear-elastic component assessments
Kussmaul, K.; Silcher, H.; Eisele, U.
1995-01-01
In this paper the procedure of safety assessment of components by fracture mechanics analysis as recommended in TECDOC 717 is applied to two standard specimens of ductile cast iron. It is shown that the use of a pseudo-elastic K IJ -value in linear elastic safety analysis may lead to non-conservative results, when elastic-plastic material behaviour can be expected. (author)
DESTRUCTION CRITERION IN MODEL OF NON-LINEAR ELASTIC PLASTIC MEDIUM
O. L. Shved
2014-01-01
Full Text Available The paper considers a destruction criterion in a specific phenomenological model of elastic plastic medium which significantly differs from the known criteria. In case of vector interpretation of rank-2 symmetric tensors yield surface in the Cauchy stress space is formed by closed piecewise concave surfaces of its deviator sections with due account of experimental data. Section surface is determined by normal vector which is selected from two private vectors of criterial “deviator” operator. Such selection is not always possible in the case of anisotropy growth. It is expected that destruction can only start when a process point in the stress space is located in the current deviator section of the yield surface. It occurs when a critical point appears in the section, and a private value of an operator becomes N-fold in the point that determines the private vector corresponding to the normal vector. Unique and reasonable selection of the normal vector becomes impossible in the critical point and an yield criteria loses its significance in the point.When the destruction initiation is determined there is a possibility of a special case due to the proposed conic form of the yield surface. The deviator section degenerates into the point at the yield surface peak. Criterion formulation at the surface peak lies in the fact that there is no physically correct solution while using a state equation in regard to elastic distortion measures with a fixed tensor of elastic turn. Such usage of the equation is always possible for the rest points of the yield surface and it is considered as an obligatory condition for determination of the deviator section. A critical point is generally absent at any deviator section of the yield surface for isotropic material. A limiting value of the mean stress has been calculated at uniform tension.
Elastic plastic fracture mechanics
Simpson, L.A.
1978-07-01
The application of linear elastic fracture mechanics (LEFM) to crack stability in brittle structures is now well understood and widely applied. However, in many structural materials, crack propagation is accompanied by considerable crack-tip plasticity which invalidates the use of LEFM. Thus, present day research in fracture mechanics is aimed at developing parameters for predicting crack propagation under elastic-plastic conditions. These include critical crack-opening-displacement methods, the J integral and R-curve techniques. This report provides an introduction to these concepts and gives some examples of their applications. (author)
Streit, R.D.
1981-01-01
The failure evaluation of Pressurized Water Reactor (PWR) primary coolant loop pipe is often based on a plastic limit load criterion; i.e., failure occurs when the stress on the pipe section exceeds the material flow stress. However, in addition the piping system must be safe against crack propagation at stresses less than those leading to plastic instability. In this paper, elastic, elastic-plastic, and fully-plastic failure models are evaluated, and the requirements for piping integrity based on these models are compared. The model yielding the 'more' critical criteria for the given geometry and loading conditions defines the appropriate failure criterion. The pipe geometry and loading used in this study was choosen based on an evaluation of a guillotine break in a PWR primary coolant loop. It is assumed that the piping may contain cracks. Since a deep circumferential crack, can lead to a guillotine pipe break without prior leaking and thus without warning it is the focus of the failure model comparison study. The hot leg pipe, a 29 in. I.D. by 2.5 in. wall thickness stainless pipe, was modeled in this investigation. Cracks up to 90% through the wall were considered. The loads considered in this evaluation result from the internal pressure, dead weight, and seismic stresses. For the case considered, the internal pressure contributes the most to the failure loading. The maximum moment stress due to the dead weight and seismic moments are simply added to the pressure stress. Thus, with the circumferential crack geometry and uniform pressure stress, the problem is axisymmetric. It is analyzed using NIKE2D--an implicit, finite deformation, finite element code for analyzing two-dimensional elastic-plastic problems. (orig./GL)
Nonlinear Subincremental Method for Determination of Elastic-Plastic-Creep Behaviour
Ottosen, N. Saabye; Gunneskov, O.
1985-01-01
to general elastic-plastic-creep behaviour including problems with a highly nonlinear total strain path caused by the occurrence of creep hardening. This nonlinear method degenerates to the linear approach for elastic-plastic behaviour and when secondary creep is present. It is also linear during step......The frequently used subincremental method has so far been used on a linear interpolation of the total strain path within each main step. This method has proven successful when elastic-plastic behaviour and secondary creep is involved. The authors propose a nonlinear subincremental method applicable...
Elastic-plastic fracture mechanics study of thermal shock cracking
Hirano, K.; Kobayashi, H.; Nakazawa, H.
1980-01-01
This paper describes thermal shock experiments conducted on a nuclear pressure vessel steel (A533 Grade B Class 1), an AISI304 steel and a tool steel (JIS SKD62) using both a new thermal shock test facility and method. Analysis of their quasi-static thermal stress intensity factors is performed on the basis of linear-elastic fracture mechanics; and a thermal shock fracture toughness value, Ksub(tsc) is evaluated. Then elastic-plastic fracture toughness tests are carried out in the same high temperature range of the thermal shock experiment, and a relation between the stretched zone width, SZW, formed as a result of the fatigue precrack tip plastic blunting and the J-integral is clarified. An elastic-plastic thermal shock fracture toughness value, Jsub(tsc), is evaluated from a critical value of the stretched zone width, SZWsub(tsc), at the initiation of the thermal shock cracking by using the relation between SZW and J. The Jsub(tsc) value is compared with an elastic-plastic fracture toughness value, Jsub(Ic), and the difference between these Jsub(tsc) and Jsub(Ic) values is discussed on the basis of fractography. (author)
Elastic-plastic-creep analysis of shells
Pai, D.H.
1979-01-01
This paper presents the recent experience of a designer/fabricator of nuclear heat transport components in the area of elastic-plastic-creep analysis of shell-like structures. A brief historical perspective is first given to highlight the evolution leading to the present industry practice. The ASME elevated temperature design criteria will be discussed followed by examples of actual computations performed to support the design/analysis and fabrication of a breeder reactor component in which a substantial amount of elastic-plastic-creep analysis was performed. Mathematical challenges encountered by the design analyst in these problems will be highlighted. Developmental needs and future trends will then be given
Continuum mechanics elasticity, plasticity, viscoelasticity
Dill, Ellis H
2006-01-01
FUNDAMENTALS OF CONTINUUM MECHANICSMaterial ModelsClassical Space-TimeMaterial BodiesStrainRate of StrainCurvilinear Coordinate SystemsConservation of MassBalance of MomentumBalance of EnergyConstitutive EquationsThermodynamic DissipationObjectivity: Invariance for Rigid MotionsColeman-Mizel ModelFluid MechanicsProblems for Chapter 1BibliographyNONLINEAR ELASTICITYThermoelasticityMaterial SymmetriesIsotropic MaterialsIncompressible MaterialsConjugate Measures of Stress and StrainSome Symmetry GroupsRate Formulations for Elastic MaterialsEnergy PrinciplesGeometry of Small DeformationsLinear ElasticitySpecial Constitutive Models for Isotropic MaterialsMechanical Restrictions on the Constitutive RelationsProblems for Chapter 2BibliographyLINEAR ELASTICITYBasic EquationsPlane StrainPlane StressProperties of SolutionsPotential EnergySpecial Matrix NotationThe Finite Element Method of SolutionGeneral Equations for an Assembly of ElementsFinite Element Analysis for Large DeformationsProblems for Chapter 3Bibliograph...
Elastic-plastic dynamic analysis of a reactor building
Umemura, Hajime; Tanaka, Hiroshi.
1976-01-01
The basic characteristics of the dynamic response of a reactor building to severe earthquake ground motion are very important for the evaluation of the safety of nuclear plant systems. A computer program for elastic-plastic dynamic analysis of reactor buildings using lumped mass models is developed. The box and cylindrical walls of boiling water reactor buildings are treated as vertical beams. The nonlinear moment-rotation and shear force-shear deformation relationships of walls are based in part upon the experiments of prototype structures. The geometrical non-linearity of the soil rocking spring due to foundation separation is also considered. The nonlinear equation of motion is expressed in incremental form using tangent stiffness matrices, following the algorithm developed by E.L. Wilson et al. The damping matrix in the equation is formulated as the combination of the energy evaluation method and Penzien-Wilson's approach to accomodate the different characteristics of soil and building damping. The analysis examples and the comparison of elastic and elastic-plastic analysis results are presented. (auth.)
Thermodynamic analysis of elastic-plastic deformation
Lubarda, V.
1981-01-01
The complete set of constitutive equations which fully describes the behaviour of material in elastic-plastic deformation is derived on the basis of thermodynamic analysis of the deformation process. The analysis is done after the matrix decomposition of the deformation gradient is introduced into the structure of thermodynamics with internal state variables. The free energy function, is decomposed. Derive the expressions for the stress response, entropy and heat flux, and establish the evolution equation. Finally, we establish the thermodynamic restrictions of the deformation process. (Author) [pt
New constitutive equations to describe infinitesimal elastic-plastic deformations
Boecke, B.; Link, F.; Schneider, G.; Bruhns, O.T.
1983-01-01
A set of constitutive equations is presented to describe infinitesimal elastic-plastic deformations of austenitic steel in the range up to 600 deg C. This model can describe the hardening behaviour in the case of mechanical loading and hardening, and softening behaviour in the case of thermal loading. The loading path can be either monotonic or cyclic. For this purpose, the well-known isotropic hardening model is continually transferred into the kinematic model according to Prager, whereby suitable internal variables are chosen. The occurring process-dependent material functions are to be determined by uniaxial experiments. The hardening function g and the translation function c are determined by means of a linearized stress-strain behaviour in the plastic range, whereby a coupling condition must be taken into account. As a linear hardening process is considered to be too unrealistic, nonlinearity is achieved by introducing a small function w, the determination procedure of which is given. (author)
Rudolph, Juergen; Goetz, Andreas; Hilpert, Roland
2012-01-01
The procedures of fatigue analyses of several relevant nuclear and conventional design codes (ASME, KTA, EN, AD) for power plant components differentiate between an elastic, simplified elastic-plastic and elastic-plastic fatigue check. As a rule, operational load levels will exclude the purely elastic fatigue check. The application of the code procedure of the simplified elastic-plastic fatigue check is common practice. Nevertheless, resulting cumulative usage factors may be overly conservative mainly due to high code based plastification penalty factors Ke. As a consequence, the more complex and still code conforming general elastic-plastic fatigue analysis methodology based on non-linear finite element analysis (FEA) is applied for fatigue design as an alternative. The requirements of the FEA and the material law to be applied have to be clarified in a first step. Current design codes only give rough guidelines on these relevant items. While the procedure for the simplified elastic-plastic fatigue analysis and the associated code passages are based on stress related cycle counting and the determination of pseudo elastic equivalent stress ranges, an adaptation to elastic-plastic strains and strain ranges is required for the elastic-plastic fatigue check. The associated requirements are explained in detail in the paper. If the established and implemented evaluation mechanism (cycle counting according to the peak and valley respectively the rainflow method, calculation of stress ranges from arbitrary load-time histories and determination of cumulative usage factors based on all load events) is to be retained, a conversion of elastic-plastic strains and strain ranges into pseudo elastic stress ranges is required. The algorithm to be applied is described in the paper. It has to be implemented in the sense of an extended post processing operation of FEA e.g. by APDL scripts in ANSYS registered . Variations of principal stress (strain) directions during the loading
Elastic-plastic transition on rotating spherical shells in dependence of compressibility
Thakur Pankaj
2017-01-01
Full Text Available The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.
Converging shocks in elastic-plastic solids.
Ortega, A López; Lombardini, M; Hill, D J
2011-11-01
We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e=e(s)(I(1))+e(h)(ρ,ς), where e(s) accounts for shear through the first invariant of the Cauchy-Green tensor, and e(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e(h)=e(h)(ρ), with a power-law dependence e(h) is proportional to ρ(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M is proportional to [log(1/R)](α), independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M is proportional to R(-(s-1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part e(h) is that of an ideal gas, is also tested, recovering the strong-shock limit M is proportional to R(-(s-1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ-1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the
Analysis of elastic-plastic dynamic response of reinforced concrete frame structure
Li Zhongcheng
2009-01-01
Based on a set of data from seismic response test on an R/C frame, a force-based R/C beam fibre model with non-linear material properties and bond-slip effects are presented firstly in this paper, and then the applications to the tested R/C frame are presented to illustrate the model characteristics and to show the accuracy of seismic analysis including consideration of non-linear factors. It can be concluded that the elastic-plastic analysis is a potential step toward the accurate modelling for the dynamic analyses of R/C structures. Especially for the seismic safety re-evaluation of the existing NPPs, the elastic-plastic methodology with consideration of different non-linearities should be involved. (author)
Computer implementation of an elastic-plastic concrete relationship
Murray, D.W.; Chitnuyanondh, L.; Wong, C.
1979-01-01
The purpose of this paper is to describe the difficulties that arose, and the strategies that were developed to overcome these difficulties, during the incorporation of a relatively complex elastic-plastic concrete constitutive relationship into an existing computer code for the analysis of axisymmetric loading acting on thin shells of revolution. The program had the capability of elastic-plastic analysis using a von-Mises yield curve prior to any modification by the writers. (orig.)
Simplified method for elastic plastic analysis of material presenting bilinear kinematic hardening
Roche, R.
1983-12-01
A simplified method for elastic plastic analysis is presented. Material behavior is assumed to be elastic plastic with bilinear kinematic hardening. The proposed method give a strain-stress field fullfilling material constitutive equations, equations of equilibrium and continuity conditions. This strain-stress is obtained through two linear computations. The first one is the conventional elastic analysis of the body submitted to the applied load. The second one use tangent matrix (tangent Young's modulus and Poisson's ratio) for the determination of an additional stress due to imposed initial strain. Such a method suits finite elements computer codes, the most useful result being plastic strains resulting from the applied loading (load control or deformation control). Obviously, there is not unique solution, for stress-strain field is not depending only of the applied load, but of the load history. Therefore, less pessimistic solutions can be got by one or two additional linear computations [fr
Hsu, T.R.; Bertels, A.W.M.; Banerjee, S.; Harrison, W.C.
1976-07-01
This report presents the theoretical basis for a transient thermal elastic-plastic stress analysis of a nuclear reactor fuel element subject to severe transient thermo-mechanical loading. A finite element formulation is used for both the non-linear stress analysis and thermal analysis. These two major components are linked together to form an integrated program capable of predicting fuel element transient behaviour in two dimensions. Specific case studies are presented to illustrate capabilities of the analysis. (author)
Prediction of fretting fatigue behavior under elastic-plastic conditions
Shin, Ki Su
2009-01-01
Fretting fatigue generally leads to the degradation of the fatigue strength of a material due to cyclic micro-slip between two contacting materials. Fretting fatigue is regarded as an important issue in designing aerospace structures. While many studies have evaluated fretting fatigue behavior under elastic deformation conditions, few have focused on fretting fatigue behavior under elastic-plastic deformation conditions, especially the crack orientation and fatigue life prediction for Ti-6Al-4V. The primary goal of this study was to characterize the fretting fatigue crack initiation behavior in the presence of plasticity. Experimental tests were performed using pad configurations involving elastic-plastic deformations. To calculate stress distributions under elastic-plastic fretting fatigue conditions, FEA was also performed. Several parametric approaches were used to predict fretting fatigue life along with stress distribution resulting from FEA. However, those parameters using surface stresses were unable to establish an equivalence between elastic fretting fatigue data and elastic-plastic fretting fatigue data. Based on this observation, the critical distance methods, which are commonly used in notch analysis, were applied to the fretting fatigue problem. In conclusion, the effective strain range method when used in conjunction with the SMSSR parameter showed a good correlation of data points between the pad configurations involving elastic and elastic plastic deformations
Elastic-plastic analysis of fracture mechanics test specimens. Part 2
Talja, H.; Wallin, K.
1984-12-01
This is second part of the report of the research program 'Comparisons between computational and experimental elastic-plastic results' started at the Technical Research Centre of Finland in 1981. The first part of the research program was reported earlier and contained a two dimensional linear elastic finite element analysis of four specimen geometries (CT, RCT, ASTM-3P and Charpy-V) and testing and elastic-plastic analysis of the specimen (EGF71; 1TCT, material A 542). In this report the second part of the program containing the testing and 2-D elastic-plastic analyses of five specimens is described. The four specimen geometries mentioned above and two different materials (stainless steel AISI 304 and ferrite pressure vessel steel A533B) are considered. The following comparisons are presented in the report: load vs. load displacement curves, J-integral, crack opening displacement (COD), J vs. COD and the size of the plastic zone. The agreement between the computational and experimental results is quite good. Complete agreement can be achieved only with 3-dimensional calculation models. (author)
Elastic-plastic fracture mechanics of compact bone
Yan, Jiahau
Bone is a composite composed mainly of organics, minerals and water. Most studies on the fracture toughness of bone have been conducted at room temperature. Considering that the body temperature of animals is higher than room temperature, and that bone has a high volumetric percentage of organics (generally, 35--50%), the effect of temperature on fracture toughness of bone should be studied. Single-edged V-shaped notched (SEVN) specimens were prepared to measure the fracture toughness of bovine femur and manatee rib in water at 0, 10, 23, 37 and 50°C. The fracture toughness of bovine femur and manatee rib were found to decrease from 7.0 to 4.3 MPa·m1/2 and from 5.5 to 4.1 MPa·m1/2, respectively, over a temperature range of 50°C. The decreases were attributed to inability of the organics to sustain greater stresses at higher temperatures. We studied the effects of water and organics on fracture toughness of bone using water-free and organics-free SEVN specimens at 23°C. Water-free and organics-free specimens were obtained by placing fresh bone specimen in a furnace at different temperatures. Water and organics significantly affected the fracture toughness of bone. Fracture toughness of the water-free specimens was 44.7% (bovine femur) and 32.4% (manatee rib) less than that of fresh-bone specimens. Fracture toughness of the organics-free specimens was 92.7% (bovine femur) and 91.5% (manatee rib) less than that of fresh bone specimens. Linear Elastic Fracture Mechanics (LEFM) is widely used to study bone. However, bone often has small to moderate scale yielding during testing. We used J integral, an elastic-plastic fracture-mechanics parameter, to study the fracture process of bone. The J integral of bovine femur increased from 6.3 KJ/mm2 at 23°C to 6.7 KJ/mm2 at 37°C. Although the fracture toughness of bovine bone decreases as the temperature increases, the J integral results show a contrary trend. The energy spent in advancing the crack beyond the linear
Elastic-plastic transition: A universal law
Chen Zhong
2016-01-01
Full Text Available Although the initial stress-strain behavior in a tensile test is often characterized as linear elastic up to a yield stress and nonlinear plastic thereafter, the pre-yield transition region is known to exhibit significant curvature and hysteresis. Hundreds of high-precision loading-unloading-loading tensile tests were performed using 26 commercial sheet alloys exhibiting a wide range of strength, ductility and crystal structure. Analysis of the results reveals the following: 1.There is no significant linear elastic region; the proportional limit is ~0 MPa when measured with sufficient sensitivity. 2.Each of the hundreds of measured transitional stress-strain curves can be characterized by a single parameter, here called the “modulus reduction rate.”The corresponding equation captures ~80% of the observed variation, a factor of 3 to 6 better than a one-parameter linear approximation. 3.Most interestingly, the transitional behavior for all alloys follows a “Universal Law” requiring no fit parameters. The law depends only upon the strength of the material and its Young’s modulus, both of which are can be measured by independent tests or adopted from handbooks. The Universal Law captures ~90% of the variation represented by the one-parameter representation and eliminates the need for mechanical testing to implement and apply. The practical and theoretical implications of these results are discussed. The results provide a simple path to significantly improving applied constitutive models in the transitional regime. The consistency of the effect for such a wide range of metals and suggests that the origin of the behavior lies in the pile-up and relaxation of dislocation arrays.
Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration.
Piriz, A R; Sun, Y B; Tahir, N A
2015-03-01
A model is presented for the linear Rayleigh-Taylor instability taking place at the early stage of acceleration of an elastic-plastic solid, when the shock wave is still running into the solid and is driven by a time varying pressure on the interface. When the the shock is formed sufficiently close to the interface, this stage is considered to follow a previous initial phase controlled by the Ritchmyer-Meshkov instability that settles new initial conditions. The model reproduces the behavior of the instability observed in former numerical simulation results and provides a relatively simpler physical picture than the currently existing one for this stage of the instability evolution.
Multiaxial probabilistic elastic-plastic constitutive simulations of soils
Sadrinezhad, Arezoo
Fokker-Planck-Kolmogorov (FPK) equation approach has recently been developed to simulate elastic-plastic constitutive behaviors of materials with uncertain material properties. The FPK equation approach transforms the stochastic constitutive rate equation, which is a stochastic, nonlinear, ordinary differential equation (ODE) in the stress-pseudo time space into a second-order accurate, deterministic, linear FPK partial differential equation (PDE) in the probability density of stress-pseudo time space. This approach does not suffer from the drawbacks of the traditional approaches such as the Monte Carlo approach and the perturbation approach for solving nonlinear ODEs with random coefficients. In this study, the existing one dimensional FPK framework for probabilistic constitutive modeling of soils is extended to multi--dimension. However, the multivariate FPK PDEs cannot be solved using the traditional mathematical techniques such as finite difference techniques due to their high computational cost. Therefore, computationally efficient algorithms based on the Fourier spectral approach are developed for solving a class of FPK PDEs that arises in probabilistic elasto-plasticity. This class includes linear FPK PDEs in (stress) space and (pseudo) time - having space-independent but time-dependent, and both space- and time-dependent coefficients - with impulse initial conditions and reflecting boundary conditions. The solution algorithms, rely on first mapping the stress space of the governing PDE between 0 and 2pi using the change of coordinates rule, followed by approximating the solution of the PDE in the 2pi-periodic domain by a finite Fourier series in the stress space and unknown time-dependent solution coefficients. Finally, the time-dependent solution coefficients are obtained from the initial condition. The accuracy and efficiency of the developed algorithms are tested. The developed algorithms are used to simulate uniaxial and multiaxial, monotonic and cyclic
An elastic-plastic contact model for line contact structures
Zhu, Haibin; Zhao, Yingtao; He, Zhifeng; Zhang, Ruinan; Ma, Shaopeng
2018-06-01
Although numerical simulation tools are now very powerful, the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications. For the line contact structures widely used in the engineering field, few analytical models are available for predicting the mechanical behaviour when the structures deform plastically, as the classic Hertz's theory would be invalid. Thus, the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism. A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained. The proposed model was verified through an actual line contact test and a corresponding numerical simulation. The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.
A calculational round robin in elastic-plastic fracture mechanics
Larsson, L.H.
Eighteen organizations participated in this round robin which treated the same three-point bend problem as an ASTM round robin four years earlier. Overall deformation, J, CTOD and crack profile were the main results required using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. All elastic solutions were accurate to within a few percent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. Apparently no significant progress has taken place in the state of the art of numerical EPFM analysis in four years time. The paper discusses the reasons for this scatter and draws tentative conclusions on the most suitable numerical analysis methods in EPFM. (Auth.)
Progress in elastic-plastic fracture mechanics and its applications
Paris, P.C.; Zahalak, G.I.
1980-01-01
This paper surveys recent developments in the application of J-Integral methods to problems of elastic-plastic fracture. The analytical and experimental development of the J-Integral concept over the last ten years is reviewed briefly. Tearing instability theory is presented in general terms, and specific applications of the theory are discussed. Principles of fracture-proof design are shown to follow naturally from the tearing instability theory. These principles are illustrated first for simple structures, and then generalized to more complex configurations and loading conditions. Examples include multiple member tension structures, beams, frames, nuclear reactor pressure vessel nozzles and piping, and beams on elastic foundations. It is concluded that J-integral based methods offer the best immediate opportunity for the development of sound analytical techniques for treating important practical problems of elastic-plastic fracture
Lang, Hermann, E-mail: hermann.lang@areva.com [AREVA NP GmbH, PEEA-G, Henri-Dunant-Strasse 50, 91058 Erlangen (Germany); Rudolph, Juergen; Ziegler, Rainer [AREVA NP GmbH, PEEA-G, Henri-Dunant-Strasse 50, 91058 Erlangen (Germany)
2011-08-15
As code-based fully elastic plastic code conforming fatigue analyses are still time consuming, simplified elastic plastic analysis is often applied. This procedure is known to be overly conservative for some conditions due to the applied plastification (penalty) factor K{sub e}. As a consequence, less conservative fully elastic plastic fatigue analyses based on non-linear finite element analyses (FEA) or simplified elastic plastic analysis based on more realistic K{sub e} factors have to be used for fatigue design. The demand for more realistic K{sub e} factors is covered as a requirement of practical fatigue analysis. Different code-based K{sub e} procedures are reviewed in this paper with special regard to performance under thermal cyclic loading conditions. Other approximation formulae such as those by Neuber, Seeger/Beste or Kuehnapfel are not evaluated in this context because of their applicability to mechanical loading excluding thermal cyclic loading conditions typical for power plant operation. Besides the current code-based K{sub e} corrections, the ASME Code Case N-779 (e.g. Adam's proposal) and its modification in ASME Section VIII is considered. Comparison of elastic plastic results and results from the Rules for Nuclear Facility Components and Rules for Pressure Vessels reveals a considerable overestimation of usage factor in the case of ASME III and KTA 3201.2 for the examined examples. Usage factors according to RCC-M, Adams (ASME Code Case N-779), ASME VIII (alternative) and EN 13445-3 are essentially comparable and less conservative for these examples. The K{sub v} correction as well as the applied yield criterion (Tresca or von Mises) essentially influence the quality of the more advanced plasticity corrections (e.g. ASME Code Case N-779 and RCC-M). Hence, new proposals are based on a refined K{sub v} correction.
Lang, Hermann; Rudolph, Juergen; Ziegler, Rainer
2011-01-01
As code-based fully elastic plastic code conforming fatigue analyses are still time consuming, simplified elastic plastic analysis is often applied. This procedure is known to be overly conservative for some conditions due to the applied plastification (penalty) factor K e . As a consequence, less conservative fully elastic plastic fatigue analyses based on non-linear finite element analyses (FEA) or simplified elastic plastic analysis based on more realistic K e factors have to be used for fatigue design. The demand for more realistic K e factors is covered as a requirement of practical fatigue analysis. Different code-based K e procedures are reviewed in this paper with special regard to performance under thermal cyclic loading conditions. Other approximation formulae such as those by Neuber, Seeger/Beste or Kuehnapfel are not evaluated in this context because of their applicability to mechanical loading excluding thermal cyclic loading conditions typical for power plant operation. Besides the current code-based K e corrections, the ASME Code Case N-779 (e.g. Adam's proposal) and its modification in ASME Section VIII is considered. Comparison of elastic plastic results and results from the Rules for Nuclear Facility Components and Rules for Pressure Vessels reveals a considerable overestimation of usage factor in the case of ASME III and KTA 3201.2 for the examined examples. Usage factors according to RCC-M, Adams (ASME Code Case N-779), ASME VIII (alternative) and EN 13445-3 are essentially comparable and less conservative for these examples. The K v correction as well as the applied yield criterion (Tresca or von Mises) essentially influence the quality of the more advanced plasticity corrections (e.g. ASME Code Case N-779 and RCC-M). Hence, new proposals are based on a refined K v correction.
Theory of reversal nonisothermal elastic-plastic deformation
Shorr, B.F.
1979-01-01
Considered is approximated theory of nonisothermal elastic-plastic deformation at arbitrary laws of loading, permitting to describe nonisothermal isotropic and anisotropic strengthening of the material, Bauschinger effect and different tempo of plastic deformation development over different directions of loading depending on the deformation prehistory. The comparison of the theory with the experimental data showed good coincidence and sufficient simplicity permits to use it in technical calcualtions
Dynamics of shock waves in elastic-plastic solids
Favrie , Nicolas; Gavrilyuk , Sergey ,
2010-01-01
Submitted in ESAIM Procedings; The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the ability of the model to deal with complex physical phenomena.
Elastic-plastic analysis of the SS-3 tensile specimen
Majumdar, S.
1998-01-01
Tensile tests of most irradiated specimens of vanadium alloys are conducted using the miniature SS-3 specimen which is not ASTM approved. Detailed elastic-plastic finite element analysis of the specimen was conducted to show that, as long as the ultimate to yield strength ratio is less than or equal to 1.25 (which is satisfied by many irradiated materials), the stress-plastic strain curve obtained by using such a specimen is representative of the true material behavior
A calculational round robin in elastic-plastic fracture mechanics
Larsson, L.H.
1983-01-01
Eighteen organisations participated in this elastic-plastic fracture mechanics (EPFM) numerical analysis round robin which treated the same three-point bend problem as a similar round robin conducted by ASTM four years earlier. The work involved the calculation of overall deformation, J, CTOD and crack profile using plane strain elastic-plastic finite element analysis for a monotonically increasing load up to a maximum deformation which was far beyond the elastic regime. It was found that all of the elastic solutions were accurate to within a few per cent. In the elastic-plastic regime, however, there was a large scatter of the results, increasing with increasing plastic deformation and roughly of the same order as in the ASTM round robin which contained ten solutions. No significant progress has taken place in the state of the art of numerical EPFM analysis over the four-year interval. The reasons for this scatter and tentative conclusions on the most suitable numerical analysis methods in EPFM are discussed. (author)
Elastic-plastic fracture analysis of carbon steel piping using the latest CEGB R6 approach
Kanno, S.; Hasegawa, K.; Shimizu, T.; Kobayashi, H.
1991-01-01
The elastic-plastic fracture of carbon steel piping having various pipe diameters and circumferential crack angles and subjected to a bending moment is analyzed using the latest United Kingdom Central Electricity Generating Board R6 approach. The elastic-plastic fracture criterion must be applied instead of the plastic collapse criterion with increase of the pipe diameter and the crack angle. A simplified elastic-plastic fracture analysis procedure based on the R6 approach is proposed. (author)
Finite element elastic-plastic analysis of LMFBR components
Levy, A.; Pifko, A.; Armen, H. Jr.
1978-01-01
The present effort involves the development of computationally efficient finite element methods for accurately predicting the isothermal elastic-plastic three-dimensional response of thick and thin shell structures subjected to mechanical and thermal loads. This work will be used as the basis for further development of analytical tools to be used to verify the structural integrity of liquid metal fast breeder reactor (LMFBR) components. The methods presented here have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. These methods include the use of optimal stress points as well as a variable number of stress points within an element. This allows monitoring the stress history at many points within an element and hence provides an accurate representation of the elastic-plastic boundary using a minimum number of degrees of freedom. Also included is an improved thermal stress analysis capability in which the temperature variation and corresponding thermal strain variation are represented by the same functional form as the displacement variation. Various problems are used to demonstrate these improved capabilities. (Auth.)
Elastic, plastic, fracture analysis of masonry arches: A multi-span bridge case study
Lacidogna, Giuseppe; Accornero, Federico
2018-01-01
In this work a comparison is presented between elastic, plastic, and fracture analysis of the monumental arch bridge of Porta Napoli, Taranto (Italy). By means of a FEM model and applying the Mery's Method, the behavior of the curved structure under service loads is verified, while considering the Safe Theorem approach byHeyman, the ultimate carrying capacity of the structure is investigated. Moreover, by using Fracture Mechanics concepts, the damage process which takes place when the conditions assessed through linear elastic analysis are no longer valid, and before the set-in of the conditions established by means of the plastic limit analysis, is numerically analyzed. The study of these transitions returns an accurate and effective whole service life assessment of the Porta Napoli masonry arch bridge.
Elastic-plastic analysis of part-through crack propagation in piping and pressure vessels
Souza, L.A. de; Ebecken, N.F.F.
1986-01-01
The shell structures, often used in the construction of reservoirs, pipings, pressure vessels, nuclear power plants, etc, with part-through crack along its thickness, are analysed, using a computer system developed by the finite element method. The surface is discretized with three-dimensional quadratic elements, degenerated in its mid-surface, such the fracture is simulated by scalar elements (non linear springs). The results are analysed by the stress intensity factor K Sub(I) and the strain energy release rate, which is known as J-integral. The analysis is performed in the elastic and elastic-plastic regime. The basic hipothesis and the formulation adopted in the derivation of the scalar elements are also shown. (Author) [pt
Electrical resistivity response due to elastic-plastic deformations
Stout, R.B.
1987-01-01
The electrical resistivity of many materials is sensitive to changes in the electronic band configurations surrounding the atoms, changes in the electron-phonon interaction cross-sections, and changes in the density of intrinsic defect structures. These changes are most directly dependent on interatomic measures of relative deformation. For this reason, a model for resistivity response is developed in terms of interatomic measures of relative deformation. The relative deformation consists of two terms, a continuous function to describe the recoverable displacement between two atoms in the atomic lattice structure and a functional to describe the nonrecoverable displacement between two atoms as a result of interatomic discontinuities from dislocation kinetics. This model for resistivity extends the classical piezoresistance representation and relates electric resistance change directly to physical mechanisms. An analysis for the resistivity change of a thin foil ideally embedded in a material that undergoes elastic-plastic deformation is presented. For the case of elastic deformations, stress information in the material surrounding the thin foil is inferred for the cases of pure strain coupling boundary conditions, pure stress coupling boundary conditions, and a combination of stress-strain coupling boundary conditions. 42 refs., 4 figs
Mesoscopic approach to modeling elastic-plastic polycrystalline material behaviour
Kovac, M.; Cizelj, L.
2001-01-01
Extreme loadings during severe accident conditions might cause failure or rupture of the pressure boundary of a reactor coolant system. Reliable estimation of the extreme deformations can be crucial to determine the consequences of such an accident. One of important drawbacks of classical continuum mechanics is idealization of inhomogenous microstructure of materials. This paper discusses the mesoscopic approach to modeling the elastic-plastic behavior of a polycrystalline material. The main idea is to divide the continuum (e.g., polycrystalline aggregate) into a set of sub-continua (grains). The overall properties of the polycrystalline aggregate are therefore determined by the number of grains in the aggregate and properties of randomly shaped and oriented grains. The random grain structure is modeled with Voronoi tessellation and random orientations of crystal lattices are assumed. The elastic behavior of monocrystal grains is assumed to be anisotropic. Crystal plasticity is used to describe plastic response of monocrystal grains. Finite element method is used to obtain numerical solutions of strain and stress fields. The analysis is limited to two-dimensional models.(author)
Elastic-plastic analysis of tube expansion in tubesheets
Kasraie, B.; O'Donnell, W.J.; Porowski, J.S.; Selz, A.
1983-01-01
Conditions for expansion of tubes in tubesheets are often determined by the test. The tightness of the joint and pull out force are used as criteria for evaluation of the results. For closely spaced tubes, it is also necessary to control development of the plastic regions in the ligaments surrounding the tube being expanded. High local strains may occur and excessive distortion may result if the expansion of the tube is continued beyond the admissible limits. Elastic-plastic finite element analyses are performed herein in order to establish conditions for rolling of the tubes in tubesheets of low ligament efficiency. Such penetration patterns are often required in the design of tubular reactors for catalytic processes. The model considered includes individual tube expansion in tubesheets with triangular penetration patterns. The effect of prior expansion of the neighboring tubes is also evaluated. Gap elements are used to model the initial clearance of the tube in the hole. Development of the plastic zones and distortion of the ligaments is monitored during radial expansion of the tube diameter. The residual stresses between the tube and the hole surface and the history of gap closing after removal of the expansion tool are determined. The effect of axial extension of the tube on the tube thinning is determined. Tube thinning is often used as a measure of tube expansion in manufacturing processes. For the analyzed ligament efficiency, reliable joints are obtained for a thinning range within 2% to 3%
Asymptotic techniques in elastic-plastic analysis of structures
Sayir, M.
1983-01-01
Elastic-plastic structures can nowadays be analyzed with the powerful numerical procedures of the finite element method. Nevertheless, in many engineering applications, analytical expressions capable of predicting with sufficient accuracy the stress distributions, the extent of the plastic zones and the load displacement behaviour could be of great practical value. For simple structures and loading stages not too far from the elastic limit, such analytical expressions may be obtained by using perturbation methods and asymptotic expansions. A small dimensionless parameter epsilon is defined as the ratio of a length characterizing the extent of the narrow plastic zone, to a conveniently chosen typical dimension of the structure. Stresses and displacements are formally expanded as asymptotic series in terms of powers of epsilon. For each order of magnitude, the exact basic relations lead to a separate set of simplified differential equations which can be integrated analytically or numerically by using standard procedures. The method is very general and can be applied to several classes of plastic behaviour and of structural problems. Three examples of very simple structures are chosen in particular to illustrate the applicability of the perturbation method to engineering problems. (orig./RW)
Elastic Plastic Fracture Analysis of an Aluminum COPV Liner
Forth, Scott; Gregg, Bradley; Bailey, Nathaniel
2012-01-01
Onboard any space-launch vehicle, composite over-wrapped pressure vessels (COPVs) may be utilized by propulsion or environmental control systems. The failure of a COPV has the potential to be catastrophic, resulting in the loss of vehicle, crew or mission. The latest COPV designs have reduced the wall-thickness of the metallic liner to the point where the material strains plastically during operation. At this time, the only method to determine the damage tolerance lifetime (safe-life) of a plastically responding metallic liner is through full-scale COPV testing. Conducting tests costs substantially more and can be far more time consuming than performing an analysis. As a result of this cost, there is a need to establish a qualifying process through the use of a crack growth analysis tool. This paper will discuss fracture analyses of plastically responding metallic liners in COPVs. Uni-axial strain tests have been completed on laboratory specimens to collect elastic-plastic crack growth data. This data has been modeled with the crack growth analysis tool, NASGRO 6.20 to predict the response of laboratory specimens and subsequently the complexity of a COPV.
comparison of elastic-plastic FE method and engineering method for RPV fracture mechanics analysis
Sun Yingxue; Zheng Bin; Zhang Fenggang
2009-01-01
This paper described the FE analysis of elastic-plastic fracture mechanics for a crack in RPV belt line using ABAQUS code. It calculated and evaluated the stress intensity factor and J integral of crack under PTS transients. The result is also compared with that by engineering analysis method. It shows that the results using engineering analysis method is a little larger than the results using FE analysis of 3D elastic-plastic fracture mechanics, thus the engineering analysis method is conservative than the elastic-plastic fracture mechanics method. (authors)
Asperity interaction in elastic-plastic contact of rough surfaces in presence of adhesion
Sahoo, Prasanta; Banerjee, Atanu
2005-01-01
This paper presents an analysis of the effect of asperity interaction in elastic-plastic contact of rough surfaces in the presence of adhesion. The micro-contact model of asperity interactions, developed by Zhao and Chang (2001 Trans. ASME: J. Tribol. 123 857-64), is integrated into the elastic-plastic contact model developed by Roy Chowdhury and Ghosh (1994 Wear 174 9-19) to allow the asperity interaction and elastic-plastic deformation in the presence of surface forces to be considered simultaneously. The well-established elastic and plastic adhesion indices are used to consider the different conditions that arise as a result of varying load and material parameters. Results show that asperity interaction influences the loading-unloading behaviour in elastic-plastic adhesive contact of rough surfaces and in general asperity interactions reduce the effect of surface forces
Park, Jai Hak
2009-01-01
SGBEM(Symmetric Galerkin Boundary Element Method)-FEM alternating method has been proposed by Nikishkov, Park and Atluri. In the proposed method, arbitrarily shaped three-dimensional crack problems can be solved by alternating between the crack solution in an infinite body and the finite element solution without a crack. In the previous study, the SGBEM-FEM alternating method was extended further in order to solve elastic-plastic crack problems and to obtain elastic-plastic stress fields. For the elastic-plastic analysis the algorithm developed by Nikishkov et al. is used after modification. In the algorithm, the initial stress method is used to obtain elastic-plastic stress and strain fields. In this paper, elastic-plastic J integrals for three-dimensional cracks are obtained using the method. For that purpose, accurate values of displacement gradients and stresses are necessary on an integration path. In order to improve the accuracy of stress near crack surfaces, coordinate transformation and partitioning of integration domain are used. The coordinate transformation produces a transformation Jacobian, which cancels the singularity of the integrand. Using the developed program, simple three-dimensional crack problems are solved and elastic and elastic-plastic J integrals are obtained. The obtained J integrals are compared with the values obtained using a handbook solution. It is noted that J integrals obtained from the alternating method are close to the values from the handbook
Lester, Brian T. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William M. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
Lester, Brian [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Scherzinger, William [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2017-01-19
Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.
Chung, Nam Yong; Kim, Moon Young; Kim, Jong Woo
1999-01-01
In the study, the analysis of elastic-plastic J-integral was performed in high temperature components for gas turbine based on elastic-plastic fracture mechanics. It had been operated on the range of about 700 deg C and degraded by high temperature. It was tested for material properties of used component because of material properties changing at high temperature condition. The elastic-plastic fracture mechanics parameter, J is obtained with finite element method. A method is suggested which determines J Ic applying analysis of elastic-plastic finite element method and results of experimental load-displacements with CT specimen. It is also investigated that J-integral is applied for the elastic-plastic analysis in high temperature components. The elastic-plastic fracture toughness. J Ic determined by finite element was obtained with high accuracy using the experimental method.=20
Adhesive friction for elastic-plastic contacting rough surfaces considering asperity interaction
Sahoo, Prasanta
2006-01-01
The paper describes a theoretical study of adhesive friction at the contact between rough surfaces taking asperity interaction into consideration and using an elastic-plastic model of contact deformation that is based on an accurate finite element analysis of an elastic-plastic single asperity contact. The micro-contact model of asperity interactions, developed by Zhao and Chang, is integrated into the improved elastic-plastic rough surface adhesive contact analysis to consider the adhesive friction behaviour of rough surfaces. The model considers a large range of interference values from fully elastic through elastic-plastic to fully plastic regimes of contacting asperities. Two well-established adhesion indices are used to consider different conditions that arise as a result of varying load, surface and material parameters. Results are obtained for the coefficient of friction against applied load for various combinations of these parameters. The results show that the coefficient of friction depends strongly on the applied load for the no-interaction case while it becomes insensitive to the load for interaction consideration. Moreover, the inclusion of elastic-plastic asperities further reduces the friction coefficient
Elastic-plastic analysis of the toroidal field coil inner leg of the compact ignition tokamak
Horie, T.
1987-07-01
Elastic-plastic analyses were made for the inner leg of the Compact Ignition Tokamak toroidal field (TF) coil, which is made of copper-Inconel composite material. From the result of the elastic-plastic analysis, the effective Young's moduli of the inner leg were determined by the analytical equations. These Young's moduli are useful for the three-dimensional, elastic, overall TF coil analysis. Comparison among the results of the baseline design (R = 1.324 m), the bucked pressless design, the 1.527-m major radius design, and the 1.6-m major radius design was also made, based on the elastic-plastic TF coil inner leg analyses
Prediction of elastic-plastic response of structural elements subjected to cyclic loading
El Haddad, M.H.; Samaan, S.
1985-01-01
A simplified elastic-plastic analysis is developed to predict stress strain and force deformation response of structural metallic elements subjected to irregular cyclic loadings. In this analysis a simple elastic-plastic method for predicting the skeleton force deformation curve is developed. In this method, elastic and fully plastic solutions are first obtained for unknown quantities, such as deflection or local strains. Elastic and fully plastic contributions are then combined to obtain an elastic-plastic solution. The skeleton curve is doubled to establish the shape of the hysteresis loop. The complete force deformation response can therefore be simulated through reversal by reversal in accordance with hysteresis looping and material memory. Several examples of structural elements with various cross sections made from various materials and subjected to irregular cyclic loadings, are analysed. A close agreement is obtained between experimental results found in the literature and present predictions. (orig.)
Two-zone elastic-plastic single shock waves in solids.
Zhakhovsky, Vasily V; Budzevich, Mikalai M; Inogamov, Nail A; Oleynik, Ivan I; White, Carter T
2011-09-23
By decoupling time and length scales in moving window molecular dynamics shock-wave simulations, a new regime of shock-wave propagation is uncovered characterized by a two-zone elastic-plastic shock-wave structure consisting of a leading elastic front followed by a plastic front, both moving with the same average speed and having a fixed net thickness that can extend to microns. The material in the elastic zone is in a metastable state that supports a pressure that can substantially exceed the critical pressure characteristic of the onset of the well-known split-elastic-plastic, two-wave propagation. The two-zone elastic-plastic wave is a general phenomenon observed in simulations of a broad class of crystalline materials and is within the reach of current experimental techniques.
ELASTIC-PLASTIC AND RESIDUAL STRESS ANALYSIS OF AN ALUMINUM DISC UNDER INTERNAL PRESSURES
Numan Behlül BEKTAŞ
2004-02-01
Full Text Available This paper deals with elastic-plastic stress analysis of a thin aluminum disc under internal pressures. An analytical solution is performed for satisfying elastic-plastic stress-strain relations and boundary conditions for small plastic deformations. The Von-Mises Criterion is used as a yield criterion, and elastic perfectly plastic material is assumed. Elastic-plastic and residual stress distributions are obtained from inner radius to outer radius, and they are presented in tables and figures. All radial stress components, ?r, are compressive, and they are highest at the inner radius. All tangential stress components, ??, are tensile, and they are highest where the plastic deformation begins. Magnitude of the tangential residual stresses is higher than those the radial residual stresses.
An Elastic Plastic Contact Model with Strain Hardening for the LAMMPS Granular Package
Kuhr, Bryan [Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States); Brake, Matthew Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Component Science and Mechanics; Lechman, Jeremy B. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Nanoscale and Reactive Processes
2015-03-01
The following details the implementation of an analytical elastic plastic contact model with strain hardening for normal im pacts into the LAMMPS granular package. The model assumes that, upon impact, the co llision has a period of elastic loading followed by a period of mixed elastic plas tic loading, with contributions to each mechanism estimated by a hyperbolic seca nt weight function. This function is implemented in the LAMMPS source code as the pair style gran/ep/history. Preliminary tests, simulating the pouring of pure nickel spheres, showed the elastic/plastic model took 1.66x as long as similar runs using gran/hertz/history.
Elastic-plastic deformation of fiber composites with a tetragonal structure
Makarova, E.IU.; Svistkova, L.A. (Permskii Politekhnicheskii Institut, Perm (USSR))
1991-02-01
Results of numerical solutions are presented for elastic-plastic problems concerning arbitrary loading of unidirectional composites in the transverse plane. The nucleation and evolution of microplastic zones in the matrix and the effect of this process on the macroscopic characteristics of the composite are discussed. Attention is also given to the effect of the fiber shape on the elastic-plastic deformation of the matrix and to deformation paths realized in simple microdeformation processes. The discussion is illustrated by results obtained for a composite consisting of a VT1-0 titanium alloy matrix reinforced by Ti-Mo fibers.
Elastic-plastic Fracture Mechanics Assessment of nozzle corners submitted to thermal shock loading
Chapuliot, S.; Marie, S.
2016-01-01
This paper focuses on the development of a simplified analytical scheme for the elastic-plastic Fracture Mechanics Assessment of large nozzle corners. Within that frame, following the specific numerical effort performed for the definition of a Stress Intensity Factor compendium, complementary elastic-plastic developments are proposed here for the consideration of the thermal shock loading in the elastic-plastic domain: this type of loading is a major loading for massive structures such as nozzle corners of large components. Thus, an important numerical was performed in order to extend the applicability domain of existing analytical schemes to those complex geometries. The final formulation is a simple one, applicable to a large variety of materials and geometrical configurations as long as the structure is large and the defect remains small in comparison to the internal radius of the nozzle. - Highlights: • Fracture Mechanics Assessment of large nozzle corners. • Elastic-plastic Stress Intensity Factor determination under thermal shock loading. • Semi-analytical schemes for J calculation.
Practical solution of plastic deformation problems in elastic-plastic range
Mendelson, A; Manson, S
1957-01-01
A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.
Elastic-plastic-creep analysis of brazed carbon-carbon/OFHC divertor tile concepts for TPX
Chin, E.; Reis, E.E.
1995-01-01
The 7.5 MW/m 2 heat flux requirements for the TPX divertor necessitate the use of high conductivity carbon-carbon (C-C) tiles that are brazed to annealed copper (OFHC) coolant tubes. Significant residual stresses are developed in the C-C tiles during the braze process due to large differences in the thermal expansion coefficients between these materials. Analyses which account for only the elastic-plastic strains developed in the OFHC tube may not accurately characterize the behavior of the tube during brazing. The elevated temperature creep behavior of the copper coolant tubes intuitively should reduce the calculated residual stresses in the C-C tiles. Two divertor tile concepts, the monoblock and the archblock, were analyzed for residual stress using 2-D finite element analysis for elastic-plastic-creep behavior of the OFHC tube during an assumed braze cooldown cycle. The results show that the inclusion of elevated temperature creep effects decrease the calculated residual stresses by only about 10% when compared to those analyses in which only elastic-plastic behavior of the OFHC is accounted for. The primary reason that creep effects at higher temperatures are not more significant is due to the low yield stress and nearly flat-top stress-strain curve of annealed OFHC. Since high temperature creep plays less of a role in the residual stress levels than previously thought, future scoping studies can be done in an elastic-plastic analysis with confidence that the stresses will be within approximately 10% of an elastic-plastic-creep analysis
A elastic-plastic model for pipe whip
Maneschy, J.E.A.
1980-04-01
The dynamic behavior of a cantilever beam simulating a pipe after full rupture at a given cross-section is investigated. This problem, known as pipe whip, has to be analysed within the frame of plastic deformations. The physical model is represented by a cantilever, subjected to a step-load at the free end, and a support designed to absorb the maximum possible kinetic energy of the tube generated by suddenly applied force. The analysis is performed using the Bernoulli theory for straight beams, assuming for the moment-curvature relation a bi-linear law. (author)
Hutula, D.N.; Wiancko, B.E.
1980-03-01
ACCEPT is a three-dimensional finite element computer program for analysis of large-deformation elastic-plastic-creep response of Zircaloy tubes subjected to temperature, surface pressures, and axial force. A twenty-mode, tri-quadratic, isoparametric element is used along with a Zircaloy materials model. A linear time-incremental procedure with residual force correction is used to solve for the time-dependent response. The program features an algorithm which automatically chooses the time step sizes to control the accuracy and numerical stability of the solution. A contact-separation capability allows modeling of interaction of reactor fuel rod cladding with fuel pellets or external supports
Elastic-plastic failure analysis of pressure burst tests of thin toroidal shells
Jones, D.P.; Holliday, J.E.; Larson, L.D.
1998-07-01
This paper provides a comparison between test and analysis results for bursting of thin toroidal shells. Testing was done by pressurizing two toroidal shells until failure by bursting. An analytical criterion for bursting is developed based on good agreement between structural instability predicted by large strain-large displacement elastic-plastic finite element analysis and observed burst pressure obtained from test. The failures were characterized by loss of local stability of the membrane section of the shells consistent with the predictions from the finite element analysis. Good agreement between measured and predicted burst pressure suggests that incipient structural instability as calculated by an elastic-plastic finite element analysis is a reasonable way to calculate the bursting pressure of thin membrane structures
A comparison of time-history elastic plastic piping analysis with measurement
Scavuzzo, R.J.; Sansalone, K.H.
1992-01-01
The GE/ETEC Green piping system was subjected to high seismic inputs from hydraulic sleds at each pipe foundation. These inputs were high enough to force bending stresses into the plastic regime. Strain gages recorded the pipe response at various positions within the system. The ABAQUS finite element code was used to model this piping system and the dynamic input. Problems associated with the dynamic input are discussed. Various types of finite elements were evaluated for accurancy. Both an elastic time-history analysis and an elastic-plastic time-history analysis of the system were conducted. Results of these analyses are compared to each other and the experimental data. These comparisons indicated that elastic analysis of dynamic strains are conservative at all points of comparison and that there is good agreement between the nonlinear elastic-plastic analysis and experimental data. (orig.)
Energy based methods for determining elastic plastic fracture
Witt, F.J.
1979-01-01
Several methods are currently in use or under study for calculating various conditions of fracturing for varying degrees of plasticity. Among these are innovations on the J-integral concept, crack opening displacement or angle, the two parameter concept and the equivalent energy method. Methods involving crack arrest and ductile tearing also fall in this category. Each of these methods have many salient points and some efforts are underway to establish the underlying relationship between them. In this paper, the current research directions of J-integral and equivalent energy methodologies are reviewed with a broader discussion presented for the equivalent energy methodology. The fundamental basis of equivalent energy methodology rests with the volumetric energy ratio. For fractures governed by linear elastic fracture mechanics, the volumetric energy ratio is independent of flaw size and geometry and depends only on the scale factor between model and prototype and temperature. The behavioral aspects of the volumetric energy ratios have been investigated throughout the temperature range from brittle fracture to fully ductile fracture. For five different specimen and structural configurations it has been shown experimentally that the volumetric energy ratio retains its basic properties. That is, the volumetric energy ratio while changing in actual value, maintains its independence of geometry and flaw size while retaining a unique dependence on scale factor and temperature. This property interpreted in terms of fracture mechanics leads to the equivalent energy method. (orig.)
The elastic-plastic failure assessment diagram of surface cracked structure
Ning, J.; Gao, Q.
1987-01-01
The simplified NLSM is able to calculate the EPFM parameters and failure assessment curve for the surface cracked structure correctly and conveniently. The elastic-plastic failure assessment curve of surface crack is relevant to crack geometry, loading form and material deformation behaviour. It is necessary to construct the EPFM failure assessment curve of the surface crack for the failure assessment of surface cracked structure. (orig./HP)
An analysis of heat field of metal sheet during elastic-plastic deformation
Li, S.X.; Huang, Y.; Shih, C.H.
1985-08-01
This paper describes the application of the finite element analysis to calculate the temperature distribution generated during the process of elastic-plastic deformation. A better agreement is found between the results of heat field computed by use of the finite element analysis and that measured by use of an infrared camera. The results indicate that the method of finite element analysis used for heat field evaluation is reliable. (author)
Numerical estimate of fracture parameters under elastic and elastic-plastic conditions
Soba, Alejandro; Denis, Alicia C.
2003-01-01
The importance of the stress intensity factor K in the elastic fracture analysis is well known. In this work three methods are developed to estimate the parameter K I , corresponding to the normal loading mode, employing the finite elements method. The elastic-plastic condition is also analyzed, where the line integral J is the relevant parameter. Two cases of interest are studied: sample with a crack in its center and tubes with internal pressure. (author)
Study on elastic-plastic deformation analysis using a cyclic stress-strain curve
Igari, Toshihide; Setoguchi, Katsuya; Yamauchi, Masafumi
1983-01-01
This paper presents the results of the elastic-plastic deformation analysis using a cyclic stress-strain curve with an intention to apply this method for predicting the low-cycle fatigue life. Uniaxial plastic cycling tests were performed on 2 1/4Cr-1Mo steel to investigate the correspondence between the cyclic stress-strain curve and the hysteresis loop, and also to determine what mathematical model should be used for analysis of deformation at stress reversal. Furthermore, a cyclic in-plane bending test was performed on a flat plate to clarify the validity of the cyclic stress-strain curve-based theoretical analysis. The results obtained are as follows: (1) The cyclic stress-strain curve corresponds nearly to the ascending curve of hysteresis loop scaled by a factor of 1/2 for both stress and strain. Therefore, the cyclic stress-strain curve can be determined from the shape of hysteresis loop, for simplicity. (2) To perform the elastic-plastic deformation analysis using the cyclic stress-strain curve is both practical and effective for predicting the cyclic elastic-plastic deformation of structures at the stage of advanced cycles. And Masing model can serve as a suitable mathematical model for such a deformation analysis. (author)
A method of solution of the elastic-plastic thermal stress problem
Rafalski, P.
1975-01-01
The purpose of the work is an improvement of the numerical technique for calculating the thermal stress distribution in an elastic-plastic structural element. The work consists of two parts. In the first a new method of solution of the thermal stress problem for the elastic-plastic body is presented. In the second a particular numerical technique, based on the above method, for calculating the stress and strain fields is proposed. A new mathematical approach consists in treating the stress and strain fields as mathematical objects defined in the space-time domain. The methods commonly applied use the stress and strain fields defined in the space domain and establish the relations between them at a given instant t. They reduce the problem to the system of ordinary differential equations with respect to time, which are usually solved with a step-by-step technique. The new method reduces the problem to the system of nonlinear algebraic equations. In the work the Hilbert space of admissible tensor fields is constructed. This space is the orthogonal sum of two subspaces: of statically admissible and kinematically admissible fields. Two alternative orthogonality conditions, which correspond to the equilibrium and compatibility equations with the appropriate boundary conditions, are derived. The results of the work are to be used for construction of the computer program for calculation the stress and strain fields in the elastic-plastic body with a prescribed temperature field in the interior and appropriate displacement and force conditions on the boundary
Metamodel-based inverse method for parameter identification: elastic-plastic damage model
Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb
2017-04-01
This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.
Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology
Allen, P. A.; Wells, D. N.
2013-01-01
No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.
Wu, Szu-Ying; Tsai, Bor-Jiun; Chen, Jien-Jong
2015-01-01
In this study, a 3-D automatic elastic-plastic finite element mesh generator is established to accurately predict the J-integral value of an arbitrary reducer with a constant-depth internal circumferential surface crack under bending and axial force. The contact pairs are used on the crack surfaces to simulate the actual contact behaviors of the crack model under loadings. In order to verify the accuracy of the proposed elastic-plastic finite element model for a reducer with a surface crack, the cracked straight pipe models are generated according to a special modeling procedure for a flawed reducer. The J-integral values along the crack front of surface crack are calculated and compared with the straight pipe models which have been verified in the previous published studies. Based on the comparison of computed results, good agreements are obtained to show the accuracy of present numerical models. More confidence on using the 3-D elastic-plastic finite element analysis for reducers with internal circumferential surface cracks can be thus established in this work
A work-hardening rule for finite elastic-plastic deformation of metals at elevated temperatures
Lee, L.H.N.; Horng, J.T.
1975-01-01
The paper is concerned with an extension of Prager-Ziegler's kinematic work-hardening rule for infinitesimal elastic-plastic deformation to a work-hardening rule for finite elastic-plastic deformation of a polycrystalline metal. It is shown that the finite work-hardening rule, which accounts for the Bauschinger and temperature effects within certain pressure and temperature ranges, satisfies certain invariant, continuity and thermodynamic requirements. A description of the kinematics of an elastic-plastic body is employed with reference to three separate configurations: initial, current and an intermediate configuration. The intermediate configuration is a conceptual, local configuration obtained by removing the stress and temperature changes in the neighborhood of an element. A rigid body rotation of the intermediate configuration is allowed. Piola-Kirchhoff stresses and Green deformation tensors referred to the initial and intermediate configurations are employed as stress and strain measures. The plastic deformation has been associated with the motion and production of dislocations. It has been observed that the motion of mobile dislocations usually occur in the narrow slip bands in each grain, leaving the basic lattice structure practically intact, so that the macroscopic elastic properties of the material are essentially independent of plastic deformation. Employing this fact and the thermodynamic laws, a simplified elastic stress-strain relationship of the plastically deformed material, which agrees with the results of Naghdi and Trapp, is obtained
Ning, Po; Feng, Zhi-Qiang; Quintero, Juan Antonio Rojas; Zhou, Yang-Jing; Peng, Lei
2018-03-01
This paper deals with elastic and elastic-plastic fretting problems. The wear gap is taken into account along with the initial contact distance to obtain the Signorini conditions. Both the Signorini conditions and the Coulomb friction laws are written in a compact form. Within the bipotential framework, an augmented Lagrangian method is applied to calculate the contact forces. The Archard wear law is then used to calculate the wear gap at the contact surface. The local fretting problems are solved via the Uzawa algorithm. Numerical examples are performed to show the efficiency and accuracy of the proposed approach. The influence of plasticity has been discussed.
Mechanically equivalent elastic-plastic deformations and the problem of plastic spin
Steigmann David J.
2011-01-01
Full Text Available The problem of plastic spin is phrased in terms of a notion of mechanical equivalence among local intermediate configurations of an elastic/ plastic crystalline solid. This idea is used to show that, without further qualification, the plastic spin may be suppressed at the constitutive level. However, the spin is closely tied to an underlying undistorted crystal lattice which, once specified, eliminates the freedom afforded by mechanical equivalence. As a practical matter a constitutive specification of plastic spin is therefore required. Suppression of plastic spin thus emerges as merely one such specification among many. Restrictions on these are derived in the case of rate-independent response.
Isa Kolo
2016-01-01
Full Text Available A coupled elastic-plasticity-damage constitutive model, AK Model, is applied to predict fracture propagation in rocks. The quasi-brittle material model captures anisotropic effects and the distinct behavior of rocks in tension and compression. Calibration of the constitutive model is realized using experimental data for Carrara marble. Through the Weibull distribution function, heterogeneity effect is captured by spatially varying the elastic properties of the rock. Favorable comparison between model predictions and experiments for single-flawed specimens reveal that the AK Model is reliable and accurate for modelling fracture propagation in rocks.
Elastic-plastic code in the static regime for two-dimensional structures
Giuliani, S.
1976-07-01
The finite-element computer code STEP-2D, which was conceived as a numerical tool for basic research in fracture mechanics presently under way in the Materials Division of JRC Ispra is described. The code employs 8-node isoparametric elements for calculating elastic-plastic stress and strain distributions in 2-D geometries. The von Mises yield criterion is used. Material strain hardening is described by means of either the isotropic or the so-called 'overlay' model. An incremental solution is employed in the plastic range. The program has been written in Fortran IV and compiled on an IBM 370-165
Elastic-plastic behaviour of thick-walled containers considering plastic compressibility
Betten, J.; Frosch, H.G.
1983-01-01
In this paper the elastic-plastic behaviour of thick-walled pressure vessels with internal and external pressure is studied. To describe the mechanical behaviour of isotropic, plastic compressible materials we use a plastic potential which is a single-valued function of the principle stresses. For cylinders and spheres an analytic expression for the computation of stresses and residual stresses is specified. Afterwards the strains are calculated by using the finite difference method. Some examples will high-light the influence of the plastic compressibility on the behaviour of pressure vessels. (orig.) [de
Bellucci, H.J.
1975-11-01
The report describes the continuation of research into capability for three-dimensional elastic-plastic stress and strain analysis for fracture mechanics. A computer program, MARC-3D, has been completed and was used to analyze a cylindrical pressure vessel with a nozzle insert. A method for generating crack tip elements was developed and a model was created for a cylindrical pressure vessel with a nozzle and an imbedded flaw at the inside nozzle corner. The MARC-3D program was again used to analyze this flawed model. Documentation for the use of the MARC-3D computer program has been included as an appendix
Elastic-plastic adhesive contact of rough surfaces using n-point asperity model
Sahoo, Prasanta; Mitra, Anirban; Saha, Kashinath
2009-01-01
This study considers an analysis of the elastic-plastic contact of rough surfaces in the presence of adhesion using an n-point asperity model. The multiple-point asperity model, developed by Hariri et al (2006 Trans ASME: J. Tribol. 128 505-14) is integrated into the elastic-plastic adhesive contact model developed by Roy Chowdhury and Ghosh (1994 Wear 174 9-19). This n-point asperity model differs from the conventional Greenwood and Williamson model (1966 Proc. R. Soc. Lond. A 295 300-19) in considering the asperities not as fixed entities but as those that change through the contact process, and hence it represents the asperities in a more realistic manner. The newly defined adhesion index and plasticity index defined for the n-point asperity model are used to consider the different conditions that arise because of varying load, surface and material parameters. A comparison between the load-separation behaviour of the new model and the conventional one shows a significant difference between the two depending on combinations of mean separation, adhesion index and plasticity index.
Aihara, S.; Atsumi, K.; Ujiie, K.; Satoh, S.
1981-01-01
Self-restraining stresses generate not only moments but also axial forces. Therefore the moment and force equilibriums of cross section are considered simultaneously, in combination with other external forces. Thus, under this theory, two computer programs are prepared for. Using these programs, the design procedures which considered the reduction of self-restraining stress, become easy if the elastic design stresses, which are separated normal stresses and self-restraining stresses, are given. Numerical examples are given to illustrate the application of the simplified elastic-plastic analysis and to study its effectiveness. First this method is applied to analyze an upper shielding wall in MARK-2 type's Reactor building. The results are compared with those obtained by the elastic-plastic analysis of Finite Element Method. From this comparison it was confirmed that the method described, had adequate accuracy for re-bar design. As a second example, Mat slab of Reactor building is analyzed. The quantity of re-bars calculated by this method, comes to about two third of re-bars less than those required when self-restraining stress is considered as normal stress. Also, the self-restraining stress reduction factor is about 0.5. (orig./HP)
Elastic-plastic fracture assessment using a J-R curve by direct method
Asta, E.P.
1996-01-01
In the elastic-plastic evaluation methods, based on J integral and tearing modulus procedures, an essential input is the material fracture resistance (J-R) curve. In order to simplify J-R determination direct, a method from load-load point displacement records of the single specimen tests may be employed. This procedure has advantages such as avoiding accuracy problems of the crack growth measuring devices and reducing testing time. This paper presents a structural integrity assessment approach, for ductile fracture, using the J-R obtained by a direct method from small single specimen fracture tests. The J-R direct method was carried out by means of a developed computational program based on theoretical elastic-plastic expressions. A comparative evaluation between the direct method J resistance curves and those obtained by the standard testing methodology on typical pressure vessel steels has been made. The J-R curves estimated from the direct method give an acceptable agreement with the approach proposed in this study which is reliable to use for engineering determinations. (orig.)
Elastic-plastic analysis of high speed rotors with no plane of symmetry
Anantha Ramu, S.
1981-01-01
A general method of analysis of elastic plastic shells has been developed. The material of the shell is assumed to obey von Mises yield condition and a stress strain law on the basis of deformation theory of plasticity. The method permits an easy iterative solution of the complete set of coupled nonlinear differential equations. The iterative procedure is essentially the solution of the elastic problem several times with different sets of loads. The solution finally yields among other things, the location of the elastic-plastic boundary in the shell wall. The second approach suggested is a three-dimensional hexahedral isoparametric solid element. The computer program developed is capable of modelling perfectly plastic, bilinear as well as nonlinear strain hardening behaviour of materials. As an example, a radial impeller is analysed by both the approaches by idealizing it as a rotating conical shell. The complete history of plastification of the shell wall as the speed increases is determined. The results of both approaches are found to be in good agreement with each other. (orig./HP)
Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu
2018-04-01
A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.
Elastic-plastic analysis of AS4/PEEK composite laminate using a one-parameter plasticity model
Sun, C. T.; Yoon, K. J.
1992-01-01
A one-parameter plasticity model was shown to adequately describe the plastic deformation of AS4/PEEK (APC-2) unidirectional thermoplastic composite. This model was verified further for unidirectional and laminated composite panels with and without a hole. The elastic-plastic stress-strain relations of coupon specimens were measured and compared with those predicted by the finite element analysis using the one-parameter plasticity model. The results show that the one-parameter plasticity model is suitable for the analysis of elastic-plastic deformation of AS4/PEEK composite laminates.
Dynamic elastic-plastic response of a 2-DOF mass-spring system.
Corona, Edmundo [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2018-02-01
The objective of the work presented here arose from abnormal, drop scenarios and specifically the question of how the accelerations and accumulation of plastic strains of internal components could be a ected by the material properties of the external structure. In some scenarios, the impact loads can induce cyclic motion of the internal components. Therefore, a second objective was to explore di erences that could be expected when simulations are conducted using isotropic hardening vs. kinematic hardening plasticity models. The simplest model that can be used to investigate the objectives above is a two-degree-offreedom mass/spring model where the springs exhibit elastic-plastic behavior. The purpose of this memo is to develop such model and present a few results that address the objectives.
Steady-state, elastic-plastic growth of slanted cracks in symmetrically loaded plates
Nielsen, Kim Lau; Hutchinson, J. W.
2017-01-01
parameter through the plate in the plastic zone at the crack tip. The distribution of the mode I and mode III stress intensity factors along the crack front are obtained for the elastic problem. The out-of-plane bending constraint imposed on the plate significantly influences the mixed mode behavior along......Elastic and elastic-plastic results are obtained for a semi-infinite slanted through-crack propagating in a symmetrically loaded plate strip with the aim of providing theoretical background to commonly observed plate tearing behavior. Were it is not for the slant of the crack through the thickness...... of the plate, the problem would be mode I, but due to the slant the local conditions along the crack front are a combination of mode I and mode III. A three-dimensional formulation for steady-state crack propagation is employed to generate distributions of effective stress, stress triaxiality and Lode...
Sensitivity of using blunt and sharp crack models in elastic-plastic fracture mechanics
Pan, Y.C.; Kennedy, J.M.; Marchertas, A.H.
1985-01-01
J-integral values are calculated for both the blunt (smeared) crack and the sharp (discrete) crack models in elastic-plastic fracture mechanics problems involving metallic materials. A sensitivity study is performed to show the relative strengths and weaknesses of the two cracking models. It is concluded that the blunt crack model is less dependent on the orientation of the mesh. For the mesh which is in line with the crack direction, however, the sharp crack model is less sensitive to the mesh size. Both models yield reasonable results for a properly discretized finite-element mesh. A subcycling technique is used in this study in the explicit integration scheme so that large time steps can be used for the coarse elements away from the crack tip. The savings of computation time by this technique are reported. 6 refs., 9 figs
Elastic-plastic fracture mechanics analysis of a pressure vessel with an axial outer surface flaw
Aurich, D.
1988-04-01
Elastic-plastic finite element analyses of a test vessel (steel 1.6310=20 MnMoNi 55) with a semi-elliptical axial outer surface crack have been performed. The variations of J and CTOD along the crack front and the stresse state in the vicinity of the crack are presented. The applicability of approaches to determine J is examined. The FE results are compared with the experimental data. The results are analyzed with respect to the validity of J-controlled crack growth. It will be shown that the local ductile crack growth and, especially, the 'canoe effect' for a semi-elliptical crack can only be described correctly if local J R -curves are used which account for the varying triaxiality of the stress state along the crack front. (orig./HP) [de
Comparison of experiment and theory for elastic-plastic plane strain crack growth
Hermann, L.; Rice, J.R.
1980-02-01
Recent theoretical results on elastic-plastic plane strain crack growth, and experimental results for crack growth in a 4140 steel in terms of the theoretical concepts are reviewed. The theory is based on a recent asymptotic analysis of crack surface opening and strain distributions at a quasi-statically advancing crack tip in an ideally-plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large scale yielding. Nevertheless, it suffices to derive a relation between the imposed loading and amount of crack growth, prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens
Elastic-plastic analysis of an axi-symmetric problem by a finite element method
Isozaki, Toshikuni
1984-06-01
Generally speaking, many structures are designed and fabricated on the basis of an axi-symmetric structure. Finite Element Method is the capable method to solve these axi-symmetric problems beyond the elastic limit. As the first step to solve these problems, the computer program for the elastic-plastic analysis of the axi-symmetric problem is composed. The basic program is based upon that described in Zienkiewicz's text book to solve the elastic plane stress problem, taking the plastic stress matrix by Yamada's method into consideration and it is converted to solve the axi-symmetric problem. For the verification of the program, the plane strain problem of a cylindrical tube under internal pressure was solved. The computed results were compared with those shown in ADINA's user's manual. They showed close agreement. (author)
Simplified computational methods for elastic and elastic-plastic fracture problems
Atluri, Satya N.
1992-01-01
An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.
Plane strain analytical solutions for a functionally graded elastic-plastic pressurized tube
Eraslan, Ahmet N.; Akis, Tolga
2006-01-01
Plane strain analytical solutions to functionally graded elastic and elastic-plastic pressurized tube problems are obtained in the framework of small deformation theory. The modulus of elasticity and the uniaxial yield limit of the tube material are assumed to vary radially according to two parametric parabolic forms. The analytical plastic model is based on Tresca's yield criterion, its associated flow rule and ideally plastic material behaviour. Elastic, partially plastic and fully plastic stress states are investigated. It is shown that the elastoplastic response of the functionally graded pressurized tube is affected significantly by the material nonhomogeneity. Different modes of plasticization may take place unlike the homogeneous case. It is also shown mathematically that the nonhomogeneous elastoplastic solution presented here reduces to that of a homogeneous one by appropriate choice of the material parameters
Elastic-plastic and creep analyses by assumed stress finite elements
Pian, T.H.H.; Spilker, R.L.; Lee, S.W.
1975-01-01
A formulation is presented of incremental finite element solutions for both initial stress and initial strain problems based on modified complementary energy principle with relaxed inter-element continuity requirement. The corresponding finite element model is the assumed stress hybrid model which has stress parameters in the interior of each element and displacements at the individual nodes as unknowns. The formulation includes an important consideration that the states of stress and strain and the beginning of each increment may not satisfy the equilibrium and compatibility equations. These imbalance and mismatch conditions all lead to correction terms for the equivalent nodal forces of the matrix equations. The initial stress method is applied to elastic-plastic analysis of structures. In this case the stress parameters for the individual elements can be eliminated resulting to a system of equations with only nodal displacements as unknowns. Two different complementary energy principles can be formulated, in one of which the equilibrium of the final state of stress is maintained while in the other the equilibrium of the stress increments is maintained. Each of these two different formulations can be combined with different iterative schemes to be used at each incremental steps of the elastic-plastic analysis. It is also indicated clearly that for the initial stress method the state of stress at the beginning of each increments is in general, not in equilibrium and an imbalance correction is needed. Results of a comprehensive evaluation of various solution procedures by the initial stress method using the assumed stress hybrid elements are presented. The example used is the static response of a thick wall cylinder of elastic-perfectly plastic material under internal pressure. Solid of revolution elements with rectangular cross sections are used
Mir Hamid Reza Ghoreishy
2014-12-01
Full Text Available A theoretical and experimental study was conducted on the mechanical behavior of nanocomposites based on PA6/NBR thermoplastic elastomer reinforced by single wall carbon nanotubes (SWNTs. The selected samples include 60 and 40% NBR with 0.5, 1.0 and 1.5% SWNT. The modeling methodology was based on the use of two-dimensional "representative volume elements" (RVE. The Abaqus/standard code was employed to carry out the non-linear finite element calculations. Plane stress elements were selected for discretization of the domain. Linear elastic and isotropic hardening elastic-plastic models were utilized to describe the mechanical behaviors of the carbon nanotubes and polymer matrix, respectively. The samples were simultaneously prepared using melt mixing method in a laboratory internal mixer. Different orientations including regular in both longitudinal and transverse directions and random were selected for the nanotubes in the matrix. Also, two structural forms including hollow and solid for the carbon nanotubes were chosen. The highest and lowest predicted moduli were obtained from models with regular orientation in longitudinal and transverse directions, respectively. On the other hand, comparison between the predicted elastic modulus and elastic-plastic behaviors of the samples with their corresponding experimental data revealed that the random orientation in conjunction with hollow structural form gives the best results. Moreover, the selected material model for the thermoplastic elastomer i.e., isotropic hardening can precisely describe the mechanical behavior in both tension and compression modes. It is also concluded that the main source of error in this modeling methodology can be attributed to the effects of interface between polymer and nanotubes and orientation in perpendicular directions.
S. Psakhie
2013-04-01
Full Text Available A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA method, which integrates the possibilities of particle-based discrete element method (DEM and cellular automaton methods. Emergent advantages of the developed approach to formulation of many-body interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elastic-plastic and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.
Scarth, D.A.; Kim, Y.J.; Vanderglas, M.L.
1985-10-01
A comprehensive literature survey on the application of Elastic-Plastic Fracture Mechanics to the assessment of the structural integrity of nuclear pressure vessels and piping is presented. In particular, the J-integral/Tearing Modulus (J/T) approach and the Failure Assessment Diagram (FAD) are covered in detail because of their general suitability for use in Ontario Hydro. (25 refs.)
Moreno, A.
1977-01-01
A new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (author)
Moreno, A.
1977-01-01
In this work a new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (Author) 91 refs
Strain localization and elastic-plastic coupling during deformation of porous sandstone
Dewers, Thomas A. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Geomechanics Dept.; Issen, Kathleen A. [Clarkson Univ., Potsdam, NY (United States). Mechanical and Aeronautical Engineering; Holcomb, David J. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Geomechanics Dept.; Olsson, William A. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Geomechanics Dept.; Ingraham, Mathew D. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States). Geomechanics Dept.
2017-09-12
Results of axisymmetric compression tests on weak, porous Castlegate Sandstone (Cretaceous, Utah, USA), covering a range of dilational and compactional behaviors, are examined for localization behavior. Assuming isotropy, bulk and shear moduli evolve as increasing functions of mean stress and Mises equivalent shear stress respectively, and as decreasing functions of work-conjugate plastic strains. Acoustic emissions events located during testing show onset of localization and permit calculation of observed shear and low-angle compaction localization zones, or bands, as localization commences. Total strain measured experimentally partitions into: A) elastic strain with constant moduli, B) elastic strain due to stress dependence of moduli, C) elastic strain due to moduli degradation with increasing plastic strain, and D) plastic strain. The third term is the elastic-plastic coupling strain, and though often ignored, contributes significantly to pre-failure total strain for brittle and transitional tests. Constitutive parameters and localization predictions derived from experiments are compared to theoretical predictions. In the brittle regime, predictions of band angles (angle between band normal and maximum compression) demonstrate good agreement with observed shear band angles. Compaction localization was observed in the transitional regime in between shear localization and spatially pervasive compaction, over a small range of mean stresses. In contrast with predictions however, detailed acoustic emissions analyses in this regime show low angle, compaction-dominated but shear-enhanced, localization.
Finite plate thickness effects on the Rayleigh-Taylor instability in elastic-plastic materials
Polavarapu, Rinosh; Banerjee, Arindam
2017-11-01
The majority of theoretical studies have tackled the Rayleigh-Taylor instability (RTI) problem in solids using an infinitely thick plate. Recent theoretical studies by Piriz et al. (PRE 95, 053108, 2017) have explored finite thickness effects. We seek to validate this recent theoretical estimate experimentally using our rotating wheel RTI experiment in an accelerated elastic-plastic material. The test section consists of a container filled with air and mayonnaise (a non-Newtonian emulsion) with an initial perturbation between two materials. The plate thickness effects are studied by varying the depth of the soft-solid. A set of experiments is run by employing different initial conditions with different container dimensions. Additionally, the effect of acceleration rate (driving pressure rise time) on the instability threshold with reference to the finite thickness will also be inspected. Furthermore, the experimental results are compared to the analytical strength models related to finite thickness effects on RTI. Authors acknowledge financial support from DOE-SSAA Grant # DE-NA0003195 and LANL subcontract #370333.
Application of elastic and elastic-plastic fracture mechanics methods to surface flaws
McCabe, Donald E.; Ernst, Hugo A.; Newman, James C., Jr.
Fuel tanks that are a part of the External Tank assembly for the Space Shuttle are made of relatively thin 2219-T87 aluminum plate. These tanks contain about 917 m of fusion weld seam, all of which is nondestructively inspected for flaws and all those found are repaired. The tanks are subsequently proof-tested to a pressure that is sufficiently severe to cause weld metal yielding in a few local regions of the weld seam. The work undertaken in the present project was to develop a capability to predict flaw growth from undetected surface flaws that are assumed to be located in the highly stressed regions. The technical challenge was to develop R-curve prediction capability for surface cracks in specimens that contain the flaws of unusual sizes and shapes deemed to be of interest. The test techniques developed and the elastic-plastic analysis concepts adopted are presented. The flaws of interest were quite small surface cracks that were narrow-deep ellipses that served to exacerbate the technical difficulties involved.
RN Lidam
2012-12-01
Full Text Available This paper investigates the angular distortion induced by the gas metal arc welding (GMAW process on the combined butt and T-joint with a thickness of 9 mm. The material used in this study was low manganese carbon steel S355J2G3. A 2-D and 3-D thermo-elastic-plastic finite element (FE analysis has been developed to simulate the induced distortion of multipassed welding. In this research, SYSWELD 2010 with its computation management tool, known as multipassed welding advisor (MPA, was applied to analyze the distortion behavior of combined joint types. To model the heat source of GMAW, Goldak's double ellipsoid representation, which is available within this finite element analysis (FEA code was selected. Prior to the results discussion, this paper also shows the step-bystep procedures to simulate combined jointing which begins with metallurgical and customized heat source modeling, and is followed by creating geometrical mesh using Visual-Mesh 6.5 for analyzing and processing the results. Apart from 2-D and 3-D comparison analysis, the final objective of this research is also aimed to be a baseline study to provide preliminary information in preparing the tools and equipment for experimental investigation.
Elastic-Plastic Behavior of U6Nb Under Ramp Wave Loading
Hayes, D. B.; Hall, C.; Hixson, R. S.
2005-07-01
Prior shock experiments on the alloy uranium-niobium-6 wt.% (U6Nb) were absent an elastic precursor when one was expected (A. K. Zurek, et. al., Journal de Physique IV, 10 (#9) p677-682). This was later explained as a consequence of shear stress relaxation from time-dependent twinning that prevented sufficient shear stress for plastic yielding. (D. B. Hayes, et. al., Shock Compression of Condensed Matter-2003, p1177, American Institute of Physics 2004) Pressure was ramped to 13 GPa in 150-ns on eight U6Nb specimens with thicknesses from 0.5 -- 1.1-mm and the back surface velocities were measured with laser interferometry. This pressure load produces a stress wave with sufficiently fast rise time so that, according to the prior work, twins do not have time to form. Four of the U6Nb specimens had been cold-rolled which increased the yield stress. Each velocity history was analyzed with a backward integration analysis to give the stress-strain response of the U6Nb. Comparison of these results with prior Hugoniot measurements shows that the U6Nb in the present experiments responds as an elastic-plastic material and the deduced yield strength of the baseline and of the cold-rolled material agree with static results.
Evaluation of elastic-plastic fracture of toughness and fracture resistance of carbon steel STS42
Kobayashi, Hideo; Nakamura, Haruo; Kashiwagi, Kohmei
1987-01-01
The elastic-plastic fracture toughness (J Ic ) and fracture resistance (J-R curve) of a carbon steel, STS42, used for piping in a nuclear reactor were evaluated according to the several evaluating methods recommended or proposed so far, to discuss their applicability and utility. The results obtained are as follows: (1) In evaluating J Ic , the multiple specimen method recommended by the Japan Society for Mechanical Engineers (JSME standard S001) gives the most reliable results by using smaller sized specimens. (2) The single-specimen methods by using the compliance technique, adopted in the ASTM standards (E813, E813 modified, Tentative test procedure for determining the plain strain J-R curve), do not give an accurate J-R curve or J Ic , due to an error in the calculated crack length. (3) In evaluating the J-R curve, it is necessary to account for crack extension in calculating the J-integral. (4) According to the above results, a new standard method for determining the J-R curve including the J Ic test method should be poprosed. (author)
Elastic-Plastic Constitutive Equation of WC-Co Cemented Carbides with Anisotropic Damage
Hayakawa, Kunio; Nakamura, Tamotsu; Tanaka, Shigekazu
2007-01-01
Elastic-plastic constitutive equation of WC-Co cemented carbides with anisotropic damage is proposed to predict a precise service life of cold forging tools. A 2nd rank symmetric tensor damage tensor is introduced in order to express the stress unilaterality; a salient difference in uniaxial behavior between tension and compression. The conventional framework of irreversible thermodynamics is used to derive the constitutive equation. The Gibbs potential is formulated as a function of stress, damage tensor, isotropic hardening variable and kinematic hardening variable. The elastic-damage constitutive equation, conjugate forces of damage, isotropic hardening and kinematic hardening variable is derived from the potential. For the kinematic hardening variable, the superposition of three kinematic hardening laws is employed in order to improve the cyclic behavior of the material. For the evolution equation of the damage tensor, the damage is assumed to progress by fracture of the Co matrix - WC particle interface and by the mechanism of fatigue, i.e. the accumulation of microscopic plastic strain in matrix and particles. By using the constitutive equations, calculation of uniaxial tensile and compressive test is performed and the results are compared with the experimental ones in the literature. Furthermore, finite element analysis on cold forward extrusion was carried out, in which the proposed constitutive equation was employed as die insert material
Elastic-Plastic Behaviour of Ultrasonic Assisted Compression of Polyvinyl Chloride (PVC) Foam
Muhalim, N. A. D.; Hassan, M. Z.; Daud, Y.
2018-04-01
The present study aims to investigate the elastic-plastic behaviour of ultrasonic assisted compression of PVC closed-cell foam. A series of static and ultrasonic compression test of PVC closed-cell foam were conducted at a constant cross head speed of 30 mm/min on dry surface condition. For quasi-static test, specimen was compressed between two rigid platens using universal testing machine. In order to evaluate the specimen behavior under ultrasonic condition, specimen was placed between a specifically design double-slotted block horn and rigid platen. The horn was designed and fabricated prior to the test as a medium to transmit the ultrasonic vibration from the ultrasonic transducer to the working specimen. It was tuned to a frequency of 19.89 kHz in longitudinal mode and provided an average oscillation amplitude at 6 µm on the uppermost surface. Following, the characteristics of stress-strain curves for quasi-static and ultrasonic compression tests were analyzed. It was found that the compressive stress was significantly reduced at the onset of superimposed ultrasonic vibration during plastic deformation.
Effect of temperature on the elastic-plastic fracture toughness behavior of Inconel X-750
Mills, W.J.
1977-09-01
The elastic-plastic J/sub Ic/ fracture toughness response of precipitation heat treated Inconel X-750 has been evaluated by the multi-specimen resistance curve (R-curve) technique at room temperature, 800 0 F (427 0 C), and 1000 0 F (538 0 C). The value of J/sub Ic/ for this nickel-base superalloy was found to be relatively independent of temperature over the test temperature range. On the other hand, the slopes of the fracture toughness R-curves were steeper at 800 and 1000 0 F (427 and 538 0 C) than at 75 0 F (24 0 C), thereby indicating that the resistance to crack extension was considerably greater at elevated temperatures, Metallographic and electron fractographic examination of the Inconel X-750 fracture surfaces revealed that this slope change phenomenon was associated with an intergranular to transgranular fracture mechanism transition. Under room temperature conditions, crack extension occurred primarily by an intergranular dimple rupture mechanism attributed to microvoid coalescence along a grain boundary denuded region. In the 800 to 1000 0 F (427 to 538 0 C) regime, the fracture surface was dominated by a faceted transgranular morphology
Elastic-plastic collapse of super-elastic shock waves in face-centered-cubic solids
Zhakhovsky, Vasily V; Demaske, Brian J; Oleynik, Ivan I; Inogamov, Nail A; White, Carter T
2014-01-01
Shock waves in the [110] and [111] directions of single-crystal Al samples were studied using molecular dynamics (MD) simulations. Piston-driven simulations were performed to investigate the split shock-wave regime. At low piston velocities, the material is compressed initially to a metastable over-compressed elastic state leading to a super-elastic single shock wave. This metastable elastic state later collapses to a plastic state resulting in the formation of a two-wave structure consisting of an elastic precursor followed by a slower plastic wave. The single two-zone elastic-plastic shock-wave regime appearing at higher piston velocities was studied using moving window MD. The plastic wave attains the same average speed as the elastic precursor to form a single two-zone shock wave. In this case, repeated collapse of the highly over-compressed elastic state near the plastic shock front produces ultrashort triangle pulses that provide the pressure support for the leading elastic precursor.
Study on elastic-plastic fracture toughness test in high temperature water
Miura, Yasufumi
2016-01-01
Structural integrity of internal components in light water reactors is important for the safety of operation and service lifetime. Fracture toughness is important parameter for structural integrity assessment of nuclear power plant. In general, fracture toughness of materials which compose the components in light water reactor is obtained with fracture toughness tests in air although some components are subjected to high temperature water because of the difficulty of fracture toughness test in high temperature water. However, the effects of high temperature water and hydrogen on fracture behavior of the structural materials in nuclear power plant such as low alloy steel, cast austenitic stainless steel, and Ni base alloy are concerned recently. In this study, elastic-plastic fracture toughness test of low alloy steel in simulated BWR water environment was studied. Fracture toughness test in high temperature water with original clip gage and normalization data reduction technique was established. The difference of fracture toughness J_Q tested in air between using elastic unload compliance method and normalization data reduction technique was also discussed. As a result, obtained value with normalization data reduction technique tended to be higher than the value with elastic unload compliance. (author)
Elastic-plastic fracture mechanics for nuclear pressure vessels: a preliminary appraisal
Hahn, G.T.; Broek, D.; Marschall, C.W.; Rosenfield, A.R.; Rybicki, E.F.; Schmueser, D.W.; Stonesifer, R.B.; Kanninen, M.F.
1978-01-01
A research program directed at assessing the margin of safety of flawed nuclear pressure vessels near and beyond general yielding is described. The program has the general objective of developing an elastic-plastic fracture mechanics methodology. The approach is based on the use of finite element models together with experimental results to identify criteria appropriate for the onset of crack extension and for stable crack growth. A number of criteria beyond the conventional LEFM R curve are being evaluated. These include the critical values of the J-integral, its derivative, the crack tip opening angle, the average crack opening angle, a generalized energy release rate, its components and a crack tip force. The optimum fracture criterion for nuclear vessels is being determined by systematic measurements of load extension curves, strain distribution, crack opening displacement, stable crack growth and instability on 'toughness scaled' model materials. Computations have been performed for center cracked panels of a model material (2219-T87 aluminium) for full shear failure. (author)
Elastic-Plastic Behavior of U6Nb under Ramp Wave Loading
Hayes, D. B.; Gray, G. T. III; Hixson, R. S.; Hall, C. A.
2006-01-01
When uranium-niobium (6 wt.%) alloy is shock loaded, the expected elastic precursor is absent. A prior model attributed this absence to shear-induced twinning and the concomitant shear stress reduction that prevented the shocked material from reaching the plastic yield point. In the present study, carefully prepared U6Nb was subjected to shock loading to verify the adequacy of the prior model. Other samples were loaded with a ramp pressure pulse with strain rate large enough so that significant twinning would not occur during the experiment. Backward integration analyses of these latter experiments' back surface motion give stress-strain loading paths in U6Nb that suggest ordinary elastic-plastic flow. Some of the U6Nb was pre-strained by cold rolling in an effort to further ensure that twinning did not affect wave propagation. Shock and ramp loadings yielded similar results to the baseline material except, as expected, they are consistent with a higher yield stress and twinning shear stress threshold
The finite element part of the LAMCAL program. Elastic-plastic fracture mechanics applications
Lamain, L.G.; Blanckenburg, J.F.G.
1982-01-01
The elastic-plastic FEM code described in this report is the third part of the Lamcal program of which the two other parts for mesh generating and plotting were presented previously. Also this part uses the dynamic core storage. All variables and problem defining data are stored in one common array-SPACE. If all three parts are used together, the same common-SPACE is reused in each part. The lay-out of the complete program is given. J-integral evaluation and plotting can be done immediately in the FE run or afterwards in a post processing run. Post processing is done within the FEM part with a reduced core space. Originally developed as a general code, the use of the present version is mainly focussed on research in the field of the fracture mechanics. Several J-integral routines are available as well as crack growth modelling by node release or stiffness reduction, energy calculations, crack tip elements, etc. In this report the theory is discussed and some sample problems are given. The theory is presented in two parts, the general FEM and the more specific EPFM theory. For the sample problems, a choice has been made to show the accuracy of the program under more or less severe loading conditions
Analysis of elastic-plastic problems using edge-based smoothed finite element method
Cui, X.Y.; Liu, G.R.; Li, G.Y.; Zhang, G.Y.; Sun, G.Y.
2009-01-01
In this paper, an edge-based smoothed finite element method (ES-FEM) is formulated for stress field determination of elastic-plastic problems using triangular meshes, in which smoothing domains associated with the edges of the triangles are used for smoothing operations to improve the accuracy and the convergence rate of the method. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and the numerical integration becomes a simple summation over the edge-based smoothing domains. The pseudo-elastic method is employed for the determination of stress field and Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as field variables and considered as functions of the final state of stress fields. The effective elastic material parameters are then obtained in an iterative manner based on the strain controlled projection method from the uniaxial material curve. Some numerical examples are investigated and excellent results have been obtained demonstrating the effectivity of the present method.
Petruschke, W.; Strunk, G.
1987-01-01
The investigations according to the system identification show that the piping model using beam theory and flexibility factors according to the Karman theory are adequate for evaluating natural frequencies, mode shapes, static displacements and stresses. The same accuracy can be seen by comparing the piping response due to blowdown within the elastic range. The simplified elastic-plastic analysis in general overestimates the maximum amplitudes while the frequency content is not simulated very well. For practical purposes, it can be an adequate tool in many cases. The elastic-plastic analysis is the most expensive procedure but gives also the best results. The use of beam elements with multilinear moment-curvature relationships results in a good approximation for the global behaviour (displacements). The strains according to this theory only include the beam deformation modes
Lee Kyung-Hun
2015-01-01
Full Text Available The purpose of this study is to investigate the elastic-plastic behavior of inclusions, i.e. SiO2 particles, in cold drawn wire using reverse analysis and nanoindentation test. First, the nanoindentation tests were performed to obtain indentation load P – penetration depth h curves. Second, the reverse analysis which is consisted of various dimensionless functions including change in E∗/σr, Wp/Wt and n was used to extract the elastic-plastic properties of the indented inclusions and metals from indentation responses. To verify the accuracy of calculated properties, uniaxial tensile tests were performed for different materials which are AISI 1045 and AISI 1080. Results (E, σy, n of tensile tests for each material were also compared with those of nanoindentation tests.
Knight, Norman F., Jr.; Warren, Jerry E.; Elliott, Kenny B.; Song, Kyongchan; Raju, Ivatury S.
2012-01-01
Elastic-plastic, large-deflection nonlinear thermo-mechanical stress analyses are performed for the Space Shuttle external tank s intertank stringers. Detailed threedimensional finite element models are developed and used to investigate the stringer s elastic-plastic response for different thermal and mechanical loading events from assembly through flight. Assembly strains caused by initial installation on an intertank panel are accounted for in the analyses. Thermal loading due to tanking was determined to be the bounding loading event. The cryogenic shrinkage caused by tanking resulted in a rotation of the intertank chord flange towards the center of the intertank, which in turn loaded the intertank stringer feet. The analyses suggest that the strain levels near the first three fasteners remain sufficiently high that a failure may occur. The analyses also confirmed that the installation of radius blocks on the stringer feet ends results in an increase in the stringer capability.
Kotaro eKojima
2016-01-01
Full Text Available The double impulse is introduced as a substitute of the fling-step near-fault ground motion. A closed-form solution of the elastic-plastic response of a structure on compliant (flexible ground by the ‘critical double impulse’ is derived for the first time based on the solution for the corresponding structure with fixed base. As in the case of fixed-base model, only the free-vibration appears under such double impulse and the energy approach plays an important role in the derivation of the closed-form solution of a complicated elastic-plastic response on compliant ground. It is remarkable that no iteration is needed in the derivation of the critical elastic-plastic response. It is shown via the closed-form expression that, in the case of a smaller input level of double impulse to the structural strength, as the ground stiffness becomes larger, the maximum plastic deformation becomes larger. On the other hand, in the case of a larger input level of double impulse to the structural strength, as the ground stiffness becomes smaller, the maximum plastic deformation becomes larger. The criticality and validity of the proposed theory are investigated through the comparison with the response analysis to the corresponding one-cycle sinusoidal input as a representative of the fling-step near-fault ground motion. The applicability of the proposed theory to actual recorded pulse-type ground motions is also discussed.
Elastic-Plastic Endochronic Constitutive Model of 0Crl7Ni4Cu4Nb Stainless Steels
Jinquan Guo
2016-01-01
Full Text Available We presented an elastic-plastic endochronic constitutive model of 0Crl7Ni4Cu4Nb stainless steel based on the plastic endochronic theory (which does not need the yield surface and experimental stress-strain curves. The key feature of the model is that it can precisely describe the relation of stress and strain under various loading histories, including uniaxial tension, cyclic loading-unloading, cyclic asymmetric-stress axial tension and compression, and cyclic asymmetric-stress axial tension and compression. The effects of both mean stress and amplitude of stress on hysteresis loop based on the elastic-plastic endochronic constitutive model were investigated. Compared with the experimental and calculated results, it is demonstrated that there was a good agreement between the model and the experiments. Therefore, the elastic-plastic endochronic constitutive model provides a method for the accurate prediction of mechanical behaviors of 0Crl7Ni4Cu4Nb stainless steel subjected to various loadings.
The creep low application for numerical modeling of elastic-plastic flows
Tyapin, Anatoly; Rudenko, Vladimir; Chekhunov, Evgeny; Shaburov, Michail
1999-06-01
The present paper demonstrates the applicability of Lomnitz logarithm creep law [1] in some approximated version for calculating the elastic-plastic flows. The model has been developed resulting from the intention to have appropriate calculation approximation for particle-velocity -vs-time histories observed in plate 6061-T6 Al samples of various thickness under shock loading and subsequent release and additional compression. The approximation is unique in the whole loading range, from very low to such that elastic precursor is swallowed up by plastic wave . The model is based on Lipkin and Asay [2] remark on scale similarity of the above mentioned particle velocity -vs-time histories for equal shock loading and on approximate equality of velocities that initial portions of release and recompression waves travel at. A Lomnitz creep law presents an ideal phenomenological tool providing both of the requirements be fulfilled at the same time. Its application to high rate processes of loading and release has required some law modification and a nontrivial review of the dislocation mechanism for stress relaxation. The agreement achieved with the experiment is illustrated in figures. The model is worked out and realized in the 1D user software MAG. 1. Lomnitz C. Joun. of Geology, 1956, vol. 64, p. 473-479. 2. Lipkin J., Asay J.R. J. Appl. Phys. ,1977, vol. 48, 1, p.182-189. 3. Johnson J., Barker L. J. Appl. Phys., 1969, vol. 40, 11, p. 4321-4334. 4. Asay J.R., Chhabildas L. M.: Metallurgia., 1984, p. 110-120.
FRICTION ANALYSIS ON SCRATCH DEFORMATION MODES OF VISCO-ELASTIC-PLASTIC MATERIALS
Budi Setiyana
2013-11-01
Full Text Available Understanding of abrasion resistance and associated surfaces deformation mechanisms is of primary importance in materials engineering and design. Instrumented scratch testing has proven to be a useful tool for characterizing the abrasion resistance of materials. Using a conical indenter in a scratch test may result in different deformation modes, like as elastic deformation, ironing, ductile ploughing and cutting. This paper presents the friction analysis of some deformation modes of visco-elastic-plastic behaving polymer materials, especially PEEK (poly ether ether ketone.In general, it is accepted that the friction consist of an adhesion and a deformation component, which can be assumed to be independent to each others. During a scratch test, the friction coefficient is influenced by some parameters, such as the sharpness of indenter, the deformation modes and the degree of elastic recovery. Results show that the adhesion component strongly influences the friction in the elastic and ironing deformation mode (scratching with a blunt cone, friction for the cutting deformation mode (scratching with a sharp cone is dominantly influenced by the deformation component. From the analysis, it can be concluded that the adhesion friction model is suitable for ironing - elastic deformation mode and the deformation friction model with elastic recovery is good for cutting mode. Moreover, the ductile ploughing mode is combination of the adhesion and plastic deformation friction model. ANALISIS FRIKSI PADA BENTUK DEFORMASI AKIBAT GORESAN PADA MATERIAL VISKO-ELASTIK-PLASTIK. Pemahaman tentang ketahanan abrasi dan deformasi permukaan yang menyertainya merupakan hal yang penting dalam rekayasa dan disain material. Peralatan uji gores terbukti ampuh untuk menyatakan ketahanan abrasi dari material. Pemakaian indenter kerucut dalam uji gores akan menghasilkan beberapa bentuk deformasi seperti halnya deformasi elastik, penyetrikaan, plowing dan pemotongan
Kim, Jong Min; Huh, Nam Su
2010-01-01
The crack-tip stress fields and fracture mechanics assessment parameters for a surface crack, such as the elastic stress intensity factor or the elastic-plastic J-integral, can be affected significantly by the adjacent cracks. Such a crack interaction effect due to multiple cracks can alter the fracture mechanics assessment parameters significantly. There are many factors to be considered, for instance the relative distance between adjacent cracks, the crack shape, and the loading condition, to quantify the crack interaction effect on the fracture mechanics assessment parameters. Thus, the current assessment codes on crack interaction effects (crack combination rules), including ASME Sec. XI, BS7910, British Energy R6 and API 579-1/ASME FFS-1, provide different rules for combining multiple surface cracks into a single surface crack. The present paper investigates crack interaction effects by evaluating the elastic stress intensity factor and the elastic-plastic J-integral of adjacent in-plane surface cracks in a plate through detailed 3-dimensional elastic and elastic-plastic finite element analyses. The effects on the fracture mechanics assessment parameters of the geometric parameters, the relative distance between two cracks, and the crack shape are investigated systematically. As for the loading condition, an axial tension is considered. Based on the finite element results, the acceptability of the crack combination rules provided in the existing guidance was investigated, and the relevant recommendations on a crack interaction for in-plane surface cracks are discussed. The present results can be used to develop more concrete guidance on crack interaction effects for crack shape characterization to evaluate the integrity of defective components
Rack, H.J.; Knorovsky, G.A.
1978-09-01
Stress-strain data which describes the influence of strain rate and temperature on the mechanical response of materials presently being used for light water reactor fuel shipping containers have been assembled. Selection of data has been limited to that which is suitable for use in finite-element elastic--plastic analysis of shipping containers (e.g., they must include complete material history profiles). Based on this information, recommendations have been made for further work which is required to complete the necessary data base
Sanjeev Sharma
2013-01-01
Full Text Available Elastic-plastic stresses, strains, and displacements have been obtained for a thin rotating annular disk with exponentially variable thickness and exponentially variable density with nonlinear strain hardening material by finite difference method using Von-Mises' yield criterion. Results have been computed numerically and depicted graphically. From the numerical results, it can be concluded that disk whose thickness decreases radially and density increases radially is on the safer side of design as compared to the disk with exponentially varying thickness and exponentially varying density as well as to flat disk.
Chang, T.Y.; Prachuktam, S.; Reich, M.
1975-01-01
The formulation of the stiffness equation for an 8 to 21 node isoparametric element with elastic-plastic material and large deformation is presented. The formulation has been implemented in a nonlinear finite element program for the analysis of three-dimensional continuums. To demonstrate the utility of the formulation, a thick-walled cylinder was analyzed and the results are compared favorably with a known solution. The element type presented can be applied not only to 3-D continuums, but also to plate or shell structures, for which degenerated isoparametric elements may be used
Asada, Seiji; Hirano, Takashi; Nagata, Tetsuya; Kasahara, Naoto
2008-01-01
A structural evaluation method by using elastic-plastic finite element analysis has been developed and published as a code case of Rules on Design and Construction for Nuclear Power Plants (The First Part: Light Water Reactor Structural Design Standard) in the JSME Codes for Nuclear Power Generation Facilities. Its title is 'Alternative Structural Evaluation Criteria for Class 1 Vessels Based on Elastic-Plastic Finite Element Analysis' (NC-CC-005). This code case applies elastic-plastic analysis to evaluation of such failure modes as plastic collapse, thermal ratchet, fatigue and so on. Advantage of this evaluation method is free from stress classification, consistently use of Mises stress and applicability to complex 3-dimensional structures which are hard to be treated by the conventional stress classification method. The evaluation method for plastic collapse has such variation as the Lower Bound Approach Method, Twice-Elastic-Slope Method and Elastic Compensation Method. Cyclic Yield Area (CYA) based on elastic analysis is applied to screening evaluation of thermal ratchet instead of secondary stress evaluation, and elastic-plastic analysis is performed when the CYA screening criteria is not satisfied. Strain concentration factors can be directly calculated based on elastic-plastic analysis. (author)
Ali, Mohammed Ali Nasser
The research project presents a fundamental understanding of the fatigue crack growth mechanisms of AISI 420 martensitic stainless steel, based on the comparison analysis between the theoretical and numerical modelling, incorporating research findings under isothermal fatigue loading for solid cylindrical specimen and the theoretical modelling with the numerical simulation for tubular specimen when subjected to cyclic mechanical loading superimposed by cyclic thermal shock.The experimental part of this research programme studied the fatigue stress-life data for three types of surface conditions specimen and the isothermal stress-controlled fatigue testing at 300 °C - 600 °C temperature range. It is observed that the highest strength is obtained for the polished specimen, while the machined specimen shows lower strength, and the lowest strength is the notched specimen due to the high effect of the stress concentration. The material behaviour at room and high temperatures shows an initial hardening, followed by slow extension until fully plastic saturation then followed by crack initiation and growth eventually reaching the failure of the specimen, resulting from the dynamic strain ageing occurred from the transformation of austenitic microstructure to martensite and also, the nucleation of precipitation at grain boundaries and the incremental temperature increase the fatigue crack growth rate with stress intensity factor however, the crack growth rate at 600 °C test temperature is less than 500 °C because of the creep-fatigue taking place.The theoretical modelling presents the crack growth analysis and stress and strain intensity factor approaches analysed in two case studies based on the addition of thermo-elastic-plastic stresses to the experimental fatigue applied loading. Case study one estimates the thermal stresses superimposed sinusoidal cyclic mechanical stress results in solid cylinder under isothermal fatigue simulation. Case study two estimates the
Ranganath, S.
1979-01-01
Nuclear pressure vessel components are designed to meet the requirements of Section III of the ASME Boiler and Pressure Vessel Code. Specifically, the design must satisfy the limits on stress range and fatigue usage prescribed in NB-3200, Section III ASME Code for the various design and operating conditions for the component. The Code requirements assure that the component does not experience gross yielding and that in general, elastic shakedown occurs following cyclic loading. When elastic stress analysis is performed this can be shown by meeting the limits in the Code on Primary and Primary plus Secondary (P+Q) stress intensities. However, when the P+Q limits cannot be met and elastic Shakedown cannot be demonstrated, plastic analysis may be performed to meet the requirements of the Code. This paper describes the elastic-plastic stress analysis of a Boiling Water Reactor Vessel bottom head in-core penetration and illustrates how plastic analysis can be used in ASME Code evaluations to show Code compliance. Details of the thermal analysis, elastic-plastic stress analysis and fatigue evaluation are presented and it is shown that the in-core penetration satisfies the code requirements. 6 refs
Turangan, C. K.; Ball, G. J.; Jamaluddin, A. R.; Leighton, T. G.
2017-09-01
We present a study of shock-induced collapse of single bubbles near/attached to an elastic-plastic solid using the free-Lagrange method, which forms the latest part of our shock-induced collapse studies. We simulated the collapse of 40 μm radius single bubbles near/attached to rigid and aluminium walls by a 60 MPa lithotripter shock for various scenarios based on bubble-wall separations, and the collapse of a 255 μm radius bubble attached to aluminium foil with a 65 MPa lithotripter shock. The coupling of the multi-phases, compressibility, axisymmetric geometry and elastic-plastic material model within a single solver has enabled us to examine the impingement of high-speed liquid jets from the shock-induced collapsing bubbles, which imposes an extreme compression in the aluminium that leads to pitting and plastic deformation. For certain scenarios, instead of the high-speed jet, a radially inwards flow along the aluminium surface contracts the bubble to produce a `mushroom shape'. This work provides methods for quantifying which parameters (e.g. bubble sizes and separations from the solid) might promote or inhibit erosion on solid surfaces.
Elastic-plastic response of a piping system due to simulated double-ended guillotine break events
Kussmaul, K.; Diem, H.; Hunger, H.; Katzenmeier, G.
1987-01-01
From the blowdown experiments performed on the HDR feedwater line with feedwater check valve the conclusion can be drawn that high transient loads of up to plastic strains of 3%, acting on an initially integer piping system, can be sustained without loss of integrity for a low number of load cycles due to the plasticizing capacity of the pipework materials nowadays used in reactor technology. In the experiments carried out with ferritic piping of ND 400 pressure peaks up to about 31,5 MPa were achieved which resulted in excessive strains of up to 3%. By nonlinear finite element computations (ABAQUS) it was possible to describe the elastic-plastic behaviour of the piping in a good approximation. (orig./GL)
Schnabel, F.
1987-01-01
The present report deals with the influence of time-dependent material behavior on the load-carrying capacity of thin-walled shells of revolution. In the first part various creep-hardening hypotheses as well as the spatial and temporal discretization procedures employed are described. The adaptation of a well-tested finite element method based on ring elements to the treatment of creep problems and several time-integration procedures, in particular the iterative treatment of the coupling between creep and elastic-plastic strains as well as the important aspect of time-step-control are discussed in detail. In the second part several typical shell configurations are analyzed and a comparison with available theoretical and experimental results is made. Finally, the time-dependent load-carrying behavior of torispherical pressure vessel ends subjected to internal and external pressure is investigated and design aids for the determination of creep collapse times are proposed. (orig.) [de
Knight, Norman F., Jr.; Song, Kyongchan; Elliott, Kenny B.; Raju, Ivatury S.; Warren, Jerry E.
2012-01-01
Elastic-plastic, large-deflection nonlinear stress analyses are performed for the external hat-shaped stringers (or stiffeners) on the intertank portion of the Space Shuttle s external tank. These stringers are subjected to assembly strains when the stringers are initially installed on an intertank panel. Four different stringer-feet configurations including the baseline flat-feet, the heels-up, the diving-board, and the toes-up configurations are considered. The assembly procedure is analytically simulated for each of these stringer configurations. The location, size, and amplitude of the strain field associated with the stringer assembly are sensitive to the assumed geometry and assembly procedure. The von Mises stress distributions from these simulations indicate that localized plasticity will develop around the first eight fasteners for each stringer-feet configuration examined. However, only the toes-up configuration resulted in high assembly hoop strains.
Thomsen, N.B.; Fischer-Cripps, A.C.; Swain, M.V.
1998-01-01
of cracking and the fracture mechanisms taking place. In the study various diamond-like carbon (DLC) coatings deposited onto stainless steel and tool steel were investigated. Results primarily for one DLC system will be presented here. (C) 1998 Published by Elsevier Science S.A. All rights reserved.......In the present study crack formation is investigated on both micro and macro scale using spherical indenter tips. in particular, systems consisting of elastic coatings that are well adhered to elastic-plastic substrates are studied. Depth sensing indentation is used on the micro scale and Rockwell...... indentation on the macro scale. The predominant driving force for coating failure and crack formation during indentation is plastic deformation of the underlying substrate. The aim is to relate the mechanisms creating both delamination and cohesive cracking on both scales with fracture mechanical models...
Comparison of theory and experiment for elastic-plastic plane-strain crack growth. [AISI 4140 steel
Hermann, L.; Rice, J.R.
1980-08-01
Recent theoretical results on elastic-plastic plane-strain crack growth are reviewed and experimental results for crack growth in a 4140 steel are discussed in terms of the theoretical concepts. The theory is based on a recent asymptotic analysis of crack surface opening and strain distributions at a quasistatically advancing crack tip in an ideally plastic solid. The analysis is incomplete in that some of the parameters which appear in it are known only approximately, especially at large-scale yielding. Nevertheless, it is sufficient for the derivation of a relation between the imposed loading and amount of crack growth prior to general yielding, based on the assumption that a geometrically similar near-tip crack profile is maintained during growth. The resulting predictions for the variation of J with crack growth are found to fit well to the experimental results obtained on deeply cracked compact specimens.
Song, Tae Kwang; Oh, Chang Kyun; Kim, Yun Jae; Kim, Jong Sung; Jin, Tae Eun
2007-01-01
This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes
Song, Tae Kwang; Kim, Yun Jae; Oh, Chang Kyun; Kim, Jong Sung; Jin, Tae Eun
2007-01-01
This paper presents plastic limit loads and approximate J-integral estimates for circumferential part-through surface crack at the interface between elbows and pipes. Based on finite element limit analyses using elastic-perfectly plastic materials, plastic limit moments under in-plane bending are obtained and it is found that they are similar those for circumferential part-through surface cracks in the center of elbow. Based on present FE results, closed-form limit load solutions are proposed. Welds are not explicitly considered and all materials are assumed to be homogeneous. And the method to estimate the elastic-plastic J-integral for circumferential part-through surface cracks at the interface between elbows and straight pipes is proposed based on the reference stress approach, which was compared with corresponding solutions for straight pipes
Nakamura, Izumi; Shiratori, Masaki; Morishita, Masaki; Otani, Akihito; Shibutani, Tadahito
2015-01-01
According to investigations of several nuclear power plants (NPPs) hit by actual seismic events and a number of experimental researches on the failure behavior of piping systems under seismic loads, it is recognized that piping systems used in NPPs include a large seismic safety margin until boundary failure. Since the stress assessment based on the elastic analysis does not reflect actual seismic capability of piping systems including plastic region, it is necessary to develop a rational procedures to estimate the elastic-plastic behavior of piping systems under a large seismic load. With the aim of establishing a procedure that takes into account the elastic-plastic behavior effect in the seismic safety estimation of nuclear piping systems, a task force activity has been planned. Through the activity, the authors intend to establish guidelines to estimate the elastic-plastic behavior of piping systems rationally and conservatively, and to provide new rational seismic safety criteria taking the effect of elastic-plastic behavior into account. As the first step of making out the analysis guideline, benchmark analyses are conducted for a pipe element test and a piping system test. In this paper, the outline of the research activity and the preliminary results of benchmark analyses are described. (author)
Fernandez-Saez, J.; Luna de, S.; Rubio, L.; Perez-Castellanos, J. L.; Navarro, C.
2001-01-01
An earlier paper dealt with the experimental techniques used to determine the dynamic fracture properties of linear elastic materials. Here we describe those most commonly used as elastoplastic materials, limiting the study to the initiation fracture toughness at the intermediate strain rate (of around 10''2 s''-1). In this case the inertial forces are negligible and it is possible to apply the static solutions. With this stipulation, the analysis can be based on the methods of testing in static conditions. The dynamic case differs basically, from the static one, in the influence of the strain rate on the properties of the material. (Author) 57 refs
Brocks, W.; Kuenecke, G.
1989-06-01
Continuing preceding investigations, a further elastic-plastic finite element analysis of a test vessel with a semi-elliptical axial outer surface crack has been performed. The variations of J and CTOD along the crack front and the stress state in the vicinity of the crack are presented. The applicability of analytical approaches to determine J is examined. The FE results are used to analyze the experimental data with respect to the validity of J-controlled crack growth. Local J R -curves of the surface flaw are compared with J R -curves of various specimens of different geometries. Again, it became evident that the local ductile crack growth and, especially, the developing 'canoe shape' of the surface crack cannot be described by a single resistance curve which is assumed to be a material property. A method described in a previous report to predict the ductile crack growth by using local J R -curves which depend on the triaxiality of the stress state did not result in a satisfactory outcome, in the present case. The presumed reasons will be discussed. (orig.) [de
Elastic-plastic response of a piping system due to simulated double-ended guillotine break events
Kussmaul, K.; Diem, H.; Hunger, H.; Katzenmeier, G.
1987-01-01
From the blowdown experiments performed on the HDR feedwater line with feedwater check valve the conclusion can be drawn that high transient loads of up to plastic strains of 3%, acting on an initially integer piping system, can be sustained without loss of integrity for a low number of load cycles due to the plasticizing capacity of the pipework materials nowadays used in the reactor technology. In the experiments carried out with ferritic piping of ND 400 pressure peaks up to about 31,5 mPA were achieved which resulted in excessive strains of up to 3%. By nonlinear finite element computations (ABAQUS) it was possible to describe the elastic-plastic behaviour of the piping in a good approximation. On account of the safety margins proved in the experiments, potential inaccuracies in theoretical structure analyses are recommended so as to be on the safe side. On the other hand, it appears that designing pipework with reference to elastic stress categories does not adequately take into account the actual reserves of the pipework material
Buchalet, C.; Riccardella, P.C.
1972-01-01
Residual stresses due to weld deposited cladding on the inside of a typical Westinghouse pressurized water reactor vessel are investigated using an axisymmetric finite element elastic-plastic analysis. At the beginning of the analysis, one head of the weld cladding is assumed to lie on the reactor vessel wall at melting temperature (2600degF), but in the solid phase, while the vessel remains at 300degF (preheat temperature). All material properties used in the calculations are taken as temperature-dependent. Temperature profiles are obtained in the cladding and base metal at several discrete time intervals. These temperatures profiles are used to obtain the stress distribution for the same time intervals. Residual hoop tensile stresses of approximately 25 ksi were found to exist in the cladding. Peak tensile stresses in the hoop direction occur in the base metal near the cladding interface and reach a value of 60 ksi at the end of the transient. The tensile stress decreases very rapidly through the thickness of the base metal and becomes insignificant at about two inches from the inside surface. In order to lower residual stresses, a post-weld heat treatment is performed by uniformly heating the vessel to 1100degF, holding at that temperature for a specified period of time and then cooling slowly. The analysis shows that after this treatment, the peak stresses in the base metal decrease from 60 ksi to 32 ksi, while the stress in the cladding does not change significantly. (author)
Huh, Nam Su; Im, Chang Ju; Kim, Young Jin; Pyo, Chang Ryul; Park, Chi Yong
2000-01-01
In order to evaluate the integrity of nuclear power plant components, the analysis based on fracture mechanics is crucial. For this purpose, finite element method is popularly used to obtain J-integral. However, it is time consuming to design the finite element model of a cracked structure. Also, the J-integral should by verified by alternative methods since it may differ depending on the calculation method. The objective of this paper is to develop a three-dimensional elastic-plastic J-integral analysis system which is named as EPAS program. The EPAS program consists of an automatic mesh generator for a through-wall crack and a surface crack, a solver based on ABAQUS program, and a J-integral calculation program which provides DI (Domain Integral) and EDI (Equivalent Domain Integral) based J-integral calculation. Using the EPAS program, an optimized finite element model for a cracked structure can be generated and corresponding J-integral can be obtained subsequently
Use of J-integral and modified J-integral as measures of elastic-plastic fracture toughness
Davis, D.A.; Hays, R.A.; Hackett, E.M.; Joyce, J.A.
1988-01-01
J-R Curve tests were conducted on 12T, 1T and 2T compact specimens of materials having J/sub IC/ values ranging from 150 in-lbsq in to over 2600 in-lbsq in. These materials were chosen such that some would exceed the maximum crack length criterion of ASTM E1152-87 prior to reaching the maximum J criterion (3-Ni steel, 5000 series Al) and some would exceed the maximum J criterion first (A533B, A710). The elastic-plastic fracture behavior of these materials was examined using both the deformation theory J-integral (J/sub D/) and the modified J-integral (J/sub M/). The J-R curve testing was performed to very large values of crack opening displacement (COD) where the crack growth was typically 75% of the original remaining ligament. The results of this work suggest that the J/sub D/-R curves exhibit no specimen size dependence to crack extensions far in excess of the E1152 allowables. The J/sub M/-R curves calculated for the same specimens show a significant amount of specimen size dependence which becomes larger as the material toughness decreases. This work suggests that it is premature to utilize the modified J-integral in assessing the flaw tolerance of structures
On the use of J-integral and modified J-integral as measures of elastic-plastic fracture toughness
Davis, D.A.; Hays, R.A.; Hackett, E.M.; Joyce, J.A.
1988-01-01
J-R Curve tests were conducted on 1/2T, 1T and 2T compact specimens of materials having J IC values ranging from 150 in-1b/sq in to over 2600 in-lb/sq in. These materials were chosen such that some would exceed the maximum crack length criterion of ASTM E1152-87 prior to reaching the maximum J criterion (3-Ni steel, 5000 series A1) and some would exceed the maximum J criterion first (A533B, A710). The elastic-plastic fracture behavior of these materials was examined using both the deformation theory J-integral (J D ) and the modified J-integral (J M ). The J-R curve testing was performed to very large values of crack opening displacement (COD) where the crack growth was typically 75% of the original remaining ligament. The results of this work suggest that the J D -R curves exhibit no specimen size dependence to crack extensions far in excess of the E1152 allowables. The J M -R curves calculated for the same specimens show a significant amount of specimen size dependence which becomes larger as the material toughness decreases. This work suggests that it is premature to utilize the modified J-integral in assessing the flaw tolerance of structures. (author)
Anderson, C.A.; Smith, P.D.
1978-01-01
The variable modulus-cracking model is capable of predicting the behavior of reinforced concrete structures (such as the reinforced plate under transverse pressure described previously) well into the range of nonlinear behavior including the prediction of the ultimate load. For unreinforced thick-walled concrete vessels under internal pressure the use of elastic--plastic concrete models in finite element codes enhances the apparent ductility of the vessels in contrast to variable modulus-cracking models that predict nearly instantaneous rupture whenever the tensile strength at the inner wall is exceeded. For unreinforced thick-walled end slabs representative of PCRV heads, the behavior predicted by finite element codes using variable modulus-cracking models is much stiffer in the nonlinear range than that observed experimentally. Although the shear type failures and crack patterns that are observed experimentally are predicted by such concrete models, the ultimate load carrying capacity and vessel-ductility are significantly underestimated. It appears that such models do not adequately model such features as aggregate interlock that could lead to an enhanced vessel reserve strength and ductility
Anderson, C.A.; Smith, P.D.
1979-01-01
Numerical prediction of the behavior of prestressed concrete reactor vessels (PCRVs) under static, dynamic and long term loadings is complicated by the currently ill-defined behavior of concrete under stress and the three-dimensional nature of PCRVs. Which constitutive model most closely approximates the behavior of concrete in PCRVs under load has not yet been decided. Many equations for accurately modeling the three-dimensional behavior of PCRVs tax the capability of a most up-to-date computing system. The main purpose of this paper is to compare the characteristics of two constitutive models which have been proposed for concrete, variable modulus cracking model and elastic-plastic model. Moreover, the behavior of typical concrete structures was compared, the materials of which obey these constitutive laws. The response to internal pressure of PCRV structure, the constitutive models for concrete, the test problems using a thick-walled concrete ring and a rectangular concrete plate, and the analysis of an axisymmetric concrete pressure vessel PV-26 using the variable modulus cracking model of the ADINA code are explained. The variable modulus cracking model can predict the behavior of reinforced concrete structures well into the range of nonlinear behavior. (Kako, I.)
Christensen, Claus Dencker; Byskov, Esben
2008-01-01
The postbuckling behavior and imperfection sensitivity of the Shanley-Hutchinson plastic model column introduced by Hutchinson in 1973 are examined. The study covers the initial, buckled state and the advanced postbuckling regime of the geometrically perfect realization as well as its sensitivity...... to geometric imperfections. In Section 1, which is concerned with the perfect structure, a new, simple explicit upper bound for all solutions to the problem is found when the tangent modulus at bifurcation vanishes compared to the linear elastic (unloading) modulus. The difference between the upper bound...... and the solution to an actual problem is determined by an asymptotic expansion involving hyperbolic trial functions (instead of polynomials) which fulfill general boundary conditions at bifurcation and infinity. The method provides an accurate estimate of the maximum load even if it occurs in an advanced...
Investigation on crack growth parameters in the elastic plastic region (interim report)
Prij, J.
1982-03-01
Some theoretical as well as numerical results are presented with respect to the 2D and 3D application of linear elastic fracture mechanics. The application of the finite element method to calculate the stress and strain field in cracked bodies has been discussed with special attention to: singularity representation, parameter extraction and mesh refinement. Detailed 3D stress analyses of fracture mechanics test specimen are presented showing that: the stress intensity concept cannot be extended simply into a 3D concept, the energy release concept is more promising within this aspect and the plastic region along the crackfront will not have a dogbone shape. The 3D elastic fracture mechanics concept is applied to evaluate the consequences of the thermal stresses due to γ-heating in an in-pile crack growth experiment
Mixed-mode elastic-plastic fracture of 2024-T351 aluminium alloy
Sakata, Masaru; Aoki, Shigeru; Kishimoto, Kikuo; Chikugo, Hiroshi; Takizawa, Masakazu.
1985-01-01
In order to evaluate accurately the strength and structural soundness of the structures made of high toughness materials, it is necessary to clarify the fracture behavior under the loading condition of mixed mode such as oblique cracks as well as the elasto-plastic fracture behavior of the materials in the case of single opening displacement type mode. About the fracture condition in the state of mixed mode, various theories based on the linear fracture mechanics have been proposed. In this study, the elasto-plastic fracture toughness test of mixed mode was carried out by using an aluminum alloy as the subject, and the behavior of dulling and development of cracks was observed with a scanning electron microscope. Moreover, the state of deformation of the test pieces was analyzed by elasto-plastic finite element method, thus the parameters controlling the elasto-plastic fracture of mixed mode were examined. In the range of this study, the limiting stretch zone width in the case of loading of mixed mode was 12 μm similarly to the case of single mode. Also in the case of mixed mode, there was distinct difference between the inclination of a dulling straight line and an R-curve, and the limit value of J intergral was determined by their intersection. (Kako, I.)
KharchenkoV.V.
2014-12-01
Full Text Available The results of calculating the stress state of a hollow cylinder with a defect in the form of cracks, which is at the top of the cavity in the elastic-plastic formulation is presented. The calculation results are compared with the results of solving this problem in the elastic formulation vand with the results of solving the problem of the stretching cylinder with a crack.
KharchenkoV.V.; Ban’koS.N.; KobelskyS.V.; KravchenkoV.I.
2014-01-01
The results of calculating the stress state of a hollow cylinder with a defect in the form of cracks, which is at the top of the cavity in the elastic-plastic formulation is presented. The calculation results are compared with the results of solving this problem in the elastic formulation vand with the results of solving the problem of the stretching cylinder with a crack.
Dynamic elastic-plastic behaviour of a frame including coupled bending and torsion
Messmer, S.; Sayir, M.
1989-01-01
The full time response of a space frame under impact loading perpendicular to the frame plane is discussed. Theoretical solutions and experimental results are presented and compared. A space frame clamped at its two ends is loaded by a 0.22 lead bullet that hits a mass in the middle of the transversal beam of the frame. The loading time is about 40 to 60 μs and the resulting linear momentum of the impact in the experiment is 0.5 to 1 N s. The time response of this frame can be divided in four phases where different physical effects are dominant: (a) The loading phase where elastic wave motion dominates the time response. Because of the high impact forces, plastic deformation occurs in the vicinity of the mass and must be included in a theoretical model. The influence of reflections at the corners on the time response is shown in theory and experiment. (b) The evolution phase. Within this phase, a plastic collapse mechanism develops. Most of this phase is dominated by elastic deformation but local plastic deformations beside the mass are also present. Because many reflections at corners, clamps and the mass occur within this phase, a modal analysis method is used to predict time histories. (c) The plastic phase with plastic zones at the clamps. The phase sets in after the bending wave reaches the clamps. It is characterized by plastic deformation near the clamps and elastic deformation of the other parts of the frame. We used a modal analysis including plastic 'modes' to get accurate results. (d) The elastic vibration phase
Elastic-plastic-creep response of structures under composite time history of loadings
Zudans, Z.
1975-01-01
The purpose of this work is to derive the theory, to develop efficient numerical techniques accounting for plasticity, creep and overall equilibrium, to describe the overall structure of the resulting computer program, and to demonstrate the capability of this analysis on a real structure. Classical plasticity theory is used to develop a novel method based on the concept of 'plastic stress' for consideration of inelastic behavior. It is shown that materials stres-strain curves can be followed to any desired degree of accuracy both for isotropic and kinematic hardening. It is further shown that for kinematic hardening it is necessary to base the incremental change on the state corresponding to the mean of the initial and the final states in order to satisfy the yield condition at the final state. The equation of state and strain hardening is used to describe the creep behavior. A novel numerical technique to describe a complex load history is developed by using time as a parameter, history breakpoint determination by scanning of various load vectors and by linear interpolation between any two breakpoints in the load history. The 'plastic stress' load vector concept is utilized with iteration and extrapolation to converge to the equilibrium states with simultaneous satisfaction of the stress-strain relations for each of the iterated states. The essential features of the computer program DYPLAS-FSH, based on the theory and techniques described above, and a postprocessor program POR-FSH, based on RDT F9-5T for ratcheting and fatigue evaluation, are identified and discussed. These computer programs are used to analyse the ellipsoidal pressure vessel head of the intermediate heat exchanger of EBR-II, penetrated by two closely spaced non-radial nozzles, subjected to four consecutive composite cycles of complex mechanical and thermal loads
Lee, So-Dam; Lee, Han-Sang; Kim, Yun-Jae; Ainsworth, Robert A.; Dean, David W.
2016-01-01
This technical note presents the effect of elastic-plastic properties on calculated time-dependent C(t) and J(t) values. This is investigated via systematic elastic-plastic-creep finite element (FE) analysis. Three different stress-strain curves are used, having essentially the same plastic properties at large strains but different tensile data near the 0.2% proof (yield) strength. It is found that the plastic property in stress-strain curve affects the FE C(t) values only at short times (within approximately 20% of the redistribution time). The plastic property affects the initial J values at time t = 0 but not the rate of change of J(t) with time. - Highlights: • The effect of elastic-plastic properties on calculated time-dependent C(t) and J(t) values is presented via FE analysis. • The plastic property affects the FE C(t) values only at short times up to ∼20% of the redistribution time. • The plastic property affects the initial J values at time t = 0 but not the rate of change of J(t) with time.
A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows
Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin
2017-11-01
A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.
Aurich, D.; Brocks, W.; Noack, D.; Veith, H.
1981-01-01
From a three-dimensional elastic-plastic stress-distortion analysis according to the finite element method (FEM) for a straight inner edge crack at room temperature in a nozzle of the intermediate vessel ZB 2 made of 22 NiMoCr 37 steel, the results obtained for stresses and strains in the ligament before the crack front, the crack opening profile, and the propagation of the plastic zone as a function of internal pressure until through-plastifying of the ligament are shown and explained. (orig.) [de
Joo, Jae Hwang; Kang, Ki Ju; Jhung, Myung Jo
2002-01-01
Performed here is an assessment study for deterministic fracture mechanics analysis of a pressurized thermal shock (PTS). The PTS event means an event or transient in pressurized water reactors (PWRs) causing severe overcooling (thermal shock) concurrent with or followed by significant pressure in the reactor vessel. The problems consisting of two transients and 10 cracks are solved and maximum stress intensity factors and maximum allowable nil-ductility reference temperatures are calculated. Their results are compared each other to address the general characteristics between transients, crack types and analysis methods. The effects of elastic-plastic material behavior and clad coating on the inner surface are explored
Zhan-ping Song
2016-01-01
Full Text Available To study the tunnel stability at various static water pressures and determine the mechanical properties and deformation behavior of surrounding rock, a modified effective stress formula was introduced into a numerical integration algorithm of elastic-plastic constitutive equation, that is, closest point projection method (CPPM. Taking the effects of water pressure and seepage into account, a CPPM-based formula was derived and a CPPM algorithm based on Drucker-Prager yield criterion considering the effect of pore water pressure was provided. On this basis, a CPPM-based elastic-plastic numerical analysis program considering pore water pressure was developed, which can be applied in the engineering of tunnels and other underground structures. The algorithm can accurately take the effects of groundwater on stability of surrounding rock mass into account and it can show the more pronounced effect of pore water pressure on stress, deformation, and the plastic zone in a tunnel. The stability of water flooding in Fusong tunnel was systematically analyzed using the developed program. The analysis results showed that the existence of groundwater seepage under tunnel construction will give rise to stress redistribution in the surrounding rock mass. Pore water pressure has a significant effect on the surrounding rock mass.
Song, Kee Nam; Hong, Sung Deok; Park, Hong Yoon
2011-01-01
A PHE (Process Heat Exchanger) is a key component required to transfer heat energy of 950 .deg. C generated in a VHTR (Very High Temperature Reactor) to a chemical reaction that yields a large quantity of hydrogen. A small-scale PHE prototype made of Hastelloy-X was scheduled for testing in a small-scale gas loop at the Korea Atomic Energy Research Institute. In this study, as a part of the evaluation of the high-temperature structural integrity of the PHE prototype, high-temperature structural analysis modeling, and macroscopic thermal and elastic-plastic structural analysis of the PHE prototype were carried out under the gas-loop test conditions as a preliminary qwer123$ study before carrying out the performance test in the gas loop. The results obtained in this study will be used to design the performance test setup for the modified PHE prototype
Moreno, A
1977-07-01
In this work a new elastic-plastic-viscous model is described. The model is one of the multiple integral type, and has been included in a numerical code to predict the behaviour of a nuclear fuel of cylindrical form. Some features of this code are also described. (Author) 91 refs.
Betekhtin, V. I.; Sklenička, Václav; Saxl, Ivan; Kardashev, B. K.; Kadomtsev, A. G.; Narykova, M. V.
52 2010, č. 8 (2010), s. 1629-1636 ISSN 1063-7834 Institutional research plan: CEZ:AV0Z20410507; CEZ:AV0Z10190503 Keywords : equal-channel angular pressing (ECAP) * severe plastic deformation * ultrafine-grained material * elastic-plastic properties Subject RIV: JG - Metallurgy Impact factor: 0.727, year: 2010
Gomez, M.P.; McMeeking, R.M.; Parks, D.M.
1980-06-01
Contributions were made toward developing a new methodology to assess the stability of cracks in pressure vessels made from materials that exhibit a significant increase in toughness during the early increments of crack growth. It has a wide range of validity from linear elastic to fully plastic behavior
Kamaya, Masayuki
2012-01-01
Although the plastic strain induced in materials increases the mechanical strength, it may reduce the fracture toughness. In this study, the change in fracture toughness of SM490 carbon steel due to pre-straining was investigated using a stress-based criterion for ductile crack initiation. The specimens with blunt notch of various radiuses were used in addition to those with conventional fatigue pre-cracking. The degree of applied plastic strain was 5%, 10% or 20%. The fracture toughness was largest when the induced plastic strain was 5%, although it decreased for the plastic strains of 10% and 20%. The stress and strain distributions near the crack tip of fracture toughness test specimens was investigated by elastic-plastic finite element analyses using a well-correlated stress-strain curve for large strain. It was shown that the critical condition at the onset of the ductile crack was better correlated with the equivalent stress than the plastic strain at the crack tip. By using the stress-based criterion, which was represented by the equivalent stress and stress triaxiality, the change in the fracture toughness due to pre-straining could be reasonably explained. Based on these results, it was concluded that the stress-based criterion should be used for predicting the ductile crack initiation. (author)
Povolotskaya Anna
2018-01-01
Full Text Available The paper reports results of magnetic measurements made on samples of the 12GB pipe steel (strength group X42SS designed for producing pipes to be used in media with high hydrogen sulphide content, both in the initial state and after exposure to hydrogen sulphide, for 96, 192 and 384 hours under uniaxial elastic-plastic tension. At the stage of elastic deformation there is a unique correlation between the coercive force measured on a minor hysteresis loop in weak fields and tensile stress, which enables this parameter to be used for the evaluation of elastic stresses in pipes made of the 12 GB pipe steel under different conditions, including a hydrogen sulphide containing medium. The effect of the value of preliminary plastic strain, viewed as the initial stress-strain state, on the magnetic behaviour of X70 pipe steels under elastic tension and compression is studied. Plastic strain history affects the magnetic behaviour of the material during subsequent elastic deformation since plastic strain induces various residual stresses, and this necessitates taking into account the initial stress-strain state of products when developing magnetic techniques for the determination of their stress-strain parameters during operation.
Ikonen, K.
1993-07-01
The report describes the work performed for achieving readiness to calculate fracture toughness dependence on dimension effects and loading conditions in fracture test specimens and real structures. In the report two- and three-dimensional computer codes developed and calculational methods applied are described. One of the main goals is to converse fracture toughness from small scale three point bending test specimens to case of a depth crack in plane strain i.e. to small scale yielding state (SSY) by numerical elastic-plastic stress analysis. Thickness effect of a test specimens and effect of a crack depth are separately investigated. Tests of three point bending specimens with and without sidegrooves and curved crack front are numerically simulated and experimental and computed results are compared. J-integral is calculated along crack front and also from force-deflection dependence of the beam. For the analyses the computing system was thoroughly automatized. Measuring capacity of three point bending test specimens was tried to evaluate. (orig.) (7 refs., 54 figs.)
Yamaguchi, Yoshihito; Katsuyama, Jinya; Onizawa, Kunio; Li, Yinsheng; Sugino, Hideharu
2011-01-01
The magnitude of Niigata-ken Chuetsu-Oki earthquake in 2007 was beyond the assumed one provided in seismic design. Therefore it becomes an important issue to evaluate the crack growth behaviors due to the cyclic overload like large earthquake. Fatigue crack growth is usually evaluated by Paris's law using the range of stress intensity factor (ΔK). However, ΔK is inappropriate in a loading condition beyond small scale yielding. In this study, the crack growth behaviors for piping materials were investigated based on an elastic-plastic fracture mechanics parameter, J-integral. It was indicated that the crack growth due to the cyclic overload beyond small scale yielding could be the sum of fatigue and ductile crack growth. The retardation effect of excessive loading on the crack growth was observed after the loading. The modified Wheeler model using J-integral has been proposed for the prediction of retardation effect. Finally, an evaluation method for crack growth behaviors due to the cyclic overload is suggested. (author)
Bui, Huy Duong
1969-01-01
In this research thesis on metal strain hardening, the author first discusses the issue of passing from microscopic values to corresponding macroscopic values. If there is generally a correspondence between them, it is not the case for plastic strain. Thus, the author studies the general properties of the boundary of the macroscopic plastic field with respect to single-crystal elastic boundaries. In the second part, the author reports an experimental study of the evolution of the elastic field boundary. In the third part, he develops elastic-plastic behaviour laws for an aggregate of cubic crystals. The objectives are to report experimental results in a more satisfying way than previous studies, and to obtain acceptable physical laws while keeping some properties of conventional laws in order to ensure the solution uniqueness, and to establish minimum principles similar to those of Nodge-Prager and of Greenberg. In order to do so, he introduces a new hypothesis: there is a statistic scattering in initial thresholds of crystals
Liu, K.C.
1975-01-01
Two tubular specimens of type 304 stainless steel with uniform thin walls were subjected to a program of segmental combined tension/compression and torsion loadings at room temperature. A proportional, or radial, loading into the plastic range was initially applied to each specimen. Two nonproportional (nonradial) loadings along straight line segments for which neither the loading paths nor their linear extrapolations passed through the origin of the stress space were then applied. The axial and torsional stress-strain curves for these segmental prestress loadings were plotted. Hence, the stress-strain response characteristics for nonproportional loadings as well as for proportional loading can be studied. In addition, the axial and torsional plastic strain components were calculated, and the total plastic strain trajectories were plotted in a plastic strain space. Finally, using results from a detailed study of yield surfaces, which was performed for the first specimen, a spectrum of initial and subsequent yield curves corresponding to the segmental prestress loadings is presented. (U.S.)
Kuhn, Matthew R.; Daouadji, Ali
2018-05-01
The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This complex behavior is explored for multi-directional loading probes that follow an initial monotonic loading. An advanced DEM model is used in the study, with non-convex non-spherical particles and two different contact models: a conventional linear-frictional model and an exact implementation of the Hertz-like Cattaneo-Mindlin model. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain), with tiny strain increments of 2 ×10-6 . At the micro-scale, contact movements were monitored during small increments of loading and load-reversal, and results show that these movements are not reversed by a reversal of strain direction, and some contacts that were sliding during a loading increment continue to slide during reversal. The probes show that the coupled part of a strain increment, the difference between the recoverable (elastic) increment and its reversible part, must be considered when partitioning strain increments into elastic and plastic parts. Small increments of irreversible (and plastic) strain and contact slipping and frictional dissipation occur for all directions of loading, and an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations.
Allen, Phillip A.; Wells, Douglas N.
2013-01-01
No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.
Maire, Pierre-Henri; Abgrall, Rémi; Breil, Jérôme; Loubère, Raphaël; Rebourcet, Bernard
2013-02-01
In this paper, we describe a cell-centered Lagrangian scheme devoted to the numerical simulation of solid dynamics on two-dimensional unstructured grids in planar geometry. This numerical method, utilizes the classical elastic-perfectly plastic material model initially proposed by Wilkins [M.L. Wilkins, Calculation of elastic-plastic flow, Meth. Comput. Phys. (1964)]. In this model, the Cauchy stress tensor is decomposed into the sum of its deviatoric part and the thermodynamic pressure which is defined by means of an equation of state. Regarding the deviatoric stress, its time evolution is governed by a classical constitutive law for isotropic material. The plasticity model employs the von Mises yield criterion and is implemented by means of the radial return algorithm. The numerical scheme relies on a finite volume cell-centered method wherein numerical fluxes are expressed in terms of sub-cell force. The generic form of the sub-cell force is obtained by requiring the scheme to satisfy a semi-discrete dissipation inequality. Sub-cell force and nodal velocity to move the grid are computed consistently with cell volume variation by means of a node-centered solver, which results from total energy conservation. The nominally second-order extension is achieved by developing a two-dimensional extension in the Lagrangian framework of the Generalized Riemann Problem methodology, introduced by Ben-Artzi and Falcovitz [M. Ben-Artzi, J. Falcovitz, Generalized Riemann Problems in Computational Fluid Dynamics, Cambridge Monogr. Appl. Comput. Math. (2003)]. Finally, the robustness and the accuracy of the numerical scheme are assessed through the computation of several test cases.
Ast, Johannes
2016-01-01
The objective of this work was to get an improved understanding of the size dependence of the fracture toughness. For this purpose notched micro-cantilevers were fabricated ranging in dimensions from the submicron regime up to some tens of microns by means of a focused ion beam. B2-NiAl and tungsten were chosen as model materials as their brittle to ductile transition temperatures are well above room temperature. In that way, fracture processes accompanied by limited plastic deformation around the crack tip could be studied at the micro scale. For this size regime, new methods to describe the local elastic-plastic fracture behavior and to measure the fracture toughness were elaborated. Particular focus was set on the J-integral concept which was adapted to the micro scale to derive crack growth from stiffness measurements. This allowed a precise analysis of the transition from crack tip blunting to stable crack growth which is necessary to accurately measure the fracture toughness. Experiments in single crystalline NiAl showed for the two investigated crack systems, namely the hard and the soft orientation, that the fracture toughness at the micro scale is the same as the one known from macroscopic testing. Thus, size effects were not found for the tested length scale. The addition of little amounts of iron did not affect the fracture toughness considerably. Yet, it influenced the crack growth in those samples and consequently the resistance curve behavior. Concerning experiments in single crystalline tungsten, the fracture toughness showed a clear dependency on sample size. The smallest cantilevers fractured purely by cleavage. Larger samples exhibited stable crack growth along with plastic deformation which was recognizable in SEM-micrographs and quantified by means of EBSD measurements. Just as in macroscopic testing, the investigated crack system {100} demonstrated a dependency on loading rate with higher loading rates leading to a more brittle behavior. This
Nakagawa, Tsuguhiko; Nuta, Kunihiro [Kawasaki Steel Corp., Okayama, (Japan). Mizushima Warks
1999-03-10
The radiant tube heating system has been widely applied to the furnaces which require isolation of the heating atmosphere from the combustion atmosphere. However, the conventional system has a short life and it is difficult to reduce NO{sub x} emission when it is used at a high furnace temperature under high combustion load, because the fuel is burned in a small space. In order to solve this problem, we have studied the cause of radiant tube life depends on the uniformity of the temperature distribution along the radiant tube. We have developed a new burner using a two-stage combustion method with exhaust gas self-recirculation. As a result, the file of the new system has been increased by a factor of two or more, and NO{sub x} emission has been reduced by 20 % from previous levels. This paper presents an outline of the elastic-plastic creep analysis and the new burner, and describes the effect of its use on system life. (author)
Peralta, Pedro
2018-04-16
a viscoplastic model to account for steady state (stage II) creep behavior, along with basic assumptions from crystal plasticity and kinematic constraints due to testing fixtures. In the micro-scale, testing of microcantilever beams at temperatures ranging from 25 to 570 °C was performed in-situ with a scanning electron microscope with a special attachment to apply load and measure displacement while the samples were at temperature. The load-displacement curves obtained showed linear behavior before fracture for all temperatures attempted except 570 °C, where clear deviations from non-linearity were observed before fracture. These deviations were consistently observed for all samples tested for a given orientation. A viscoplastic model was used to account for the presence of inelastic strain, along with basic assumptions from crystal plasticity and beam theory. These models were kept as simple as possible, and results from tests performed in a set of samples with a given crystal orientation were used to calibrate the material constants for the model, while results from a different sample set were then used for validation, thus satisfying the conditions of all main tasks within the parameters of this project. Details of these efforts are outlined in this report.
Elastic-plastic constitutive modeling of concrete
Takahashi, Y.
1983-03-01
The need to understand concrete behavior under high temperatures in the nuclear industry has become rather accute. For this purpose, a constitutive model of concrete especially developed for this severe environment is indispensable. This report reviews the presently available constitutive models of concrete at standard-temperature conditions and considers their advantages and drawbacks. A rather simple but effective approach is selected to treat concrete behavior at high temperatures. Special emphasis is devoted to the modeling of concrete up to and including failure. The derived constitutive model is checked with biaxial and triaxial benchmark experimental results. Very good agreement is obtained
Studies of elastic-plastic instabilities
Tvergaard, Viggo
1999-01-01
Analyses of plastic instabilities are reviewed, with focus on results in structural mechanics as well as continuum mechanics. First the basic theories for bifurcation and post-bifurcation behavior are briefly presented. Then, localization of plastic flow is discussed, including shear band formati...
Elastic plastic buckling of elliptical vessel heads
Alix, M.; Roche, R.L.
1981-08-01
The risks of buckling of dished vessel head increase when the vessel is thin walled. This paper gives the last results on experimental tests of 3 elliptical heads and compares all the results with some empirical formula dealing with elastic and plastic buckling
The use of a path independent integral in non-linear fracture mechanics
Hellen, T.K.
1977-01-01
A computer program for calculating the J and J* integrals has been developed as an extension to the BERSAFE finite element system. A full analysis of the cracked structure including plasticity, creep and thermal strains is conducted and the results are stored on a permanent data set. The integral values may then be calculated using the post-processor program for any number of contours and load or time steps, without recourse to further expensive computations. Numerical examples are presented comparing the J and J* integrals for a number of cracked plates under thermal, plastic and creep environments. To demonstrate the accuracy for a simple thermo-elastic case, a centre cracked plate subject to a symmetric quadratic gradient is included. Here, the J integral is shown to be path dependent whereas good independence is seen for the J* integral. The case of an elastic-plastic plate is invetigated to demonstrate path independence for both integrals in non-linear elasticity, and the effects of unloading are discussed. An alternative method for obtaining the change of potential energy over a small crack extension is briefly mentioned and compared to the J and J* results in this case. An axisymmetric bar with an internal penny-shaped crack subjected to tension is discussed under elastic-plastic materials behavior
De Donato, O.; Parisi, M.A.
1977-01-01
When loads increase proportionally beyond the elastic limit in the presence of elastic-plastic piecewise-linear constitutive laws, the problem of finding the whole evolution of the plastic strain and displacements of structures was recently shown to be amenable to a parametric linear complementary problem (PLCP) in which the parameter is represented by the load factor, the matrix is symmetric positive definite or at least semi-definite (for perfect plasticity) and the variables with a direct mechanical meaning are the plastic multipliers. With reference to plane trusses and frames with elastic-plastic linear work-hardening material behaviour numerical solutions were also fairly efficiently obtained using a recent mathematical programming algorithm (due to R.W. Cottle) which is able to provide the whole deformation history of the structure and, at the same time to rule out local unloadings along the given proportional loading process by means of 'a priori' checks carried out before each pivotal step of the procedure. Hence it becomes possible to use the holonomic (reversible, path-independent) constitutive laws in finite terms and to benefit by all the relevant numerical and computational advantages despite the non-holonomic nature of plastic behaviour. In the present paper the method of solution is re-examined in view to overcome an important drawback of the algorithm deriving from the size of PLCP fully populated matrix when structural problems with large number of variables are considered and, consequently, the updating, the storing or, generally, the handling of the current tableau may become prohibitive. (Auth.)
FEAST: a two-dimensional non-linear finite element code for calculating stresses
Tayal, M.
1986-06-01
The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
Richtmyer-Meshkov instability in elastic-plastic media
Piriz, Antonio R.; López Cela, Juan J.; Tahir, Naeem A.; Hoffmann, Dieter H. H.
2008-04-01
Hydrodynamic instabilities are of great importance in the LAPLAS (Laboratory of Planetary Sciences) experiment that is being designed for the study of high energy density states of matter in the framework of the FAIR projectDuring the implosion of the LAPLAS cylindrical target Richtmyer-Meshkov (RM) instability occurs when a shock is launched into a material pusher with elastic and plastic properties that determines the physics of the instability evolution. We have studied the evolution of the interface from which the shock is launched as a consequence of the RM instability. For this we have developed an analytical model and we have performed two-dimensional numerical simulations in order to validate the model. Model and simulations show the asymptotic stability state in which the interface oscillates elastically around a mean value higher than the initial perturbation amplitude. Such a mean value is determined by an initial plastic phase. Applications to the measurement of the yield strength of materials under extreme conditions are foreseen.
Elastic-Plastic Calculation of a Dilatation Compensation Component
Atanasiu, Costică; Iliescu, Nicolae; Sorohan, Ștefan
2017-12-01
Compensators are elastic structures that have the role of taking over the axial displacements that occur in the junction areas of the technological equipment (pipelines or containers) through which the fluids circulate at pressures and high temperatures. These elastic structures, realized in a very wide range of shapes and sizes, are sujected by the inner pressure and an axial force produced by dilatation of structures in which they are mounted. The calculation of the expansion compensators raises many problems caused by the working regimes of the technological equipments they belong to. Following previous studies, undertaken by calculus and experimental, by the authors of this paper, it was found that in operation the state of stress in these elastic structures exceeds the flow limit of the material from which they are manufacturated. For this reason, in the present paper, the authors present the results of a calculus study, by FEM, on the stress and strain state, in the elasto-plastic regime of a leticular compensator. The calculation was made for two loading modes, separately applied and superimposed. The nonlinear mechanical behavior of this compensator is analyzed and discussed comparatively to the results of previous studies performed in elastic regime on the same type of compensator.
A unified approach to elastic-plastic fracture mechanics
Neale, B.K.; Townley, C.H.A.
1976-01-01
To assess the integrity of a cracked structure, using materials data obtained from simple laboratory tests, it is essential to define materials properties which are independent of the shape and the size of the specimen and of the loading system applied to it. In those situations where either the specimen or the structure fails after significant yielding has taken place, there is considerable speculation about the materials parameters which are relevant. By extending the Griffith equation for the stability of a perfectly elastic cracked body, the authors derive a fracture criterion which is applicable in the post yield regime. Comparisons are made with procedures based on the J-contour integral, equivalent energy, and crack opening displacements and with the post yield fracture mechanics of Heald, Spink and Worthington, and Dowling and Townley. For certain materials, it is shown that the factor controlling crack initiation is the fracture toughness Ksub(1c), irrespective of the amount of prior plastic damage, and hence independent of the shape and size of the specimen tested. Load carrying capacity in the post yield regime cannot, however, be derived directly from a knowledge of fracture toughness; the ultimate tensile strength of the material is also relevant
Elastic-plastic response characteristics during frequency nonstationary waves
Miyama, T.; Kanda, J.; Iwasaki, R.; Sunohara, H.
1987-01-01
The purpose of this paper is to study fundamental effects of the frequency nonstationarity on the inelastic responses. First, the inelastic response characteristics are examined by applying stationary waves. Then simple representation of nonstationary characteristics is considered to general nonstationary input. The effects for frequency nonstationary response are summarized for inelastic systems. The inelastic response characteristics under white noise and simple frequency nonstationary wave were investigated, and conclusions can be summarized as follows. 1) The maximum response values for both BL model and OO model corresponds fairly well with those estimated from the energy constant law, even when R is small. For the OO model, the maximum displacement response forms a unique curve except for very small R. 2) The plastic deformation for the BL model is affected by wide frequency components, as R decreases. The plastic deformation for the OO model can be determined from the last stiffness. 3). The inelastic response of the BL model is considerably affected by the frequency nonstationarity of the input motion, while the response is less affected by the nonstationarity for OO model. (orig./HP)
Analytical relations between elastic-plastic fracture criteria
Merkle, J.G.
1976-07-01
The equation of the normalized COD design curve recently proposed in the UK as a basis for determining allowable crack sizes is derived from the Equivalent Energy approximation for the J Integral. It is also shown that another approximation for the J Integral recently proposed by Westinghouse is mathematically equivalent to the normalized COD approach
Fatigue crack propagation under elastic plastic medium at elevated temperature
Asada, Y.; Yuuki, R.; Sakon, T.; Sunamoto, D.; Tokimasa, K.; Makino, Y.; Kitagawa, M; Shingai, K.
1980-01-01
The purposes of the present study are to establish the testing method to obtain compatible data on the low cycle fatigue crack propagation at elevated temperature, and to investigate the parameter controlling the crack propagation rate. In the present study, the preliminary experiments have been carried out on low cycle fatigue crack propagation behaviour in type 304 stainless steel in air at 550 0 C, using two types of specimen with a through thickness notch. Both strain controlled and stress controlled fatigue tests have been done under a fully reversed strain or stress cycling. The data obtained are correlated with some fracture mechanics parameters and are discussed with the appropriate parameter for evaluating the low cycle fatigue crack propagation behaviour at elevated temperature. (author)
Suwono.
1978-01-01
A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)
Vretenar, M
2014-01-01
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics
Linearization Method and Linear Complexity
Tanaka, Hidema
We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Berberian, Sterling K
2014-01-01
Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
Olive, David J
2017-01-01
This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response trans...
Alcaraz, J.
2001-01-01
After several years of study e''+ e''- linear colliders in the TeV range have emerged as the major and optimal high-energy physics projects for the post-LHC era. These notes summarize the present status form the main accelerator and detector features to their physics potential. The LHC era. These notes summarize the present status, from the main accelerator and detector features to their physics potential. The LHC is expected to provide first discoveries in the new energy domain, whereas an e''+ e''- linear collider in the 500 GeV-1 TeV will be able to complement it to an unprecedented level of precision in any possible areas: Higgs, signals beyond the SM and electroweak measurements. It is evident that the Linear Collider program will constitute a major step in the understanding of the nature of the new physics beyond the Standard Model. (Author) 22 refs
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Karloff, Howard
1991-01-01
To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...
Ast, Johannes
2016-07-01
The objective of this work was to get an improved understanding of the size dependence of the fracture toughness. For this purpose notched micro-cantilevers were fabricated ranging in dimensions from the submicron regime up to some tens of microns by means of a focused ion beam. B2-NiAl and tungsten were chosen as model materials as their brittle to ductile transition temperatures are well above room temperature. In that way, fracture processes accompanied by limited plastic deformation around the crack tip could be studied at the micro scale. For this size regime, new methods to describe the local elastic-plastic fracture behavior and to measure the fracture toughness were elaborated. Particular focus was set on the J-integral concept which was adapted to the micro scale to derive crack growth from stiffness measurements. This allowed a precise analysis of the transition from crack tip blunting to stable crack growth which is necessary to accurately measure the fracture toughness. Experiments in single crystalline NiAl showed for the two investigated crack systems, namely the hard and the soft orientation, that the fracture toughness at the micro scale is the same as the one known from macroscopic testing. Thus, size effects were not found for the tested length scale. The addition of little amounts of iron did not affect the fracture toughness considerably. Yet, it influenced the crack growth in those samples and consequently the resistance curve behavior. Concerning experiments in single crystalline tungsten, the fracture toughness showed a clear dependency on sample size. The smallest cantilevers fractured purely by cleavage. Larger samples exhibited stable crack growth along with plastic deformation which was recognizable in SEM-micrographs and quantified by means of EBSD measurements. Just as in macroscopic testing, the investigated crack system <100>{100} demonstrated a dependency on loading rate with higher loading rates leading to a more brittle behavior
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Tanwiwat Jaikuna
2017-02-01
Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.
Oberpichler, R.
1979-01-01
The thin steel liner attached by studs or rib-type anchors to the interior wall of a Prestressed Concrete Reactor Pressure Vessel (PCRV) or a Concrete Containment Vessel (PCCV) has to provide the leak-tightness of the vessel. The liner also may serve as internal shuttering for placing concrete as well as a support for the cooling system or thermal isolation. Mainly strained by self-limited loads imposed on the liner by deformations of the vessel-wall or by heatup inside the vessel the liner predominantly will function in a compressive biaxially strained state like a membrane. The vessel-wall is assumed to be a rigid boundary without reactions caused by the liner-anchor-restraints. Furthermore it is assumed that the liner supported in a close-spaced pattern to the concrete with respect to self-limited loads and all effects of non-linear behaviour of liner-material and non-linear anchor-characteristics will not fail by instability, especially not by an effect of snapthrough. Only one essential mode of failure, the shear connector failure is assumed to be basis for all liner investigations. Design of the liner and its anchorage therefore is based on the analysis of large deformations with regard to elastic-plastic behaviour of liner-material and non-linear anchor characteristics. By this method both economical and safe sizing and spacing of the anchors can be calculated. (orig.)
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...
Linearly constrained minimax optimization
Madsen, Kaj; Schjær-Jacobsen, Hans
1978-01-01
We present an algorithm for nonlinear minimax optimization subject to linear equality and inequality constraints which requires first order partial derivatives. The algorithm is based on successive linear approximations to the functions defining the problem. The resulting linear subproblems...
Fujioka, Terutaka
2015-01-01
This paper proposes methods for assessing Bree-type ratcheting in a cylinder subjected to constant internal pressure and cyclic thermal loading. The proposed methods are elastic analysis-route and elastic–plastic analysis-route. The former is based on the polynomial approximation of the elastic stress distributions for thermal stresses and the reference stress concept for estimating primary stress. The latter elastic–plastic route method is based on the concept of relative elastic core size. The methods proposed were validated by performing elastic–plastic finite element analyses of a smooth cylinder that exhibited Bree-type ratcheting. - Highlights: • Rationalization of the ratcheting assessment has been made. • The proposed methods include both elastic and elastic-plastic routes. • The elastic route method is based on skeletal point stress by elastic FEA. • The elastic-plastic route is based on elastic core size in elastic-plastic FEA. • These have been validated by elastic-plastic FEA causing Bree-type ratcheting
Foundations of linear and generalized linear models
Agresti, Alan
2015-01-01
A valuable overview of the most important ideas and results in statistical analysis Written by a highly-experienced author, Foundations of Linear and Generalized Linear Models is a clear and comprehensive guide to the key concepts and results of linear statistical models. The book presents a broad, in-depth overview of the most commonly used statistical models by discussing the theory underlying the models, R software applications, and examples with crafted models to elucidate key ideas and promote practical model building. The book begins by illustrating the fundamentals of linear models,
Numerical modelling in non linear fracture mechanics
Viggo Tvergaard
2007-07-01
Full Text Available Some numerical studies of crack propagation are based on using constitutive models that accountfor damage evolution in the material. When a critical damage value has been reached in a materialpoint, it is natural to assume that this point has no more carrying capacity, as is done numerically in the elementvanish technique. In the present review this procedure is illustrated for micromechanically based materialmodels, such as a ductile failure model that accounts for the nucleation and growth of voids to coalescence, and a model for intergranular creep failure with diffusive growth of grain boundary cavities leading to micro-crack formation. The procedure is also illustrated for low cycle fatigue, based on continuum damage mechanics. In addition, the possibility of crack growth predictions for elastic-plastic solids using cohesive zone models to represent the fracture process is discussed.
Tuey, R. C.
1972-01-01
Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.
Peterson, David; Stofleth, Jerome H.; Saul, Venner W.
2017-07-11
Linear shaped charges are described herein. In a general embodiment, the linear shaped charge has an explosive with an elongated arrowhead-shaped profile. The linear shaped charge also has and an elongated v-shaped liner that is inset into a recess of the explosive. Another linear shaped charge includes an explosive that is shaped as a star-shaped prism. Liners are inset into crevices of the explosive, where the explosive acts as a tamper.
Classifying Linear Canonical Relations
Lorand, Jonathan
2015-01-01
In this Master's thesis, we consider the problem of classifying, up to conjugation by linear symplectomorphisms, linear canonical relations (lagrangian correspondences) from a finite-dimensional symplectic vector space to itself. We give an elementary introduction to the theory of linear canonical relations and present partial results toward the classification problem. This exposition should be accessible to undergraduate students with a basic familiarity with linear algebra.
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
Non linear system become linear system
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Linear motor coil assembly and linear motor
2009-01-01
An ironless linear motor (5) comprising a magnet track (53) and a coil assembly (50) operating in cooperation with said magnet track (53) and having a plurality of concentrated multi-turn coils (31 a-f, 41 a-d, 51 a-k), wherein the end windings (31E) of the coils (31 a-f, 41 a-e) are substantially
Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.
2009-01-01
An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)
Wiedemann, H.
1981-11-01
Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center.
Blyth, T S
2002-01-01
Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...
Wiedemann, H.
1981-11-01
Since no linear colliders have been built yet it is difficult to know at what energy the linear cost scaling of linear colliders drops below the quadratic scaling of storage rings. There is, however, no doubt that a linear collider facility for a center of mass energy above say 500 GeV is significantly cheaper than an equivalent storage ring. In order to make the linear collider principle feasible at very high energies a number of problems have to be solved. There are two kinds of problems: one which is related to the feasibility of the principle and the other kind of problems is associated with minimizing the cost of constructing and operating such a facility. This lecture series describes the problems and possible solutions. Since the real test of a principle requires the construction of a prototype I will in the last chapter describe the SLC project at the Stanford Linear Accelerator Center
Matrices and linear transformations
Cullen, Charles G
1990-01-01
""Comprehensive . . . an excellent introduction to the subject."" - Electronic Engineer's Design Magazine.This introductory textbook, aimed at sophomore- and junior-level undergraduates in mathematics, engineering, and the physical sciences, offers a smooth, in-depth treatment of linear algebra and matrix theory. The major objects of study are matrices over an arbitrary field. Contents include Matrices and Linear Systems; Vector Spaces; Determinants; Linear Transformations; Similarity: Part I and Part II; Polynomials and Polynomial Matrices; Matrix Analysis; and Numerical Methods. The first
Efficient Non Linear Loudspeakers
Petersen, Bo R.; Agerkvist, Finn T.
2006-01-01
Loudspeakers have traditionally been designed to be as linear as possible. However, as techniques for compensating non linearities are emerging, it becomes possible to use other design criteria. This paper present and examines a new idea for improving the efficiency of loudspeakers at high levels...... by changing the voice coil layout. This deliberate non-linear design has the benefit that a smaller amplifier can be used, which has the benefit of reducing system cost as well as reducing power consumption....
Faraway, Julian J
2014-01-01
A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition.New to the Second EditionReorganiz
Carr, Joseph
1996-01-01
The linear IC market is large and growing, as is the demand for well trained technicians and engineers who understand how these devices work and how to apply them. Linear Integrated Circuits provides in-depth coverage of the devices and their operation, but not at the expense of practical applications in which linear devices figure prominently. This book is written for a wide readership from FE and first degree students, to hobbyists and professionals.Chapter 1 offers a general introduction that will provide students with the foundations of linear IC technology. From chapter 2 onwa
Fault tolerant linear actuator
Tesar, Delbert
2004-09-14
In varying embodiments, the fault tolerant linear actuator of the present invention is a new and improved linear actuator with fault tolerance and positional control that may incorporate velocity summing, force summing, or a combination of the two. In one embodiment, the invention offers a velocity summing arrangement with a differential gear between two prime movers driving a cage, which then drives a linear spindle screw transmission. Other embodiments feature two prime movers driving separate linear spindle screw transmissions, one internal and one external, in a totally concentric and compact integrated module.
Superconducting linear accelerator cryostat
Ben-Zvi, I.; Elkonin, B.V.; Sokolowski, J.S.
1984-01-01
A large vertical cryostat for a superconducting linear accelerator using quarter wave resonators has been developed. The essential technical details, operational experience and performance are described. (author)
Elastic plastic analysis of fuel element assemblies - hexagonal claddings and fuel rods
Mamoun, M.M.; Wu, T.S.; Chopra, P.S.; Rardin, D.C.
1979-01-01
Analytical studies have been conducted to investigate the structural, thermal, and mechanical behavior of fuel rods, claddings and fuel element assemblies of several designs for a conceptual Safety Test Facility (STF). One of the design objectives was to seek a geometrical configuration for a clad by maximizing the volume fraction of fuel and minimizing the resultant stresses set-up in the clad. The results of studies conducted on various geometrical configurations showed that the latter design objective can be achieved by selecting a clad of an hexagonal geometry. The analytical studies necessitated developing solutions for determining the stresses, strains, and displacements experienced by fuel rods and an hexagonal cladding subjected to thermal fuel-bowing loads acting on its internal surface, the external pressure of the coolant, and elevated temperatures. This paper presents some of the initially formulated analytical methods and results. It should be emphasized that the geometrical configuration considered in this paper may not necessarily be similar to that of the final design. Several variables have been taken into consideration including cladding thickness, the dimensions of the fuel rod, the temperature of the fuel and cladding, the external pressure of the cooling fluid, and the mechanical strength properties of fuel and cladding. A finite-element computer program, STRAW Code, has also been employed to generate several numerical results which have been compared with those predicted by employing the initially formulated solutions. The theoretically predicted results are in good agreement with those of the STRAW Code. (orig.)
Load bearing capacities and elastic-plastic behavior of reactor vessel internals
Watanabe, Keita; Nagase, Ryuichi
2017-01-01
Radial Support Keys (RSKs) are installed at the bottom of Reactor Vessel Internal (RVI) of Pressurized Water Reactor (PWR) and fit into Core Support Lugs of Reactor Pressure Vessel (RPV). This structure provides reactor core horizontal support and transmits the loads between RVI and RPV. RSK is one of the critical parts of RVI from the view point of earthquake-proof safety. In order to assure the structural integrity of Nuclear Reactor in case of massive earthquake, load bearing capacities of RSK are confirmed by static loading tests with reduced-scale mockups. In addition, collapse loads of actual components calculated by Limit Analyses are conservative enough compared to the load bearing capacities confirmed by the test. Thus, the methodology to calculate collapse load by Limit Analysis is applicable to evaluation of structural integrity for RSK. (author)
Elastic-plastic creep response of structures under composite time history
Zudans, Z [Franklin Inst. Research Labs., Philadelphia, Pa. (USA)
1975-12-01
High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. The new results of this work are the efficient handling of an arbitrary load history, introduction of the 'plastic stress' concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the 'plastic stress' concept, and development of a computer code capable of solving practical three-dimensional problems.
On higher-order boundary conditions at elastic-plastic boundaries in strain-gradient plasticity
Niordson, Christian Frithiof
2008-01-01
are suppressed by using a very high artificial hardening modulus. Through numerical studies of pure bending under plane strain conditions, it is shown that this method predicts the build-up of higher order stresses in the pseudo-elastic regime. This has the effect of delaying the onset of incipient yield......, as well as extending the plastic zone further toward the neutral axis of the beam, when compared to conventional models. Arguments supporting the present method are presented that rest on both mathematical and physical grounds. The results obtained are compared with other methods for dealing with higher...
Tayal, M.
1986-10-01
The finite element code ELESTRES models the two-dimensional axisymmetric behaviour of a CANDU fuel element during normal operation. The main focus of the code is to estimate temperatures, fission gas release, and axial variations of deformation/stresses in the pellet and in the sheath. Thus the code is able to predict details like stresses/strains at circumferential ridges. This paper describes the current version of ELESTRES. The emphasis is on a recent addition: multiaxial stresses in the sheath near circumferential ridges. For accuracy in the critical region, a fine mesh is used near the ridge. To keep computing costs low, a coarse mesh is used near the midplane of the pellet. Predictions of ELESTRES show good agreement with abouth 80 measurements of fission-gas-release. In this paper, we also present ELESTRES predictions of hoop strains in sheaths, for two irradiations: element ABS and bundle GB. For both irradiations, predictions, compare favourably with measurements. An illustrative example shows that near circumferential ridges, bending contributes to multiaxial stresses in the sheath. This can have a significant effect on sheath integrity, such as during stress-corrosion-cracking due to power-increases, or during corrosion-assisted-fatigue due to power cycling
Some comment on the use of J criterion in elastic plastic fracture mechanics
Roche, R.L.
1978-01-01
In Post Yield Fracture Mechanics, several criteria have been proposed for the onset of crack propagation, one of the most popular being the J 1 integral criterion. This is only well established for elastic materials, where it can be shown that J 1 is not path dependent, and that J 1 is equal to the variation of potential energy with crack length. Extension is easy for material exhibiting deformation type plasticity, but there is no proof of path independence for flow-type plastic material. Experimental results are often given as a proof of J 1 criterion validity, but a critical analysis shows that important assumptions are made in the use of the test results. The main assumption is that the received work, known as strain energy, is not dependent on the loading history and is only dependent on the mechanical state. The study of the J 1 path dependence is the main point of the J 1 criteria validation. A general method to assess path dependence can be founded on the 'defect vector' (or driving force) concept. The space-density of defect is given by j = grad W - σ grad (W = strain-energy, σ stress tensor, epsilon strain tensor). It is shown that the virtual translation delta a of the defect vectors inside a volume, lead to a virtual work variation given by J 1 delta a and that J 1 is the resultant of all the defect vectors included in the volume surrounded by the integration surface. Using these results the path independence conditions are examined. Some numerical results are given for incremental processes such as plasticity or creep, and where the loading path is radial (proportional) and monotonic, no appreciable path variations found. Finally the results of direct applications of J 1 criterion to real structures are examined. (author)
Round-robin activities on finite element analyses of elastic-plastic fracture in Japan
Shimakawa, T.; Takahashi, Y.; Yagawa, G.
1989-01-01
The establishment of the leak-before-break (LBB) concept requires a method to evaluate the fracture characteristics. The finite element method can be used for this purpose but the solution is more or less influenced by the method employed. In this study, two round-robin analyses are performed for three-dimensional crack problems. The first problem is for surface crack growth in a carbon steel plate subjected to tension loading. Ten solutions are obtained by ten participants, and calculated results are compared with each other as to the applied load, displacement and J-integral. Though the relation between applied load and displacement is affected by modeling of the stress-strain curve, fairly good agreement is obtained between the solutions. The second problem is for a circumferential part-through crack in a carbon steel pipe subjected to a bending moment. Nine solutions are obtained by eight participants. The difference between the solutions is relatively significant as to the relation between J-integral and load-point displacement. A discussion is made about the sources of difference between each solution. (orig.)
The Nonlinear Dynamic Response of an Elastic-Plastic Thin Plate under Impulsive Loading,
1987-06-11
Among those numerical methods, the finite element method is the most effective one. The method presented in this paper is an " influence function " numerical...computational time is much less than the finite element method. Its precision is higher also. II. Basic Assumption and the Influence Function of a Simple...calculation. Fig. 1 3 2. The Influence function of a Simple Supported Plate The motion differential equation of a thin plate can be written as DV’w+ _.eluq() (1
Elastic-Plastic Deformation in Cracked Solids and Ductile Fracture Criterion.
1982-01-01
stresses fracture propertiesstanfedi; /atigue(materials)____ 0 AserivAcT ecwesu -oroe silill of1 reew-W vis t~dUiP by block nbr he main objectives of the... rubber infiltration, etc. None of these methods can avoid some degree of arbitrariness, either in the relation between the far field measurement and the
Improvement of elastic-plastic fatigue crack growth evaluation method. 2. Crack opening behavior
Takahashi, Yukio [Central Research Inst. of Electric Power Industry, Tokyo (Japan)
2001-05-01
Evaluation of crack growth behavior under cyclic loading is often required in the structural integrity assessment of cracked components. Closing and re-opening of the crack give large influence on crack growth rate through the change of fracture mechanics parameters. Based on the finite element analysis for a center-cracked plate, dependency of crack opening ratio on applied stress range and mean stress was examined. Simple formulae for representing the results were derived for plane stress and plane strain conditions. (author)
Nanomechanical quantification of elastic, plastic, and fracture properties of LiCoO{sub 2}
Qu, Meng; Woodford, William H.; Maloney, John M.; Carter, W. Craig; Chiang, Yet-Ming; Van Vliet, Krystyn J. [Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA (United States)
2012-08-15
Young's elastic modulus, hardness, and fracture toughness (K{sub Ic}) of individual grains are reported for polycrystalline LiCoO{sub 2}, a metal oxide cathode used in lithium-ion batteries, as measured via instrumented nanoindentation (indentations within circled locations; dashed line indicates grain boundary). The wide range of K{sub Ic} does not correlate strongly with grain orientation. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The J-integral concept for elastic-plastic material behavior
Schmitt, W.; Kienzler, R.
1987-03-01
A simple analytical extension of the J integral has been presented which extends the J concept to apply for materials described by an incremental theory of plasticity. The stress work density replacing the strain energy density is load-history dependent. The J integral may be made path independent by virtue of an additional volume integral and may be understood as work dissipation rate. The discussion of the consequences for the applicability of the J concept to describe fracture processes showed that validity criteria proposed in the standards are not sufficient to yield configuration-independent J-resistance curves. However, a possibility is sketched to assess those structure-dependent resistance curves based on plastic-collapse considerations. With 6 figs., 33 refs
Elastic-plastic-creep response of structures under composite time history of loadings
Zudans, Z.
1975-01-01
High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This work derives the theory, develops efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of this analysis on a real structure. (Auth.)
Wen, Jici; Wei, Yujie; Cheng, Yang-Tse
2018-07-01
Monitoring in real time the stress state in high capacity electrodes during charge-discharge processes is pivotal to the performance assessment and structural optimization of advanced batteries. The wafer curvature measurement technique broadly employed in thin-film industry, together with stress analysis using the Stoney equation, has been successfully adopted to measure in situ the stress in thin film electrodes. How large plastic deformation or interfacial delamination during electrochemical cycles in such electrodes affects the applicability of Stoney equation remains unclear. Here we develop a robust electrochemical-mechanical coupled numerical procedure to investigate the influence of large plastic deformation and interfacial failure on the measured stress in thin film electrodes. We identify how the constitutive behavior of electrode materials and film-substrate interfacial properties affect the measured stress-capacity curves of electrodes, and hence establish the relationship of electrode material parameters with the characteristics of stress-capacity curves. Using Li-ions batteries as examples, we show that plastic deformation and interfacial delamination account for the asymmetric stress-capacity loops seen in in situ stress measurements. The methods used here, along with the finite-element code in the supplementary material, may be used to model the electrode behavior as a function of the state of charge.
The crack-initiation threshold in ceramic materials subject to elastic/plastic indentation
Lankford, J.; Davidson, D.L.
1979-01-01
The threshold for indentation cracking is established for a range of ceramic materials, using the techniques of scanning electron microscopy and acoustic emission. It is found that by taking into account indentation plasticity, current theories may be successfully combined to predict threshold indentation loads and crack sizes. Threshold cracking is seen to relate to radial rather than median cracking. (author)
Computational experiences with variable modulus, elastic-plastic, and viscoelastic concrete models
Anderson, C.A.
1981-01-01
Six years ago the Reactor Safety Research Division of the Nuclear Regulatory Commission (NRC) approached the Los Alamos National Laboratory to develop a comprehensive concrete structural analysis code to predict the static and dynamic behavior of Prestressed Concrete Reactor Vessels (PCRVs) that serve as the containment structure of a High-Temperature Gas-Cooled Reactor. The PCRV is a complex concrete structure that must be modeled in three dimensions and posseses other complicating features such as a steel liner for the reactor cavity and woven cables embedded vertically in the PCRV and wound circumferentially on the outside of the PCRV. The cables, or tendons, are used for prestressing the reactor vessel. In addition to developing the computational capability to predict inelastic three dimensional concrete structural behavior, the code response was verified against documented experiments on concrete structural behavior. This code development/verification effort is described
Energy absorption during compression and impact of dry elastic-plastic spherical granules
Antonyuk, Sergiy; Heinrich, Stefan; Tomas, Jürgen; Deen, N.G.; van Buijtenen, M.S.; Kuipers, J.A.M.
2010-01-01
The discrete modelling and understanding of the particle dynamics in fluidized bed apparatuses, mixers, mills and others are based on the knowledge about the physical properties of particles and their mechanical behaviour during slow, fast and repeated stressing. In this paper model parameters
Elastic-plastic potential functionals for rates and increments of stress and strain
Feijoo, R.A.; Zouain, N.
1990-03-01
In this work attention is focused in the derivation of variational formulations of the constutive relationship in the form of conjugate potential functionals from which stress and strain rates are derived as elements of the corresponding sub-differential sets. The main result obtained is a pair of potential functionals. (A.C.A.S.) [pt
Elastic-plastic analysis using an efficient formulation of the finite element method
Aamodt, B.; Mo, O.
1975-01-01
Based on the flow theory of plasticity, the von Mises or the Tresca yield criterion and the isotropic hardening law, an incremental stiffness relationship can be established for a finite element model of the elasto-plastic structure. However, instead of including all degrees of freedom and all finite elements of the total model in a nonlinear solution process, a separation of elastic and plastic parts of the structure can be carried out. Such a separation can be obtained by identifying elastic parts of the structure as 'elastic' superelements and elasto-plastic parts of the structure as 'elasto-plastic' superelements. Also, it may be of advantage to use several levels of superelements in modelling the elastic parts of the structure. For the 'elasto-plastic' superelements the specific plastic computations such as updating of the incremental stiffness matrix and subsequent reduction (i.e. static condensation of all degrees of freedom being local to the superelements) have to be carried out repeatedly during the nonlinear solution process. The solution of the nonlinear equations is performed utilizing a combination of load incrementation and equilibrium interations. The present method of analysis is demonstrated for two larger examples of elasto-plastic analysis. (Auth.)
Jamari, Jamari; Schipper, Dirk J.
2007-01-01
This paper presents theoretical and experimental results of the residual or plastic deformation and the plastic contact area of an elastic–plastic contact of ellipsoid bodies after unloading. There are three regime responses of the deformation and contact area: elastic, elastic–plastic and fully
Definition of an instability criterion for precracked components in the elastic-plastic regime
Kussmaul, K.; Eisele, U.; Clausmeyer, H.; Roos, E.
1994-01-01
By giving examples of complexly loaded large samples with dimensions similar to components, it was shown that by the indicated failure concept the maximum load of a component, even after cracking, can be quantitatively defined and utilized, provided the crack growth law for the existing multidirectional grade of the stress state is known. However, by comparing the stress states in the component with usual small-scale sample results it is possible to define the occurring failure process after crack initiation either in the form of stable crack widening or immediate instability (rupture). (orig.) [de
Modeling Nonlinear Elastic-plastic Behavior of RDX Single Crystals During Indentation
2012-01-01
single crystals has also been probed using shock experiments (6, 12) and molecular dynamics simulations (12–14). RDX undergoes a polymorphic phase...Patterson, J.; Dreger, Z.; Gupta, Y. Shock-wave Induced Phase Transition in RDX Single Crystals. J. Phys. Chem. B 2007, 111, 10897–10904. 17. Bedrov, D...and Volume Compression of β - HMX and RDX . In Proc. Int. Symp. High Dynamic Pressures; Commissariat a l’Energie Atomique: Paris, 1978; pp 3–8. 24
Elastic-plastic creep response of structures under composite time history
Zudans, Z.
1975-01-01
High temperature nuclear reactor components are subject to a complex history of thermal and mechanical loading cycles. To evaluate the adequacy of such components, detailed information on the accumulated inelastic strains and strain cycling is required. This paper presents the theory, describes efficient numerical techniques accounting for plasticity, creep and overall equilibrium, describes the overall structure of the resulting computer program, and demonstrates the capability of the analysis method on a real three-dimensional structure. The new results of this work are the efficient handling of an arbitrary load history, introduction of the 'plastic stress' concept for inelastic computation, novel implementation of classical plasticity with recognition of incrementation conditions for the kinematic hardening, use of the load incrementation algorithm based on the 'plastic stress' concept, and development of a computer code capable of solving practical three-dimensional problems. (Auth.)
Study on the Elasticity-Plasticity-Stickiness of the Railway Crushed Stone Ballast
Gao Liang
2004-01-01
This paper is mainly aimed at the mechanics characteristic elas of ticity-plasticitystickiness existed in the CWR (continuously welded rails) track plane of the railway crushed stone ballast. As an important mechanics parameter of the CWR track plane, the ballast resistance is mainly influenced by this mechanics characteristic. Through the systematic experimental research and the theoretical analysis, this mechanics characteristic of the ballast resistance is revealed and a reasonable theoretical model is built for it. This study set a sound foundation for further studying the CWR track deformation property. It will be beneficial to the development of high-speed railway in China.
Elastic-plastic mechanical constitutive description for rock salt triaxial compression
Butcher, B.M.
1981-06-01
A model for the time-independent part of the mechanical deformation of rock salt from the Waste Isolation Pilot Plant Site in southeastern New Mexico is presented. A recently published creep model was first used to correct conventional triaxial compression data for time-dependent deformation. The experimental data was from tests at a loading rate of approximately 11.9 N/s, 23 0 C, and confining pressures from 0 to -20.7 MPa. The corrected time-independent curves were then used to determine material constants for the model. Generalization to a three-dimensional plasticity-failure theory using a general constitutive relation proposed by Rudnicki and Rice was also performed. 7 figures, 3 tables
Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials
Chao Chang
2018-01-01
Full Text Available Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF, ψ, and strain constraint factor (strain CF, β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors.
Elastic-plastic stress distributions near the endcap of a fuel element
Tayal, M.; Hallgrimson, K.D.; Sejnoha, R.; Singh, P.N.
1993-06-01
This paper discusses the stress patterns in and near the endcap of a CANDU fuel element from the perspective of stress corrosion cracking. Simulations of out-reactor burst tests suggest that local plastic strains stay comparatively low for internal pressures below 26-30 MPa. Photoelastic measurements as well as analytical assessments show that the reentrant corner at the sheath/endcap junction results in high concentration of stresses and strains. Analytical assessments show that the in-reactor stresses and strains at the reentrant corner are highly multiaxial, and well into the plastic range. The maximum principal stress correlates well with the location and the direction of circumferential endcap cracks observed in fuel that failed in the Bruce reactor. Thus the maximum principal stress appears promising in ranking various geometries of the sheath/endcap junction with respect to their relative susceptibility to stress corrosion cracking. Design studies suggest that the most effective practical ways of lowering the stresses near the weld, in order of decreasing importance, are to provide a larger interference-free length between the ridge and the endcaps; to increase the pellet/sheath radial gap; to increase the pellet/endcap axial gap; and to keep the gas pressure low. (author). 16 refs., 16 figs
1992-12-01
HH(201) REAL QQ(201), PLAS(201), PP(201) REAL AMAT(NRA,NRA), BMAT (NRA), XSOL(NRA) REAL SR(201), ST(201), SZ(201), SEFF(201) NNRA = NRA IF (JAR.EQ.0...VMU(I-1)) 30 CONTINUE C - - - Initialize A and B DO 51 I=1,2*NTOT DO 52 J-1,2*NTOT AMAT(I,J)= 0.0 52 CONTINUE BMAT (I) = 0.0 51 CONTINUE C...1))’J**2 -GG(INT+1) D0 66 I=1,NTOI AMAT(I,NTOT+I) = AA(I+l) !upvci right AMAT(NTOT+I,NTOT+I) = -FF(I±1) !lower right BMAT (I) = 0. BMAT (NTOT+I) = QQ(I
An Elastic-Plastic Finite Element Analysis of Notched Aluminum Panels.
1981-03-01
ZL. 0j W 0 WOO0 U w~ZZ%"*Q’c-- aIIUX(>-’j...W * 4%eweJW W *CI W. 4 * Q ~7.j W I~7 b-.~ i i t~e W W 00I 20 ~ ~ ~ ~ ~ t 2: aZ2a... Zaw Z Nctl-l*Z.J ’Z...34 Q"-Z=LU. LLZZoUZO 000 uzm3- LCWIn 40 Wi 0 %no* 0-4 004 to O*tt) -0 *0a -Or (* 0 . tuN * *010 ("~o 0-t a%* n Inl *0 101o 0- W* *4 -d .. *..i -4.4 144
Elastic-plastic waves in UV 0.2 Uranium alloy
Bernier, H.; Lalle, P.
1984-09-01
Release waves coming from the back face of an uranium alloy projectile in a symmetric collision are used to estimate some dynamic characteristics of this material. In the pressure range experimentally covered (<=29GPa) the velocity of the elastic precursor is about 3,45 km/s, and the Hugoniot elastic limit (HEL) is 1,15GPa. The pressure decrease behind the 20GPa (29GPa) shock wave begins with a quasi-elastic wave which velocity is 3,9 km/s (4,2 km/s), and pressure jump of 3GPa (3,7GPa)
Elastic-plastic analysis of local and integral straining behaviour in a cracked plate
Grueter, L.; Ruettenauer, B.
1982-01-01
For components of the primary coolant system of the German LMFBR prototype reactor SNR-300, integrity against anticipated accidents (Bethe-Tait) has to be shown for a cracked structure. Within this programme a number of tests with cracked wide plate specimens yielding overall limit strains of approximately 15% have been run; finite element calculations have been infinated for the wide plate geometry. The paper discusses the straining behaviour of a cracked plate by considering the numerical simulation of structures strained up to such high levels. The stress-strain diagram of the weldment of the austenitic stainless steel X6 CrNi 18 at 450 0 C has been used. Plane strain and stress conditions have been prescribed. The original plate dimensions (t = thickness = 40 mm; h = height = 400 mm) have been used as well as a similar, but smaller plate of t = 8.8 mm width. The crack length is defined as 0.1 t. The results show that for a cracked plate under high plastic strain the near-crack-tip-field values still govern the structural mechanical behaviour. Concerning the absolute dimensions the effects known for elasticity retain their influence in the plastic regime; however, the crack location becomes more unimportant with increasing strain, i.e. the appropriate pure geometry factor tends to unity in the plastic regime. The center-crack, defined as 2a = 0.1 t, corresponds to an equivalent edge crack of depth a = 0.05 t in the elastic case. It can be shown that for high plastic strains this correspondence remains fully valid. (orig.)
In situ neutron diffraction and Elastic-Plastic Self-Consistent polycrystal modeling of HT-9
Clausen, B., E-mail: clausen@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Brown, D.W.; Bourke, M.A.M.; Saleh, T.A.; Maloy, S.A. [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2012-06-15
Qualifying materials for use in reactors with fluences greater than 200 dpa (displacements per atom) requires development of advanced alloys and irradiations in fast reactors to test these alloys. Research into the mechanical behavior of these materials under reactor conditions is ongoing. In order to probe changes in deformation mechanisms due to radiation in these materials, samples of HT-9 were tested in tension in situ on the SMARTS instrument at Los Alamos Neutron Science Center. Experimental results, confirmed with modeling, show significant load sharing between the carbides and parent phase of the steel beyond yield, displaying the critical role of carbides during deformation, along with basic texture development.
A general shakedown theorem for elastic/plastic bodies with work hardening
Ponter, A.R.S.
1975-01-01
In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown of an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behavior is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem for an arbitrary time-independent material in terms of functional properties of the constitutive relationship is derived. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. It is shown that the result for all three constitutive relationships may be related to each other through certain extremal stress histories. As well as providing a sufficient condition for shakedown, the theory also provides bounds of the deflection of the structure in the process of reaching the shakedown state. The bounds are discussed and derived for two simple beam problems. Both static and dynamic problems are considered. The theory derived in this paper demonstrates that shakedown analysis may be extended to a wide range of material behavior without increasing the complexity of the resulting calculation
A general shakedown theorem for elastic/plastic bodies with work hardening
Ponter, A.R.S.
1975-01-01
In recent years the design of metallic structures under variable loading has been assisted by the application of Melan's lower bound theorem for the shakedown on an elastic/perfectly plastic structure. The design codes for both portal frames and pressure vessels have taken account of such calculations. The theory of shakedown suffers from two defects, geometry changes are ignored and the material behaviour is described by a perfectly plastic constitutive relationship which includes neither work hardening nor the Bauschinger effect. This paper is concerned with the latter problem. A very general lower bound shakedown theorem is derived for an arbitrary time-independent material in terms of functional properties of the constitutive relationship. The theorem is then applied to perfect, isotropic and kinematic hardening plasticity. (Auth.)
Influence of porosity on cavitation instability predictions for elastic-plastic solids
Tvergaard, Viggo; Vadillo, G.
2007-01-01
, while the high stress levels are reached at some distance from the void, and the interaction of these stress and strain fields determines the porosity evolution. In some cases analysed, the porosity is present initially in the metal matrix, while in other cases voids nucleate gradually during...... the deformation process. It is found that interaction with the neighbouring voids reduces the critical stress for unstable cavity growth....
Elastic-Plastic Fracture Mechanics Analysis of a CT-Specimen - a Two-Dimensional Approach
Larsen, Gunner Chr.
strain as well as a plane stress approximation. The results presented include applied loads and displacements at certain locations. Moreover, the J-integral and the crack opening displacement have been presented. The plane strain and the plane stress approximation have been compared and the plane stres......« approximation is believed to deliver the best results. The results have been obtained using the finiteelement code ADINA and the postprocessor code JINT....
Holt, J.; Goddard, D.J.
1980-01-01
Measurements of the acoustic emission behaviour of A533B and C-Mn low alloy reactor pressure vessel steels subjected to uniaxial tensile deformation are described. The effects on the emission activity of the rolling plane orientation and the carbide morphology were examined. Detailed discussions are given of the stress dependence of the emission activity below yield and of its recovery by annealing at the stress relief temperature. It is shown that the dominant emission source is the same in both steels and is associated with inclusions, such as MnS, elongated by the rolling process, the carbide morphology being relatively unimportant. A criterion for the occurrence of an emission is obtained which is directly analogous to the general criterion for yielding. It is also shown that a large fraction, at least, of the emission activity arises from a recoverable process such as localized yielding around inclusions or limited inclusion decohesion and not from inclusion fracture. Low activity in C-Mn steel taken from reactor pressure vessels, previously attributed to spheroidization of carbides, is shown to be due to the limited acoustic recovery of these relatively high sulphur content steels when annealed at the stress relief temperature. It is concluded that the limited amplitudes of these emissions during deformation severely restrict their potential application in practice. (Auth.)
Patten, B.C.
1983-04-01
Two issues concerning linearity or nonlinearity of natural systems are considered. Each is related to one of the two alternative defining properties of linear systems, superposition and decomposition. Superposition exists when a linear combination of inputs to a system results in the same linear combination of outputs that individually correspond to the original inputs. To demonstrate this property it is necessary that all initial states and inputs of the system which impinge on the output in question be included in the linear combination manipulation. As this is difficult or impossible to do with real systems of any complexity, nature appears nonlinear even though it may be linear. A linear system that displays nonlinear behavior for this reason is termed pseudononlinear. The decomposition property exists when the dynamic response of a system can be partitioned into an input-free portion due to state plus a state-free portion due to input. This is a characteristic of all linear systems, but not of nonlinear systems. Without the decomposition property, it is not possible to distinguish which portions of a system's behavior are due to innate characteristics (self) vs. outside conditions (environment), which is an important class of questions in biology and ecology. Some philosophical aspects of these findings are then considered. It is suggested that those ecologists who hold to the view that organisms and their environments are separate entities are in effect embracing a linear view of nature, even though their belief systems and mathematical models tend to be nonlinear. On the other hand, those who consider that organism-environment complex forms a single inseparable unit are implictly involved in non-linear thought, which may be in conflict with the linear modes and models that some of them use. The need to rectify these ambivalences on the part of both groups is indicated.
Linear colliders - prospects 1985
Rees, J.
1985-06-01
We discuss the scaling laws of linear colliders and their consequences for accelerator design. We then report on the SLAC Linear Collider project and comment on experience gained on that project and its application to future colliders. 9 refs., 2 figs
Richter, B.
1985-01-01
A report is given on the goals and progress of the SLAC Linear Collider. The author discusses the status of the machine and the detectors and give an overview of the physics which can be done at this new facility. He also gives some ideas on how (and why) large linear colliders of the future should be built
Rogner, H.H.
1989-01-01
The submitted sections on linear programming are extracted from 'Theorie und Technik der Planung' (1978) by W. Blaas and P. Henseler and reformulated for presentation at the Workshop. They consider a brief introduction to the theory of linear programming and to some essential aspects of the SIMPLEX solution algorithm for the purposes of economic planning processes. 1 fig
Rowe, C.H.; Wilton, M.S. de.
1979-01-01
An improved recirculating electron beam linear accelerator of the racetrack type is described. The system comprises a beam path of four straight legs with four Pretzel bending magnets at the end of each leg to direct the beam into the next leg of the beam path. At least one of the beam path legs includes a linear accelerator. (UK)
Semidefinite linear complementarity problems
Eckhardt, U.
1978-04-01
Semidefinite linear complementarity problems arise by discretization of variational inequalities describing e.g. elastic contact problems, free boundary value problems etc. In the present paper linear complementarity problems are introduced and the theory as well as the numerical treatment of them are described. In the special case of semidefinite linear complementarity problems a numerical method is presented which combines the advantages of elimination and iteration methods without suffering from their drawbacks. This new method has very attractive properties since it has a high degree of invariance with respect to the representation of the set of all feasible solutions of a linear complementarity problem by linear inequalities. By means of some practical applications the properties of the new method are demonstrated. (orig.) [de
Axler, Sheldon
2015-01-01
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...
Handbook on linear motor application
1988-10-01
This book guides the application for Linear motor. It lists classification and speciality of Linear Motor, terms of linear-induction motor, principle of the Motor, types on one-side linear-induction motor, bilateral linear-induction motor, linear-DC Motor on basic of the motor, linear-DC Motor for moving-coil type, linear-DC motor for permanent-magnet moving type, linear-DC motor for electricity non-utility type, linear-pulse motor for variable motor, linear-pulse motor for permanent magneto type, linear-vibration actuator, linear-vibration actuator for moving-coil type, linear synchronous motor, linear electromagnetic motor, linear electromagnetic solenoid, technical organization and magnetic levitation and linear motor and sensor.
Linear ubiquitination in immunity.
Shimizu, Yutaka; Taraborrelli, Lucia; Walczak, Henning
2015-07-01
Linear ubiquitination is a post-translational protein modification recently discovered to be crucial for innate and adaptive immune signaling. The function of linear ubiquitin chains is regulated at multiple levels: generation, recognition, and removal. These chains are generated by the linear ubiquitin chain assembly complex (LUBAC), the only known ubiquitin E3 capable of forming the linear ubiquitin linkage de novo. LUBAC is not only relevant for activation of nuclear factor-κB (NF-κB) and mitogen-activated protein kinases (MAPKs) in various signaling pathways, but importantly, it also regulates cell death downstream of immune receptors capable of inducing this response. Recognition of the linear ubiquitin linkage is specifically mediated by certain ubiquitin receptors, which is crucial for translation into the intended signaling outputs. LUBAC deficiency results in attenuated gene activation and increased cell death, causing pathologic conditions in both, mice, and humans. Removal of ubiquitin chains is mediated by deubiquitinases (DUBs). Two of them, OTULIN and CYLD, are constitutively associated with LUBAC. Here, we review the current knowledge on linear ubiquitination in immune signaling pathways and the biochemical mechanisms as to how linear polyubiquitin exerts its functions distinctly from those of other ubiquitin linkage types. © 2015 The Authors. Immunological Reviews Published by John Wiley & Sons Ltd.
Krivonos, S.O.; Sorin, A.S.
1994-06-01
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs
Schneider, Hans
1989-01-01
Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t
Linearity in Process Languages
Nygaard, Mikkel; Winskel, Glynn
2002-01-01
The meaning and mathematical consequences of linearity (managing without a presumed ability to copy) are studied for a path-based model of processes which is also a model of affine-linear logic. This connection yields an affine-linear language for processes, automatically respecting open......-map bisimulation, in which a range of process operations can be expressed. An operational semantics is provided for the tensor fragment of the language. Different ways to make assemblies of processes lead to different choices of exponential, some of which respect bisimulation....
Amir-Moez, A R; Sneddon, I N
1962-01-01
Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices a
Weisberg, Sanford
2013-01-01
Praise for the Third Edition ""...this is an excellent book which could easily be used as a course text...""-International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illus
Ter-Martirosyan, Z. G.; Ter-Martirosyan, A. Z.; Anzhelo, G. O.; Buslov, A. S.
2018-01-01
The task of the interaction of the sand and gravel drain pile with the surrounding loam soil after its preliminary deep compaction and formation of the composite ground cylinder from the drain pile and surrounding compacted loam soil (cells) is considered in the article. It is seen that the subsidence and carrying capacity of such cell considerably depends on physical and mechanical properties of the compacted drain piles and surrounding loam soil as well as their diameter and intercellular distance. The strain-stress state of the cell is considered not taking into account its component elements, but taking into account linear and elastic-plastic properties of the drain pile and creep flow of the surrounding loam soil. It is stated that depending on these properties the distribution and redistribution of the load on a cell takes place from the foundation raft between the drain pile and surrounding soil. Based on the results of task solving the formulas and charts are given demonstrating the ratio of the load between the drain pile and surrounding loam soil in time.
Callier, Frank M.; Desoer, Charles A.
1991-01-01
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Blyth, T S
2002-01-01
Most of the introductory courses on linear algebra develop the basic theory of finite dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num ber of illustrative and worked examples, as well as many exercises that are strategi cally placed throughout the text. Solutions to the ex...
Mamyrin, B.A.; Shmikk, D.V.
1979-01-01
A description and operating principle of a linear mass reflectron with V-form trajectory of ion motion -a new non-magnetic time-of-flight mass spectrometer with high resolution are presented. The ion-optical system of the device consists of an ion source with ionization by electron shock, of accelerating gaps, reflector gaps, a drift space and ion detector. Ions move in the linear mass refraction along the trajectories parallel to the axis of the analyzer chamber. The results of investigations into the experimental device are given. With an ion drift length of 0.6 m the device resolution is 1200 with respect to the peak width at half-height. Small-sized mass spectrometric transducers with high resolution and sensitivity may be designed on the base of the linear mass reflectron principle
Olver, Peter J
2018-01-01
This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...
Banach, S
1987-01-01
This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra.The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series.A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'''') complements this important monograph.
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four of these cri......Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....
Linear programming using Matlab
Ploskas, Nikolaos
2017-01-01
This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting ru...
Anon.
1994-01-01
The aim of the TESLA (TeV Superconducting Linear Accelerator) collaboration (at present 19 institutions from seven countries) is to establish the technology for a high energy electron-positron linear collider using superconducting radiofrequency cavities to accelerate its beams. Another basic goal is to demonstrate that such a collider can meet its performance goals in a cost effective manner. For this the TESLA collaboration is preparing a 500 MeV superconducting linear test accelerator at the DESY Laboratory in Hamburg. This TTF (TESLA Test Facility) consists of four cryomodules, each approximately 12 m long and containing eight 9-cell solid niobium cavities operating at a frequency of 1.3 GHz
Linearly Adjustable International Portfolios
Fonseca, R. J.; Kuhn, D.; Rustem, B.
2010-09-01
We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.
Linearly Adjustable International Portfolios
Fonseca, R. J.; Kuhn, D.; Rustem, B.
2010-01-01
We present an approach to multi-stage international portfolio optimization based on the imposition of a linear structure on the recourse decisions. Multiperiod decision problems are traditionally formulated as stochastic programs. Scenario tree based solutions however can become intractable as the number of stages increases. By restricting the space of decision policies to linear rules, we obtain a conservative tractable approximation to the original problem. Local asset prices and foreign exchange rates are modelled separately, which allows for a direct measure of their impact on the final portfolio value.
Barkman, W.E.; Adams, W.Q.; Berrier, B.R.
1978-01-01
A linear induction motor has been operated on a test bed with a feedback pulse resolution of 5 nm (0.2 μin). Slewing tests with this slide drive have shown positioning errors less than or equal to 33 nm (1.3 μin) at feedrates between 0 and 25.4 mm/min (0-1 ipm). A 0.86-m (34-in)-stroke linear motor is being investigated, using the SPACO machine as a test bed. Initial results were encouraging, and work is continuing to optimize the servosystem compensation
Hogben, Leslie
2013-01-01
With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of
Linear Algebra Thoroughly Explained
Vujičić, Milan
2008-01-01
Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.
2013-05-10
AND VICTIM- ~ vAP BLAMING 4. AMERICA, LINEARLY CYCUCAL AF IMT 1768, 19840901, V5 PREVIOUS EDITION WILL BE USED. C2C Jessica Adams Dr. Brissett...his desires, his failings, and his aspirations follow the same general trend throughout history and throughout cultures. The founding fathers sought
Southworth, B.
1985-01-01
The peak of the construction phase of the Stanford Linear Collider, SLC, to achieve 50 GeV electron-positron collisions has now been passed. The work remains on schedule to attempt colliding beams, initially at comparatively low luminosity, early in 1987. (orig./HSI).
Mafra Neto, F.
1992-01-01
The dose of gamma radiation from a linear source of cesium 137 is obtained, presenting two difficulties: oblique filtration of radiation when cross the platinum wall, in different directions, and dose connection due to the scattering by the material mean of propagation. (C.G.C.)
Resistors Improve Ramp Linearity
Kleinberg, L. L.
1982-01-01
Simple modification to bootstrap ramp generator gives more linear output over longer sweep times. New circuit adds just two resistors, one of which is adjustable. Modification cancels nonlinearities due to variations in load on charging capacitor and due to changes in charging current as the voltage across capacitor increases.
LINEAR COLLIDERS: 1992 workshop
Settles, Ron; Coignet, Guy
1992-01-01
As work on designs for future electron-positron linear colliders pushes ahead at major Laboratories throughout the world in a major international collaboration framework, the LC92 workshop held in Garmisch Partenkirchen this summer, attended by 200 machine and particle physicists, provided a timely focus
Brameier, Markus
2007-01-01
Presents a variant of Genetic Programming that evolves imperative computer programs as linear sequences of instructions, in contrast to the more traditional functional expressions or syntax trees. This book serves as a reference for researchers, but also contains sufficient introduction for students and those who are new to the field
Dobbs, David E.
2013-01-01
A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.
Takeda, Seishi
1992-01-01
The status of R and D of future e + e - linear colliders proposed by the institutions throughout the world is described including the JLC, NLC, VLEPP, CLIC, DESY/THD and TESLA projects. The parameters and RF sources are discussed. (G.P.) 36 refs.; 1 tab
Finite-dimensional linear algebra
Gockenbach, Mark S
2010-01-01
Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq
Linearity and Non-linearity of Photorefractive effect in Materials ...
In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...
Linearly Refined Session Types
Pedro Baltazar
2012-11-01
Full Text Available Session types capture precise protocol structure in concurrent programming, but do not specify properties of the exchanged values beyond their basic type. Refinement types are a form of dependent types that can address this limitation, combining types with logical formulae that may refer to program values and can constrain types using arbitrary predicates. We present a pi calculus with assume and assert operations, typed using a session discipline that incorporates refinement formulae written in a fragment of Multiplicative Linear Logic. Our original combination of session and refinement types, together with the well established benefits of linearity, allows very fine-grained specifications of communication protocols in which refinement formulae are treated as logical resources rather than persistent truths.
Kuznetsov, N.; Maz'ya, V.; Vainberg, B.
2002-08-01
This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'
The International Linear Collider
List Benno
2014-04-01
Full Text Available The International Linear Collider (ILC is a proposed e+e− linear collider with a centre-of-mass energy of 200–500 GeV, based on superconducting RF cavities. The ILC would be an ideal machine for precision studies of a light Higgs boson and the top quark, and would have a discovery potential for new particles that is complementary to that of LHC. The clean experimental conditions would allow the operation of detectors with extremely good performance; two such detectors, ILD and SiD, are currently being designed. Both make use of novel concepts for tracking and calorimetry. The Japanese High Energy Physics community has recently recommended to build the ILC in Japan.
The International Linear Collider
List, Benno
2014-04-01
The International Linear Collider (ILC) is a proposed e+e- linear collider with a centre-of-mass energy of 200-500 GeV, based on superconducting RF cavities. The ILC would be an ideal machine for precision studies of a light Higgs boson and the top quark, and would have a discovery potential for new particles that is complementary to that of LHC. The clean experimental conditions would allow the operation of detectors with extremely good performance; two such detectors, ILD and SiD, are currently being designed. Both make use of novel concepts for tracking and calorimetry. The Japanese High Energy Physics community has recently recommended to build the ILC in Japan.
Høskuldsson, Agnar
1996-01-01
Determination of the proper dimension of a given linear model is one of the most important tasks in the applied modeling work. We consider here eight criteria that can be used to determine the dimension of the model, or equivalently, the number of components to use in the model. Four...... the basic problems in determining the dimension of linear models. Then each of the eight measures are treated. The results are illustrated by examples....... of these criteria are widely used ones, while the remaining four are ones derived from the H-principle of mathematical modeling. Many examples from practice show that the criteria derived from the H-principle function better than the known and popular criteria for the number of components. We shall briefly review...
Goldowsky, Michael P. (Inventor)
1987-01-01
A reciprocating linear motor is formed with a pair of ring-shaped permanent magnets having opposite radial polarizations, held axially apart by a nonmagnetic yoke, which serves as an axially displaceable armature assembly. A pair of annularly wound coils having axial lengths which differ from the axial lengths of the permanent magnets are serially coupled together in mutual opposition and positioned with an outer cylindrical core in axial symmetry about the armature assembly. One embodiment includes a second pair of annularly wound coils serially coupled together in mutual opposition and an inner cylindrical core positioned in axial symmetry inside the armature radially opposite to the first pair of coils. Application of a potential difference across a serial connection of the two pairs of coils creates a current flow perpendicular to the magnetic field created by the armature magnets, thereby causing limited linear displacement of the magnets relative to the coils.
Henneaux, Marc; Teitelboim, Claudio
2005-01-01
We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two superpotentials, one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons-like structure, as in the Maxwell case
Phinney, N.
1992-01-01
The SLAC Linear Collider has begun a new era of operation with the SLD detector. During 1991 there was a first engineering run for the SLD in parallel with machine improvements to increase luminosity and reliability. For the 1992 run, a polarized electron source was added and more than 10,000 Zs with an average of 23% polarization have been logged by the SLD. This paper discusses the performance of the SLC in 1991 and 1992 and the technical advances that have produced higher luminosity. Emphasis will be placed on issues relevant to future linear colliders such as producing and maintaining high current, low emittance beams and focusing the beams to the micron scale for collisions. (Author) tab., 2 figs., 18 refs
Linear waves and instabilities
Bers, A.
1975-01-01
The electrodynamic equations for small-amplitude waves and their dispersion relation in a homogeneous plasma are outlined. For such waves, energy and momentum, and their flow and transformation, are described. Perturbation theory of waves is treated and applied to linear coupling of waves, and the resulting instabilities from such interactions between active and passive waves. Linear stability analysis in time and space is described where the time-asymptotic, time-space Green's function for an arbitrary dispersion relation is developed. The perturbation theory of waves is applied to nonlinear coupling, with particular emphasis on pump-driven interactions of waves. Details of the time--space evolution of instabilities due to coupling are given. (U.S.)
Extended linear chain compounds
Linear chain substances span a large cross section of contemporary chemistry ranging from covalent polymers, to organic charge transfer com plexes to nonstoichiometric transition metal coordination complexes. Their commonality, which coalesced intense interest in the theoretical and exper imental solid state physics/chemistry communities, was based on the obser vation that these inorganic and organic polymeric substrates exhibit striking metal-like electrical and optical properties. Exploitation and extension of these systems has led to the systematic study of both the chemistry and physics of highly and poorly conducting linear chain substances. To gain a salient understanding of these complex materials rich in anomalous aniso tropic electrical, optical, magnetic, and mechanical properties, the conver gence of diverse skills and talents was required. The constructive blending of traditionally segregated disciplines such as synthetic and physical organic, inorganic, and polymer chemistry, crystallog...
Diamond, Jared M.
1966-01-01
1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254
Fundamentals of linear algebra
Dash, Rajani Ballav
2008-01-01
FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.
Sander, K F
1964-01-01
Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies
Non linear viscoelastic models
Agerkvist, Finn T.
2011-01-01
Viscoelastic eects are often present in loudspeaker suspensions, this can be seen in the displacement transfer function which often shows a frequency dependent value below the resonance frequency. In this paper nonlinear versions of the standard linear solid model (SLS) are investigated....... The simulations show that the nonlinear version of the Maxwell SLS model can result in a time dependent small signal stiness while the Kelvin Voight version does not....
Relativistic Linear Restoring Force
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Superconducting linear colliders
Anon.
1990-01-01
The advantages of superconducting radiofrequency (SRF) for particle accelerators have been demonstrated by successful operation of systems in the TRISTAN and LEP electron-positron collider rings respectively at the Japanese KEK Laboratory and at CERN. If performance continues to improve and costs can be lowered, this would open an attractive option for a high luminosity TeV (1000 GeV) linear collider
Perturbed asymptotically linear problems
Bartolo, R.; Candela, A. M.; Salvatore, A.
2012-01-01
The aim of this paper is investigating the existence of solutions of some semilinear elliptic problems on open bounded domains when the nonlinearity is subcritical and asymptotically linear at infinity and there is a perturbation term which is just continuous. Also in the case when the problem has not a variational structure, suitable procedures and estimates allow us to prove that the number of distinct crtitical levels of the functional associated to the unperturbed problem is "stable" unde...
Miniature linear cooler development
Pruitt, G.R.
1993-01-01
An overview is presented of the status of a family of miniature linear coolers currently under development by Hughes Aircraft Co. for use in hand held, volume limited or power limited infrared applications. These coolers, representing the latest additions to the Hughes family of TOP trademark [twin-opposed piston] linear coolers, have been fabricated and tested in three different configurations. Each configuration is designed to utilize a common compressor assembly resulting in reduced manufacturing costs. The baseline compressor has been integrated with two different expander configurations and has been operated with two different levels of input power. These various configuration combinations offer a wide range of performance and interface characteristics which may be tailored to applications requiring limited power and size without significantly compromising cooler capacity or cooldown characteristics. Key cooler characteristics and test data are summarized for three combinations of cooler configurations which are representative of the versatility of this linear cooler design. Configurations reviewed include the shortened coldfinger [1.50 to 1.75 inches long], limited input power [less than 17 Watts] for low power availability applications; the shortened coldfinger with higher input power for lightweight, higher performance applications; and coldfingers compatible with DoD 0.4 Watt Common Module coolers for wider range retrofit capability. Typical weight of these miniature linear coolers is less than 500 grams for the compressor, expander and interconnecting transfer line. Cooling capacity at 80K at room ambient conditions ranges from 400 mW to greater than 550 mW. Steady state power requirements for maintaining a heat load of 150 mW at 80K has been shown to be less than 8 Watts. Ongoing reliability growth testing is summarized including a review of the latest test article results
Avram Mihai
2017-01-01
Full Text Available The paper presents a linear pneumatic actuator with short working stroke. It consists of a pneumatic motor (a simple stroke cylinder or a membrane chamber, two 2/2 pneumatic distributors “all or nothing” electrically commanded for controlling the intake/outtake flow to/from the active chamber of the motor, a position transducer and a microcontroller. There is also presented the theoretical analysis (mathematical modelling and numerical simulation accomplished.
Avram Mihai; Niţu Constantin; Bucşan Constantin; Grămescu Bogdan
2017-01-01
The paper presents a linear pneumatic actuator with short working stroke. It consists of a pneumatic motor (a simple stroke cylinder or a membrane chamber), two 2/2 pneumatic distributors “all or nothing” electrically commanded for controlling the intake/outtake flow to/from the active chamber of the motor, a position transducer and a microcontroller. There is also presented the theoretical analysis (mathematical modelling and numerical simulation) accomplished.
Scheffel, J.
1984-03-01
The linear Grad-Shafranov equation for a toroidal, axisymmetric plasma is solved analytically. Exact solutions are given in terms of confluent hyper-geometric functions. As an alternative, simple and accurate WKBJ solutions are presented. With parabolic pressure profiles, both hollow and peaked toroidal current density profiles are obtained. As an example the equilibrium of a z-pinch with a square-shaped cross section is derived.(author)
Buttram, M.T.; Ginn, J.W.
1988-06-21
A linear induction accelerator includes a plurality of adder cavities arranged in a series and provided in a structure which is evacuated so that a vacuum inductance is provided between each adder cavity and the structure. An energy storage system for the adder cavities includes a pulsed current source and a respective plurality of bipolar converting networks connected thereto. The bipolar high-voltage, high-repetition-rate square pulse train sets and resets the cavities. 4 figs.
Springer, T A
1998-01-01
"[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text." –Mathematical Reviews (Review of the Second Edition) "This book is a completely new version of the first edition. The aim of the old book was to present the theory of linear algebraic groups over an algebraically closed field. Reading that book, many people entered the research field of linear algebraic groups. The present book has a wider scope. Its aim is to treat the theory of linear algebraic groups over arbitrary fields. Again, the author keeps the treatment of prerequisites self-contained. The material of t...
Parametric Linear Dynamic Logic
Peter Faymonville
2014-08-01
Full Text Available We introduce Parametric Linear Dynamic Logic (PLDL, which extends Linear Dynamic Logic (LDL by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL that is able to express all ω-regular specifications while still maintaining many of LTL's desirable properties like an intuitive syntax and a translation into non-deterministic Büchi automata of exponential size. But LDL lacks capabilities to express timing constraints. By adding parameterized operators to LDL, we obtain a logic that is able to express all ω-regular properties and that subsumes parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our main technical contribution is a translation of PLDL formulas into non-deterministic Büchi word automata of exponential size via alternating automata. This yields a PSPACE model checking algorithm and a realizability algorithm with doubly-exponential running time. Furthermore, we give tight upper and lower bounds on optimal parameter values for both problems. These results show that PLDL model checking and realizability are not harder than LTL model checking and realizability.
Quantum linear Boltzmann equation
Vacchini, Bassano; Hornberger, Klaus
2009-01-01
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
Emma, P.
1995-01-01
The Stanford Linear Collider (SLC) is the first and only high-energy e + e - linear collider in the world. Its most remarkable features are high intensity, submicron sized, polarized (e - ) beams at a single interaction point. The main challenges posed by these unique characteristics include machine-wide emittance preservation, consistent high intensity operation, polarized electron production and transport, and the achievement of a high degree of beam stability on all time scales. In addition to serving as an important machine for the study of Z 0 boson production and decay using polarized beams, the SLC is also an indispensable source of hands-on experience for future linear colliders. Each new year of operation has been highlighted with a marked improvement in performance. The most significant improvements for the 1994-95 run include new low impedance vacuum chambers for the damping rings, an upgrade to the optics and diagnostics of the final focus systems, and a higher degree of polarization from the electron source. As a result, the average luminosity has nearly doubled over the previous year with peaks approaching 10 30 cm -2 s -1 and an 80% electron polarization at the interaction point. These developments as well as the remaining identifiable performance limitations will be discussed
Garbet, X.; Mourgues, F.; Samain, A.
1987-01-01
Among the various instabilities which could explain the anomalous electron heat transport observed in tokamaks during additional heating, a microtearing turbulence is a reasonable candidate since it affects directly the magnetic topology. This turbulence may be described in a proper frame rotating around the majors axis by a static potential vector. In strong non linear regimes, the flow of electrons along the stochastic field lines induces a current. The point is to know whether this current can sustain the turbulence. The mechanisms of this self-consistency, involving the combined effects of the thermal diamagnetism and of the electric drift are presented here
Wangler, Thomas P
2008-01-01
Thomas P. Wangler received his B.S. degree in physics from Michigan State University, and his Ph.D. degree in physics and astronomy from the University of Wisconsin. After postdoctoral appointments at the University of Wisconsin and Brookhaven National Laboratory, he joined the staff of Argonne National Laboratory in 1966, working in the fields of experimental high-energy physics and accelerator physics. He joined the Accelerator Technology Division at Los Alamos National Laboratory in 1979, where he specialized in high-current beam physics and linear accelerator design and technology. In 2007
Richter, B.; Bell, R.A.; Brown, K.L.
1980-06-01
The SLAC LINEAR COLLIDER is designed to achieve an energy of 100 GeV in the electron-positron center-of-mass system by accelerating intense bunches of particles in the SLAC linac and transporting the electron and positron bunches in a special magnet system to a point where they are focused to a radius of about 2 microns and made to collide head on. The rationale for this new type of colliding beam system is discussed, the project is described, some of the novel accelerator physics issues involved are discussed, and some of the critical technical components are described
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to
Special set linear algebra and special set fuzzy linear algebra
Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.
2009-01-01
The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...
Munehiro, H
1980-05-29
When driving the carriage of a printer through a rotating motor, there are problems regarding the limited accuracy of the carriage position due to rotation or contraction and ageing of the cable. In order to solve the problem, a direct drive system was proposed, in which the printer carriage is driven by a linear motor. If one wants to keep the motor circuit of such a motor compact, then the magnetic flux density in the air gap must be reduced or the motor travel must be reduced. It is the purpose of this invention to create an electrodynamic linear motor, which on the one hand is compact and light and on the other hand has a relatively high constant force over a large travel. The invention is characterised by the fact that magnetic fields of alternating polarity are generated at equal intervals in the magnetic field, and that the coil arrangement has 2 adjacent coils, whose size corresponds to half the length of each magnetic pole. A logic circuit is provided to select one of the two coils and to determine the direction of the current depending on the signals of a magnetic field sensor on the coil arrangement.
Kozarov, A.; Petrov, O.; Antonov, J.; Sotirova, S.; Petrova, B.
2006-01-01
The purpose of the linear wind-power generator described in this article is to decrease the following disadvantages of the common wind-powered turbine: 1) large bending and twisting moments to the blades and the shaft, especially when strong winds and turbulence exist; 2) significant values of the natural oscillation period of the construction result in the possibility of occurrence of destroying resonance oscillations; 3) high velocity of the peripheral parts of the rotor creating a danger for birds; 4) difficulties, connected with the installation and the operation on the mountain ridges and passages where the wind energy potential is the largest. The working surfaces of the generator in questions driven by the wind are not connected with a joint shaft but each moves along a railway track with few oscillations. So the sizes of each component are small and their number can be rather large. The mechanical trajectory is not a circle but a closed outline in a vertical plain, which consists of two rectilinear sectors, one above the other, connected in their ends by semi-circumferences. The mechanical energy of each component turns into electrical on the principle of the linear electrical generator. A regulation is provided when the direction of the wind is perpendicular to the route. A possibility of effectiveness is shown through aiming of additional quantities of air to the movable components by static barriers
Linearization of the Lorenz system
Li, Chunbiao; Sprott, Julien Clinton; Thio, Wesley
2015-01-01
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation
Topics in computational linear optimization
Hultberg, Tim Helge
2000-01-01
Linear optimization has been an active area of research ever since the pioneering work of G. Dantzig more than 50 years ago. This research has produced a long sequence of practical as well as theoretical improvements of the solution techniques avilable for solving linear optimization problems...... of high quality solvers and the use of algebraic modelling systems to handle the communication between the modeller and the solver. This dissertation features four topics in computational linear optimization: A) automatic reformulation of mixed 0/1 linear programs, B) direct solution of sparse unsymmetric...... systems of linear equations, C) reduction of linear programs and D) integration of algebraic modelling of linear optimization problems in C++. Each of these topics is treated in a separate paper included in this dissertation. The efficiency of solving mixed 0-1 linear programs by linear programming based...
Linearization of the Lorenz system
Li, Chunbiao, E-mail: goontry@126.com [School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China); Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 211168 (China); Sprott, Julien Clinton [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Thio, Wesley [Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 (United States)
2015-05-08
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation.
On the linear programming bound for linear Lee codes.
Astola, Helena; Tabus, Ioan
2016-01-01
Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.
Introduction to linear elasticity
Gould, Phillip L
2013-01-01
Introduction to Linear Elasticity, 3rd Edition, provides an applications-oriented grounding in the tensor-based theory of elasticity for students in mechanical, civil, aeronautical, and biomedical engineering, as well as materials and earth science. The book is distinct from the traditional text aimed at graduate students in solid mechanics by introducing the subject at a level appropriate for advanced undergraduate and beginning graduate students. The author's presentation allows students to apply the basic notions of stress analysis and move on to advanced work in continuum mechanics, plasticity, plate and shell theory, composite materials, viscoelasticity and finite method analysis. This book also: Emphasizes tensor-based approach while still distilling down to explicit notation Provides introduction to theory of plates, theory of shells, wave propagation, viscoelasticity and plasticity accessible to advanced undergraduate students Appropriate for courses following emerging trend of teaching solid mechan...
Haniger, L.; Elger, R.; Kocandrle, L.; Zdebor, J.
1986-01-01
A linear step drive is described developed in Czechoslovak-Soviet cooperation and intended for driving WWER-1000 control rods. The functional principle is explained of the motor and the mechanical and electrical parts of the drive, power control, and the indicator of position are described. The motor has latches situated in the reactor at a distance of 3 m from magnetic armatures, it has a low structural height above the reactor cover, which suggests its suitability for seismic localities. Its magnetic circuits use counterpoles; the mechanical shocks at the completion of each step are damped using special design features. The position indicator is of a special design and evaluates motor position within ±1% of total travel. A drive diagram and the flow chart of both the control electronics and the position indicator are presented. (author) 4 figs
Tjutju, R.L.
1977-01-01
Pulse amplifier is standard significant part of spectrometer. Apart from other type of amplification, it's a combination of amplification and pulse shaping. Because of its special purpose the device should fulfill the following : High resolution is desired to gain a high yield comparable to its actual state of condition. High signal to noise is desired to nhν resolution. High linearity to facilitate calibration. A good overload recovery, in order to the device will capable of analizing a low energy radiation which appear joinly on the high energy fields. Other expections of the device are its economical and practical use its extentive application. For that reason it's built on a standard NIM principle. Taking also into account the above mentioned considerations. High quality component parts are used throughout, while its availability in the domestic market is secured. (author)
1976-01-01
This report covers the activity of the Linear Accelerator Laboratory during the period June 1974-June 1976. The activity of the Laboratory is essentially centered on high energy physics. The main activities were: experiments performed with the colliding rings (ACO), construction of the new colliding rings and beginning of the work at higher energy (DCI), bubble chamber experiments with the CERN PS neutrino beam, counter experiments with CERN's PS and setting-up of equipment for new experiments with CERN's SPS. During this period a project has also been prepared for an experiment with the new PETRA colliding ring at Hamburg. On the other hand, intense collaboration with the LURE Laboratory, using the electron synchrotron radiation emitted by ACO and DCI, has been developed [fr
Van Atta, C.M.; Beringer, R.; Smith, L.
1959-01-01
A linear accelerator of heavy ions is described. The basic contributions of the invention consist of a method and apparatus for obtaining high energy particles of an element with an increased charge-to-mass ratio. The method comprises the steps of ionizing the atoms of an element, accelerating the resultant ions to an energy substantially equal to one Mev per nucleon, stripping orbital electrons from the accelerated ions by passing the ions through a curtain of elemental vapor disposed transversely of the path of the ions to provide a second charge-to-mass ratio, and finally accelerating the resultant stripped ions to a final energy of at least ten Mev per nucleon.
Tip, A.
1998-06-01
Starting from Maxwell's equations for a linear, nonconducting, absorptive, and dispersive medium, characterized by the constitutive equations D(x,t)=ɛ1(x)E(x,t)+∫t-∞dsχ(x,t-s)E(x,s) and H(x,t)=B(x,t), a unitary time evolution and canonical formalism is obtained. Given the complex, coordinate, and frequency-dependent, electric permeability ɛ(x,ω), no further assumptions are made. The procedure leads to a proper definition of band gaps in the periodic case and a new continuity equation for energy flow. An S-matrix formalism for scattering from lossy objects is presented in full detail. A quantized version of the formalism is derived and applied to the generation of Čerenkov and transition radiation as well as atomic decay. The last case suggests a useful generalization of the density of states to the absorptive situation.
Computer Program For Linear Algebra
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
Quaternion Linear Canonical Transform Application
Bahri, Mawardi
2015-01-01
Quaternion linear canonical transform (QLCT) is a generalization of the classical linear canonical transfom (LCT) using quaternion algebra. The focus of this paper is to introduce an application of the QLCT to study of generalized swept-frequency filter
Recursive Algorithm For Linear Regression
Varanasi, S. V.
1988-01-01
Order of model determined easily. Linear-regression algorithhm includes recursive equations for coefficients of model of increased order. Algorithm eliminates duplicative calculations, facilitates search for minimum order of linear-regression model fitting set of data satisfactory.
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
Linear spaces: history and theory
Albrecht Beutelspracher
1990-01-01
Linear spaces belong to the most fundamental geometric and combinatorial structures. In this paper I would like to give an onerview about the theory of embedding finite linear spaces in finite projective planes.
Linear versus non-linear supersymmetry, in general
Ferrara, Sergio [Theoretical Physics Department, CERN,CH-1211 Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati,Via Enrico Fermi 40, I-00044 Frascati (Italy); Department of Physics and Astronomy, UniversityC.L.A.,Los Angeles, CA 90095-1547 (United States); Kallosh, Renata [SITP and Department of Physics, Stanford University,Stanford, California 94305 (United States); Proeyen, Antoine Van [Institute for Theoretical Physics, Katholieke Universiteit Leuven,Celestijnenlaan 200D, B-3001 Leuven (Belgium); Wrase, Timm [Institute for Theoretical Physics, Technische Universität Wien,Wiedner Hauptstr. 8-10, A-1040 Vienna (Austria)
2016-04-12
We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.
Linear versus non-linear supersymmetry, in general
Ferrara, Sergio; Kallosh, Renata; Proeyen, Antoine Van; Wrase, Timm
2016-01-01
We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM’s: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.
Monahan, John F
2008-01-01
Preface Examples of the General Linear Model Introduction One-Sample Problem Simple Linear Regression Multiple Regression One-Way ANOVA First Discussion The Two-Way Nested Model Two-Way Crossed Model Analysis of Covariance Autoregression Discussion The Linear Least Squares Problem The Normal Equations The Geometry of Least Squares Reparameterization Gram-Schmidt Orthonormalization Estimability and Least Squares Estimators Assumptions for the Linear Mean Model Confounding, Identifiability, and Estimability Estimability and Least Squares Estimators F
Templates for Linear Algebra Problems
Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der
1995-01-01
The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and
Linearization of CIF through SOS
Nadales Agut, D.E.; Reniers, M.A.; Luttik, B.; Valencia, F.
2011-01-01
Linearization is the procedure of rewriting a process term into a linear form, which consist only of basic operators of the process language. This procedure is interesting both from a theoretical and a practical point of view. In particular, a linearization algorithm is needed for the Compositional
Engberg, Uffe Henrik; Winskel, Glynn
This article shows how individual Petri nets form models of Girard's intuitionistic linear logic. It explores questions of expressiveness and completeness of linear logic with respect to this interpretation. An aim is to use Petri nets to give an understanding of linear logic and give some apprai...
Richards, J.A.
1977-01-01
A linear particle accelerator which provides a pulsed beam of charged particles of uniform energy is described. The accelerator is in the form of an evacuated dielectric tube, inside of which a particle source is located at one end of the tube, with a target or window located at the other end of the dielectric tube. Along the length of the tube are externally located pairs of metal plates, each insulated from each other in an insulated housing. Each of the plates of a pair are connected to an electrical source of voltage of opposed polarity, with the polarity of the voltage of the plates oriented so that the plate of a pair, nearer to the particle source, is of the opposed polarity to the charge of the particle emitted by the source. Thus, a first plate about the tube located nearest the particle source, attracts a particle which as it passes through the tube past the first plate is then repelled by the reverse polarity of the second plate of the pair to continue moving towards the target
Generalized Linear Covariance Analysis
Carpenter, James R.; Markley, F. Landis
2014-01-01
This talk presents a comprehensive approach to filter modeling for generalized covariance analysis of both batch least-squares and sequential estimators. We review and extend in two directions the results of prior work that allowed for partitioning of the state space into solve-for'' and consider'' parameters, accounted for differences between the formal values and the true values of the measurement noise, process noise, and textita priori solve-for and consider covariances, and explicitly partitioned the errors into subspaces containing only the influence of the measurement noise, process noise, and solve-for and consider covariances. In this work, we explicitly add sensitivity analysis to this prior work, and relax an implicit assumption that the batch estimator's epoch time occurs prior to the definitive span. We also apply the method to an integrated orbit and attitude problem, in which gyro and accelerometer errors, though not estimated, influence the orbit determination performance. We illustrate our results using two graphical presentations, which we call the variance sandpile'' and the sensitivity mosaic,'' and we compare the linear covariance results to confidence intervals associated with ensemble statistics from a Monte Carlo analysis.
Equipartitioning in linear accelerators
Jameson, R.A.
1982-01-01
Emittance growth has long been a concern in linear accelerators, as has the idea that some kind of energy balance, or equipartitioning, between the degrees of freedom, would ameliorate the growth. M. Prome observed that the average transverse and longitudinal velocity spreads tend to equalize as current in the channel is increased, while the sum of the energy in the system stays nearly constant. However, only recently have we shown that an equipartitioning requirement on a bunched injected beam can indeed produce remarkably small emittance growth. The simple set of equations leading to this condition are outlined. At the same time, Hofmann has investigated collective instabilities in transported beams and has identified thresholds and regions in parameter space where instabilities occur. Evidence is presented that shows transport system boundaries to be quite accurate in computer simulations of accelerating systems. Discussed are preliminary results of efforts to design accelerators that avoid parameter regions where emittance is affected by the instabilities identified by Hofmann. These efforts suggest that other mechanisms are present. The complicated behavior of the RFQ linac in this framework also is shown
Equipartitioning in linear accelerators
Jameson, R.A.
1981-01-01
Emittance growth has long been a concern in linear accelerators, as has the idea that some kind of energy balance, or equipartitioning, between the degrees of freedom, would ameliorate the growth. M. Prome observed that the average transverse and longitudinal velocity spreads tend to equalize as current in the channel is increased, while the sum of the energy in the system stays nearly constant. However, only recently have we shown that an equipartitioning requirement on a bunched injected beam can indeed produce remarkably small emittance growth. The simple set of equations leading to this condition are outlined below. At the same time, Hofmann, using powerful analytical and computational methods, has investigated collective instabilities in transported beams and has identified thresholds and regions in parameter space where instabilities occur. This is an important generalization. Work that he will present at this conference shows that the results are essentially the same in r-z coordinates for transport systems, and evidence is presented that shows transport system boundaries to be quite accurate in computer simulations of accelerating systems also. Discussed are preliminary results of efforts to design accelerators that avoid parameter regions where emittance is affected by the instabilities identified by Hofmann. These efforts suggest that other mechanisms are present. The complicated behavior of the RFQ linac in this framework also is shown
Briggs, R.J.
1986-06-01
The development of linear induction accelerators has been motivated by applications requiring high-pulsed currents of charged particles at voltages exceeding the capability of single-stage, diode-type accelerators and at currents too high for rf accelerators. In principle, one can accelerate charged particles to arbitrarily high voltages using a multi-stage induction machine, but the 50-MeV, 10-kA Advanced Test Accelerator (ATA) at LLNL is the highest voltage machine in existence at this time. The advent of magnetic pulse power systems makes sustained operation at high-repetition rates practical, and this capability for high-average power is very likely to open up many new applications of induction machines in the future. This paper surveys the US induction linac technology with primary emphasis on electron machines. A simplified description of how induction machines couple energy to the electron beam is given, to illustrate many of the general issues that bound the design space of induction linacs
Berkeley Proton Linear Accelerator
Alvarez, L. W.; Bradner, H.; Franck, J.; Gordon, H.; Gow, J. D.; Marshall, L. C.; Oppenheimer, F. F.; Panofsky, W. K. H.; Richman, C.; Woodyard, J. R.
1953-10-13
A linear accelerator, which increases the energy of protons from a 4 Mev Van de Graaff injector, to a final energy of 31.5 Mev, has been constructed. The accelerator consists of a cavity 40 feet long and 39 inches in diameter, excited at resonance in a longitudinal electric mode with a radio-frequency power of about 2.2 x 10{sup 6} watts peak at 202.5 mc. Acceleration is made possible by the introduction of 46 axial "drift tubes" into the cavity, which is designed such that the particles traverse the distance between the centers of successive tubes in one cycle of the r.f. power. The protons are longitudinally stable as in the synchrotron, and are stabilized transversely by the action of converging fields produced by focusing grids. The electrical cavity is constructed like an inverted airplane fuselage and is supported in a vacuum tank. Power is supplied by 9 high powered oscillators fed from a pulse generator of the artificial transmission line type.
Random linear codes in steganography
Kamil Kaczyński
2016-12-01
Full Text Available Syndrome coding using linear codes is a technique that allows improvement in the steganographic algorithms parameters. The use of random linear codes gives a great flexibility in choosing the parameters of the linear code. In parallel, it offers easy generation of parity check matrix. In this paper, the modification of LSB algorithm is presented. A random linear code [8, 2] was used as a base for algorithm modification. The implementation of the proposed algorithm, along with practical evaluation of algorithms’ parameters based on the test images was made.[b]Keywords:[/b] steganography, random linear codes, RLC, LSB
Linear Algebraic Method for Non-Linear Map Analysis
Yu, L.; Nash, B.
2009-01-01
We present a newly developed method to analyze some non-linear dynamics problems such as the Henon map using a matrix analysis method from linear algebra. Choosing the Henon map as an example, we analyze the spectral structure, the tune-amplitude dependence, the variation of tune and amplitude during the particle motion, etc., using the method of Jordan decomposition which is widely used in conventional linear algebra.
Linear Programming and Network Flows
Bazaraa, Mokhtar S; Sherali, Hanif D
2011-01-01
The authoritative guide to modeling and solving complex problems with linear programming-extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research
LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections
2007-01-01
1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table
Elementary linear programming with applications
Kolman, Bernard
1995-01-01
Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear program
Hood, John Linsley
2013-01-01
The Art of Linear Electronics presents the principal aspects of linear electronics and techniques in linear electronic circuit design. The book provides a wide range of information on the elucidation of the methods and techniques in the design of linear electronic circuits. The text discusses such topics as electronic component symbols and circuit drawing; passive and active semiconductor components; DC and low frequency amplifiers; and the basic effects of feedback. Subjects on frequency response modifying circuits and filters; audio amplifiers; low frequency oscillators and waveform generato
Linearity and Non-linearity of Photorefractive effect in Materials ...
Linearity and Non-linearity of Photorefractive effect in Materials using the Band transport ... For low light beam intensities the change in the refractive index is ... field is spatially phase shifted by /2 relative to the interference fringe pattern, which ...
The linear programming bound for binary linear codes
Brouwer, A.E.
1993-01-01
Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.
Linear operator inequalities for strongly stable weakly regular linear systems
Curtain, RF
2001-01-01
We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov
Linear and non-linear optics of condensed matter
McLean, T.P.
1977-01-01
Part I - Linear optics: 1. General introduction. 2. Frequency dependence of epsilon(ω, k vector). 3. Wave-vector dependence of epsilon(ω, k vector). 4. Tensor character of epsilon(ω, k vector). Part II - Non-linear optics: 5. Introduction. 6. A classical theory of non-linear response in one dimension. 7. The generalization to three dimensions. 8. General properties of the polarizability tensors. 9. The phase-matching condition. 10. Propagation in a non-linear dielectric. 11. Second harmonic generation. 12. Coupling of three waves. 13. Materials and their non-linearities. 14. Processes involving energy exchange with the medium. 15. Two-photon absorption. 16. Stimulated Raman effect. 17. Electro-optic effects. 18. Limitations of the approach presented here. (author)
Advanced statistics: linear regression, part I: simple linear regression.
Marill, Keith A
2004-01-01
Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.
Crasmareanu Mircea
2017-12-01
Full Text Available We consider the paracomplex version of the notion of mixed linear spaces introduced by M. Jurchescu in [4] by replacing the complex unit i with the paracomplex unit j, j2 = 1. The linear algebra of these spaces is studied with a special view towards their morphisms.
Linear Algebra and Image Processing
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Efficient Searching with Linear Constraints
Agarwal, Pankaj K.; Arge, Lars Allan; Erickson, Jeff
2000-01-01
We show how to preprocess a set S of points in d into an external memory data structure that efficiently supports linear-constraint queries. Each query is in the form of a linear constraint xd a0+∑d−1i=1 aixi; the data structure must report all the points of S that satisfy the constraint. This pr...
Johnson, Bruce G.; Gerver, Michael J.; Hawkey, Timothy J.; Fenn, Ralph C.
1993-01-01
Improved linear actuator comprises air slide and linear electric motor. Unit exhibits low friction, low backlash, and more nearly even acceleration. Used in machinery in which positions, velocities, and accelerations must be carefully controlled and/or vibrations must be suppressed.
Linear morphoea follows Blaschko's lines.
Weibel, L; Harper, J I
2008-07-01
The aetiology of morphoea (or localized scleroderma) remains unknown. It has previously been suggested that lesions of linear morphoea may follow Blaschko's lines and thus reflect an embryological development. However, the distribution of linear morphoea has never been accurately evaluated. We aimed to identify common patterns of clinical presentation in children with linear morphoea and to establish whether linear morphoea follows the lines of Blaschko. A retrospective chart review of 65 children with linear morphoea was performed. According to clinical photographs the skin lesions of these patients were plotted on to standardized head and body charts. With the aid of Adobe Illustrator a final figure was produced including an overlay of all individual lesions which was used for comparison with the published lines of Blaschko. Thirty-four (53%) patients had the en coup de sabre subtype, 27 (41%) presented with linear morphoea on the trunk and/or limbs and four (6%) children had a combination of the two. In 55 (85%) children the skin lesions were confined to one side of the body, showing no preference for either left or right side. On comparing the overlays of all body and head lesions with the original lines of Blaschko there was an excellent correlation. Our data indicate that linear morphoea follows the lines of Blaschko. We hypothesize that in patients with linear morphoea susceptible cells are present in a mosaic state and that exposure to some trigger factor may result in the development of this condition.
Campagnoli, Patrizia; Petris, Giovanni
2009-01-01
State space models have gained tremendous popularity in as disparate fields as engineering, economics, genetics and ecology. Introducing general state space models, this book focuses on dynamic linear models, emphasizing their Bayesian analysis. It illustrates the fundamental steps needed to use dynamic linear models in practice, using R package.
Linear Programming across the Curriculum
Yoder, S. Elizabeth; Kurz, M. Elizabeth
2015-01-01
Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…
Introduction to RF linear accelerators
Weiss, M.
1994-01-01
The basic features of RF linear accelerators are described. The concept of the 'loaded cavity', essential for the synchronism wave-particle, is introduced, and formulae describing the action of electromagnetic fields on the beam are given. The treatment of intense beams is mentioned, and various existing linear accelerators are presented as examples. (orig.)
Spatial Processes in Linear Ordering
von Hecker, Ulrich; Klauer, Karl Christoph; Wolf, Lukas; Fazilat-Pour, Masoud
2016-01-01
Memory performance in linear order reasoning tasks (A > B, B > C, C > D, etc.) shows quicker, and more accurate responses to queries on wider (AD) than narrower (AB) pairs on a hypothetical linear mental model (A -- B -- C -- D). While indicative of an analogue representation, research so far did not provide positive evidence for spatial…
Andersen, O. Krogh
1975-01-01
of Korringa-Kohn-Rostoker, linear-combination-of-atomic-orbitals, and cellular methods; the secular matrix is linear in energy, the overlap integrals factorize as potential parameters and structure constants, the latter are canonical in the sense that they neither depend on the energy nor the cell volume...
Introduction to generalized linear models
Dobson, Annette J
2008-01-01
Introduction Background Scope Notation Distributions Related to the Normal Distribution Quadratic Forms Estimation Model Fitting Introduction Examples Some Principles of Statistical Modeling Notation and Coding for Explanatory Variables Exponential Family and Generalized Linear Models Introduction Exponential Family of Distributions Properties of Distributions in the Exponential Family Generalized Linear Models Examples Estimation Introduction Example: Failure Times for Pressure Vessels Maximum Likelihood Estimation Poisson Regression Example Inference Introduction Sampling Distribution for Score Statistics Taylor Series Approximations Sampling Distribution for MLEs Log-Likelihood Ratio Statistic Sampling Distribution for the Deviance Hypothesis Testing Normal Linear Models Introduction Basic Results Multiple Linear Regression Analysis of Variance Analysis of Covariance General Linear Models Binary Variables and Logistic Regression Probability Distributions ...
Acoustic emission linear pulse holography
Collins, H.D.; Busse, L.J.; Lemon, D.K.
1983-01-01
This paper describes the emission linear pulse holography which produces a chronological linear holographic image of a flaw by utilizing the acoustic energy emitted during crack growth. A thirty two point sampling array is used to construct phase-only linear holograms of simulated acoustic emission sources on large metal plates. The concept behind the AE linear pulse holography is illustrated, and a block diagram of a data acquisition system to implement the concept is given. Array element spacing, synthetic frequency criteria, and lateral depth resolution are specified. A reference timing transducer positioned between the array and the inspection zone and which inititates the time-of-flight measurements is described. The results graphically illustrate the technique using a one-dimensional FFT computer algorithm (ie. linear backward wave) for an AE image reconstruction
Linear and Generalized Linear Mixed Models and Their Applications
Jiang, Jiming
2007-01-01
This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models, and it presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it has included recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
Linear and quasi-linear equations of parabolic type
Ladyženskaja, O A; Ural′ceva, N N; Uralceva, N N
1968-01-01
Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.
The Theory of Linear Prediction
Vaidyanathan, PP
2007-01-01
Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistical signal processing. Although prediction is only a part of the more general topics of linear estimation, filtering, and smoothing, this book focuses on linear prediction. This has enabled detailed discussion of a number of issues that are normally not found in texts. For example, the theory of vecto
Correlation and simple linear regression.
Zou, Kelly H; Tuncali, Kemal; Silverman, Stuart G
2003-06-01
In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, simple linear regression analysis is conducted. These statistical concepts are illustrated by using a data set from published literature to assess a computed tomography-guided interventional technique. These statistical methods are important for exploring the relationships between variables and can be applied to many radiologic studies.
Saravanan, R
2018-01-01
Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.
Optimal control linear quadratic methods
Anderson, Brian D O
2007-01-01
This augmented edition of a respected text teaches the reader how to use linear quadratic Gaussian methods effectively for the design of control systems. It explores linear optimal control theory from an engineering viewpoint, with step-by-step explanations that show clearly how to make practical use of the material.The three-part treatment begins with the basic theory of the linear regulator/tracker for time-invariant and time-varying systems. The Hamilton-Jacobi equation is introduced using the Principle of Optimality, and the infinite-time problem is considered. The second part outlines the
Alvarez, J.A.; Gutierrez-Solana, F.
1999-01-01
Cracking processes suffered by new structural and piping steels when used in petroleum or other energy installations have demonstrated the need for a cracking resistance characterization methodology. This methodology, valid for both elastic and elastoplastic regimes, should be able to define crack propagation kinetics as a function of their controlling local parameters. This work summarizes an experimental and analytical methodology that has been shown to be suitable for characterizing cracking processes using compact tensile specimens, especially subcritical environmentally assisted ones, such as those induced by hydrogen in microalloyed steels. The applied and validated methodology has been shown to offer quantitative results of cracking behavior and to correlate these with the existing fracture micromechanisms. (orig.)
Iqbal, F.; Pyczak, F.; Neumeier, S.; Göken, M.
2017-03-24
The crack propagation mechanisms of γ-titanium aluminides with fully lamellar microstructure have been studied using in-situ deformation in the Atomic Force Microscope (AFM). AFM demonstrated the unique capability to detect elastic as well as plastic deformation during in-situ tests from topography changes on the surface. It was found that the crack nucleation, which can occur at γ/γ and α{sub 2}/γ interfaces as well as inside the γ-phase, is always preceded by strong local elastic deformation. No cracking inside the α{sub 2}-phase was observed. The elastic and plastic deformation was confined inside the γ-phase and especially pronounced near interfaces which can be explained by the differences of the elastic and plastic deformation behavior of the γ- and α{sub 2}- phase.
Lee, Seong Won; Lee, Jung Min; Joun, Man Soo; Kim, Dong Hwan
2016-01-01
During a galvannealed sheet metal forming, the failures of coating layers (powdering, flaking and cracking) frequently affect the strain state of sheets and deteriorate the frictional characteristic between sheets and tools. Two FE-models in this study were suggested to investigate the effects of the mechanical behavior of coating layers on the formability and friction of the coated steel sheets in FE analysis; the first is one-layer model to express the coated sheet as one stress-strain curve and the second is a multiple-layer model which is composed of substrates and coating layers, separately. First, the frictional properties and the formability of the coated sheets were experimentally investigated using a cup deep-drawing trial. After, the drawing process was simulated by FE analysis of the two models. In the multiplelayer model, the mechanical behavior of the coating is defined as a stress-strain curve which was determined using the nanoindentation test of the coating, its FE analysis and artificial neural network method. The result showed that the multiple-layer model provides more accuracy predictions of drawing loads than the one-layer model in the FE analysis, compared to the actual cup drawing test.
Bykov, V.; Kavin, A.; Krivchenkov, Y.; Panin, A.
1996-01-01
The ''GLOBUS-M'' is a compact resistive tokamak with a central solenoid (CS) wound around the inner portion of the toroidal field coils. The magnetic field at the solenoid axis amounts to 8.3 T. The CS incorporates two layers of conductor (CuCr copper alloy) baked into insulation. The solenoid is designed to sustain 80,000 energizing. During each loading cycle the solenoid is subjected to the radial forces accompanied with the vertical compression. The most loaded region has been considered and modeled with the use of 2D axisymmetric finite element (FE) model. The model includes two conductor turns baked into insulation compound, copper cooling tubes and solder. The stress analysis shows that there is some plastic deformation in the copper tube and solder during loading and there is some back plastic deformation in the solder during unloading. The reloading does not cause any change in the solenoid stress-strain state in comparison with the case of loading. The number of cycles to failure has been simulated for all metallic components of the solenoid
Jan Valíček
2015-11-01
Full Text Available The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ, especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ.
Lee, K. J.; Choi, Y.; Choi, H. J.; Lee, J. Y.; Lee, M. G.
2018-06-01
Finite element simulations and experiments for the split-ring test were conducted to investigate the effect of anisotropic constitutive models on the predictive capability of sheet springback. As an alternative to the commonly employed associated flow rule, a non-associated flow rule for Hill1948 yield function was implemented in the simulations. Moreover, the evolution of anisotropy with plastic deformation was efficiently modeled by identifying equivalent plastic strain-dependent anisotropic coefficients. Comparative study with different yield surfaces and elasticity models showed that the split-ring springback could be best predicted when the anisotropy in both the R value and yield stress, their evolution and variable apparent elastic modulus were taken into account in the simulations. Detailed analyses based on deformation paths superimposed on the anisotropic yield functions predicted by different constitutive models were provided to understand the complex springback response in the split-ring test.
Pulungan, Ditho Ardiansyah
2018-02-24
Polymers in general exhibit pressure- and rate-dependent behavior. Modeling such behavior requires extensive, costly and time-consuming experimental work. Common simplifications may lead to severe inaccuracy when using the model for predicting the failure of structures. Here, we propose a viscoelastic viscoplastic damage model for polypropylene-based polymers. Such a set of constitutive equations can be used to describe the response of polypropylene under various strain-rates and stress-triaxiality conditions. Our model can also be applied to a broad range of thermoplastic polymers. We detail the experimental campaign that is needed to identify every parameter of the model at best. We validated the proposed model by performing 3-point bending tests at different loading speeds, where the load-displacement response of polypropylene beam up to failure was accurately predicted.
Hagiwara, Yutaka; Yamamoto, Kohsuke; Kawamoto, Yoji; Nakagawa, Masaki; Akiyama, Hiroshi
1998-01-01
Plastic shear-bending buckling under seismic loadings is one of the major problems in the structural design of FBR main vessels. Pseudo-dynamic and dynamic buckling tests of cylinders were performed in order to study the effects of nonlinear seismic response on buckling strength, ductility, and plastic response reduction. The buckling strength formulae and the rule for ductility factors both derived from static tests were confirmed to be valid for the tests under dynamic loads. The displacement-constant rule for response reduction effect was modified by acceleration amplification factor in order to maintain applicability for various spectral profiles of seismic excitations. The response reduction estimated by the proposed rule was reasonably conservative for all cases of the pseudo-dynamic and the dynamic tests. Finally, a seismic safety assessment rule was proposed for plastic shear-bending buckling of cylinders, which include the proposed response reduction rule. (author)
Ter-Martirosyan Zaven
2016-01-01
Full Text Available Modern regulations in the field of design and construction of buildings in seismically dangerous areas provide for stability calculation of bases, foundations and underground structures, i.e. calculations for the first group of limited states. At the same time, calculations for the second group of limited states, like deformations (yields, relative difference in yields, as a rule, are not fulfilled. This state of affairs is due to insufficient knowledge of the issues of appearance and development of additional stress and strain in ground arrays during seismic influences, that ultimately leads to residual yields and rolls of foundations of industrial and civil buildings. Essentially, residual displacements depend on the type and intensity of dynamic effects, as well as on the model foundation soils. At the same time, the most important factor is the compulsory registration of collaboration between the subgrade and the structure. Therefore, quantification of additional residual displacements of foundations of industrial buildings and structures under dynamic loads, is an actual problem of the modern earthquake-resistant construction.
Bohn, F.H.; Czymek, G.; Giesen, B.; Bondarchuk, E.; Doinikov, N.; Kozhukhovskaja, N.; Panin, A.
2001-01-01
The present liner of the TEXTOR 94 tokamak installed inside the vacuum vessel represents the thin toroidal shell that is rested on the vessel inner surface. In order to integrate the dynamic ergodic divertor into the tokamak the liner design has been drastically changed. The 120 deg. sector of the liner shell facing the ergodic coils system is removed and some additional holes in the liner are provisioned. This demands a new liner supporting system allowing for the liner thermal expansion and taking the electromagnetic load occurring in the liner during plasma disruption. The cyclic elasto-plastic deformations of the liner caused by the electromagnetic forces and temperature rise have been studied. It is shown that the local plastic deformations occur in the liner elements after the first heating and electromagnetic loading. The most thermal stresses take place in the reinforcing structures around the holes because of the thermal expansion difference of the inconel shell and the steel reinforcements. These stresses are coupled with the bending stress due to the electromagnetic loading. Subsequent repetitive loading does not lead to any significant increment of the plastic deformation. After the materials' hardening the structure cyclically works mostly in the elastic range
Lee, Seong Won; Lee, Jung Min [Korea Institute of Industrial Technology, Jinju (Korea, Republic of); Joun, Man Soo [Gyeongsang National University, Jinju (Korea, Republic of); Kim, Dong Hwan [International University of Korea, Jinju (Korea, Republic of)
2016-07-15
During a galvannealed sheet metal forming, the failures of coating layers (powdering, flaking and cracking) frequently affect the strain state of sheets and deteriorate the frictional characteristic between sheets and tools. Two FE-models in this study were suggested to investigate the effects of the mechanical behavior of coating layers on the formability and friction of the coated steel sheets in FE analysis; the first is one-layer model to express the coated sheet as one stress-strain curve and the second is a multiple-layer model which is composed of substrates and coating layers, separately. First, the frictional properties and the formability of the coated sheets were experimentally investigated using a cup deep-drawing trial. After, the drawing process was simulated by FE analysis of the two models. In the multiplelayer model, the mechanical behavior of the coating is defined as a stress-strain curve which was determined using the nanoindentation test of the coating, its FE analysis and artificial neural network method. The result showed that the multiple-layer model provides more accuracy predictions of drawing loads than the one-layer model in the FE analysis, compared to the actual cup drawing test.
Valíček, Jan; Harničárová, Marta; Öchsner, Andreas; Hutyrová, Zuzana; Kušnerová, Milena; Tozan, Hakan; Michenka, Vít; Šepelák, Vladimír; Mitaľ, Dušan; Zajac, Jozef
2015-01-01
The paper solves the problem of the nonexistence of a new method for calculation of dynamics of stress-deformation states of deformation tool-material systems including the construction of stress-strain diagrams. The presented solution focuses on explaining the mechanical behavior of materials after cutting by abrasive waterjet technology (AWJ), especially from the point of view of generated surface topography. AWJ is a flexible tool accurately responding to the mechanical resistance of the material according to the accurately determined shape and roughness of machined surfaces. From the surface topography, it is possible to resolve the transition from ideally elastic to quasi-elastic and plastic stress-strain states. For detecting the surface structure, an optical profilometer was used. Based on the analysis of experimental measurements and the results of analytical studies, a mathematical-physical model was created and an exact method of acquiring the equivalents of mechanical parameters from the topography of surfaces generated by abrasive waterjet cutting and external stress in general was determined. The results of the new approach to the construction of stress-strain diagrams are presented. The calculated values agreed very well with those obtained by a certified laboratory VÚHŽ. PMID:28793645
Pfiefle, T.W.; Senseny, P.E.
1981-05-01
Constant stress-rate triaxial compression experiments were performed on specimens of anhydrite and polyhalite at low confining pressure and at two temperatures. The loading rate was 5.75 x 10 -2 MPa s -1 ; the confining pressures were 1, 5, 10, and 20 MPa and the two temperatures were 25 0 C and 100 0 C. The specimens were loaded to failure in a soft testing machine so that failure occurred at peak stress. Results from these experiments were used to construct yield envelopes, failure envelopes and stress-strain curves, and to determine mechanical properties. Yield, determined by the onset of dilatancy, occurs at about sixty percent of peak stress. The effect of temperature on both the yield and failure envelopes is negligible. The polyhalite specimens were found to be about twice as strong as the anhydrite specimens. The stress-strain data were fitted to a constitutive law
Liu, T.H.; Patel, R.B.; Condrac, R.
1993-01-01
The current design by rules of the ASME Section III Code for the nuclear power plant piping system is principally based on the elastic design concept Such design often results in a more rigid piping system, structurally, that may not be so desirable from the viewpoint of long term plant operation. The so called 'elastic design' approach has failed to utilize the ductility that steel pipe exhibits, and therefore, the resulting system maintains a great deal of reserve margin in seismic design. This study does not attempt to assess the amount of this reserve margin but provides some findings and discussions with respect to dynamic inelastic analysis results in the piping system design. Using a test correlation analysis it was found that, while the analytical tools that exist are conservative for low strain levels, further studies with loadings at high strain levels are recommended for a more reasonable design. (author)
Pulungan, Ditho Ardiansyah; Yudhanto, Arief; Goutham, Shiva; Lubineau, Gilles; Yaldiz, Recep; Schijve, Warden
2018-01-01
Polymers in general exhibit pressure- and rate-dependent behavior. Modeling such behavior requires extensive, costly and time-consuming experimental work. Common simplifications may lead to severe inaccuracy when using the model for predicting
Pankaj Thakur
2014-01-01
Full Text Available Steady thermal stresses in a rotating disc with shaft having density variation parameter subjected to thermal load have been derived by using Seth's transition theory. Neither the yields criterion nor the associated flow rule is assumed here. Results are depicted graphically. It has been seen that compressible material required higher percentage increased angular speed to become fully-plastic as compare to rotating disc made of incompressible material. Circumferential stresses are maximal at the outer surface of the rotating disc. With the introduction of thermal effect it decreases the value of radial and circumferential stresses at inner and outer surface for fully-plastic state.
Murphy, M.C.; Batte, A.D.; Stringer, M.B.
1979-01-01
High strain fatigue problem in steam turbine. Cyclic stress strain hysteresis loops and stress relaxation behaviour in 16 h dwell period tests. Variation of stress and strain during tests under nominally strain controlled conditions. Definition of test conditions and of criteria for crack initiation and failure. Comparison of reverse bend and push pull failure data. (orig.) 891 RW/orig. 892 RKD [de
Cellular Automata Rules and Linear Numbers
Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika
2012-01-01
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
Feedback systems for linear colliders
Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...
An introduction to linear algebra
Mirsky, L
2003-01-01
Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter.
CLIC: developing a linear collider
Laurent Guiraud
1999-01-01
Compact Linear Collider (CLIC) is a CERN project to provide high-energy electron-positron collisions. Instead of conventional radio-frequency klystrons, CLIC will use a low-energy, high-intensity primary beam to produce acceleration.
1988 linear accelerator conference proceedings
1989-06-01
This report contains papers presented at the 1988 Linear Accelerator Conference. A few topics covered are beam dynamics; beam transport; superconducting components; free electron lasers; ion sources; and klystron research
CERN balances linear collider studies
ILC Newsline
2011-01-01
The forces behind the two most mature proposals for a next-generation collider, the International Linear Collider (ILC) and the Compact Linear Collider (CLIC) study, have been steadily coming together, with scientists from both communities sharing ideas and information across the technology divide. In a support of cooperation between the two, CERN in Switzerland, where most CLIC research takes place, recently converted the project-specific position of CLIC Study Leader to the concept-based Linear Collider Study Leader. The scientist who now holds this position, Steinar Stapnes, is charged with making the linear collider a viable option for CERN’s future, one that could include either CLIC or the ILC. The transition to more involve the ILC must be gradual, he said, and the redefinition of his post is a good start. Though not very much involved with superconducting radiofrequency (SRF) technology, where ILC researchers have made significant advances, CERN participates in many aspect...
Linear Methods for Image Interpolation
Pascal Getreuer
2011-01-01
We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Acoustic emission linear pulse holography
Collins, H.D.; Busse, L.J.; Lemon, D.K.
1983-10-25
This device relates to the concept of and means for performing Acoustic Emission Linear Pulse Holography, which combines the advantages of linear holographic imaging and Acoustic Emission into a single non-destructive inspection system. This unique system produces a chronological, linear holographic image of a flaw by utilizing the acoustic energy emitted during crack growth. The innovation is the concept of utilizing the crack-generated acoustic emission energy to generate a chronological series of images of a growing crack by applying linear, pulse holographic processing to the acoustic emission data. The process is implemented by placing on a structure an array of piezoelectric sensors (typically 16 or 32 of them) near the defect location. A reference sensor is placed between the defect and the array.
Functionalized linear and cyclic polyolefins
Tuba, Robert; Grubbs, Robert H.
2018-02-13
This invention relates to methods and compositions for preparing linear and cyclic polyolefins. More particularly, the invention relates to methods and compositions for preparing functionalized linear and cyclic polyolefins via olefin metathesis reactions. Polymer products produced via the olefin metathesis reactions of the invention may be utilized for a wide range of materials applications. The invention has utility in the fields of polymer and materials chemistry and manufacture.
Rumen Daskalov
2017-07-01
Full Text Available Let an $[n,k,d]_q$ code be a linear code of length $n$, dimension $k$ and minimum Hamming distance $d$ over $GF(q$. One of the most important problems in coding theory is to construct codes with optimal minimum distances. In this paper 22 new ternary linear codes are presented. Two of them are optimal. All new codes improve the respective lower bounds in [11].
Explorative methods in linear models
Høskuldsson, Agnar
2004-01-01
The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....
Polarized Electrons for Linear Colliders
Clendenin, J.
2004-01-01
Future electron-positron linear colliders require a highly polarized electron beam with a pulse structure that depends primarily on whether the acceleration utilizes warm or superconducting rf structures. The International Linear Collider (ILC) will use cold structures for the main linac. It is shown that a dc-biased polarized photoelectron source such as successfully used for the SLC can meet the charge requirements for the ILC micropulse with a polarization approaching 90%
Primordial black holes in linear and non-linear regimes
Allahyari, Alireza; Abolhasani, Ali Akbar [Department of Physics, Sharif University of Technology, Tehran (Iran, Islamic Republic of); Firouzjaee, Javad T., E-mail: allahyari@physics.sharif.edu, E-mail: j.taghizadeh.f@ipm.ir [School of Astronomy, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)
2017-06-01
We revisit the formation of primordial black holes (PBHs) in the radiation-dominated era for both linear and non-linear regimes, elaborating on the concept of an apparent horizon. Contrary to the expectation from vacuum models, we argue that in a cosmological setting a density fluctuation with a high density does not always collapse to a black hole. To this end, we first elaborate on the perturbation theory for spherically symmetric space times in the linear regime. Thereby, we introduce two gauges. This allows to introduce a well defined gauge-invariant quantity for the expansion of null geodesics. Using this quantity, we argue that PBHs do not form in the linear regime irrespective of the density of the background. Finally, we consider the formation of PBHs in non-linear regimes, adopting the spherical collapse picture. In this picture, over-densities are modeled by closed FRW models in the radiation-dominated era. The difference of our approach is that we start by finding an exact solution for a closed radiation-dominated universe. This yields exact results for turn-around time and radius. It is important that we take the initial conditions from the linear perturbation theory. Additionally, instead of using uniform Hubble gauge condition, both density and velocity perturbations are admitted in this approach. Thereby, the matching condition will impose an important constraint on the initial velocity perturbations δ {sup h} {sub 0} = −δ{sub 0}/2. This can be extended to higher orders. Using this constraint, we find that the apparent horizon of a PBH forms when δ > 3 at turn-around time. The corrections also appear from the third order. Moreover, a PBH forms when its apparent horizon is outside the sound horizon at the re-entry time. Applying this condition, we infer that the threshold value of the density perturbations at horizon re-entry should be larger than δ {sub th} > 0.7.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M.B.; Saa, S.; Kanshin, K.; Machado, P.A.N.
2016-01-01
The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)
Advanced statistics: linear regression, part II: multiple linear regression.
Marill, Keith A
2004-01-01
The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.
The linear-non-linear frontier for the Goldstone Higgs
Gavela, M.B.; Saa, S. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Kanshin, K. [Universita di Padova, Dipartimento di Fisica e Astronomia ' G. Galilei' , Padua (Italy); INFN, Padova (Italy); Machado, P.A.N. [IFT-UAM/CSIC, Universidad Autonoma de Madrid, Departamento de Fisica Teorica y Instituto de Fisica Teorica, Madrid (Spain); Fermi National Accelerator Laboratory, Theoretical Physics Department, Batavia, IL (United States)
2016-12-15
The minimal SO(5)/SO(4) σ-model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone-boson ancestry. Varying the σ mass allows one to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry-breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy-fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators. (orig.)
Linearization: Geometric, Complex, and Conditional
Asghar Qadir
2012-01-01
Full Text Available Lie symmetry analysis provides a systematic method of obtaining exact solutions of nonlinear (systems of differential equations, whether partial or ordinary. Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form. Not much work was done in this direction to start with, but recently there have been various developments. Here, first the original work of Lie (and the early developments on it, and then more recent developments based on geometry and complex analysis, apart from Lie’s own method of algebra (namely, Lie group theory, are reviewed. It is relevant to mention that much of the work is not linearization but uses the base of linearization.
Window observers for linear systems
Utkin Vadim
2000-01-01
Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications
Topics in quaternion linear algebra
Rodman, Leiba
2014-01-01
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses...
Towards the International Linear Collider
Lopez-Fernandez, Ricardo
2006-01-01
The broad physics potential of e+e- linear colliders was recognized by the high energy physics community right after the end of LEP in 2000. In 2007, the Large Hadron Collider (LHC) now under construction at CERN will obtain its first collisions. The LHC, colliding protons with protons at 14 TeV, will discover a standard model Higgs boson over the full potential mass range, and should be sensitive to new physics into the several TeV range. The program for the Linear Collider (LC) will be set in the context of the discoveries made at the LHC. All the proposals for a Linear Collider will extend the discoveries and provide a wealth of measurements that are essential for giving deeper understanding of their meaning, and pointing the way to further evolution of particle physics in the future. For the mexican groups is the right time to join such an effort
Linear Synchronous Motor Repeatability Tests
Ward, C.R.
2002-01-01
A cart system using linear synchronous motors was being considered for the Plutonium Immobilization Plant (PIP). One of the applications in the PIP was the movement of a stack of furnace trays, filled with the waste form (pucks) from a stacking/unstacking station to several bottom loaded furnaces. A system was ordered to perform this function in the PIP Ceramic Prototype Test Facility (CPTF). This system was installed and started up in SRTC prior to being installed in the CPTF. The PIP was suspended and then canceled after the linear synchronous motor system was started up. This system was used to determine repeatability of a linear synchronous motor cart system for the Modern Pit Facility
Linearly polarized photons at ELSA
Eberhardt, Holger [Physikalisches Institut, Universitaet Bonn (Germany)
2009-07-01
To investigate the nucleon resonance regime in meson photoproduction, double polarization experiments are currently performed at the electron accelerator ELSA in Bonn. The experiments make use of a polarized target and circularly or linearly polarized photon beams. Linearly polarized photons are produced by coherent bremsstrahlung from an accurately aligned diamond crystal. The orientation of the crystal with respect to the electron beam is measured using the Stonehenge-Technique. Both, the energy of maximum polarization and the plane of polarization, can be deliberately chosen for the experiment. The linearly polarized beam provides the basis for the measurement of azimuthal beam asymmetries, such as {sigma} (unpolarized target) and G (polarized target). These observables are extracted in various single and multiple meson photoproduction channels.
Linear programming foundations and extensions
Vanderbei, Robert J
2001-01-01
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...
Uniqueness theorems in linear elasticity
Knops, Robin John
1971-01-01
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniquenes...
Bayes linear statistics, theory & methods
Goldstein, Michael
2007-01-01
Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field. The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples. The book covers:The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification...
Scalar-tensor linear inflation
Artymowski, Michał [Institute of Physics, Jagiellonian University, Łojasiewicza 11, 30-348 Kraków (Poland); Racioppi, Antonio, E-mail: Michal.Artymowski@uj.edu.pl, E-mail: Antonio.Racioppi@kbfi.ee [National Institute of Chemical Physics and Biophysics, Rävala 10, 10143 Tallinn (Estonia)
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f (φ) R /2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
Permafrost Hazards and Linear Infrastructure
Stanilovskaya, Julia; Sergeev, Dmitry
2014-05-01
The international experience of linear infrastructure planning, construction and exploitation in permafrost zone is being directly tied to the permafrost hazard assessment. That procedure should also consider the factors of climate impact and infrastructure protection. The current global climate change hotspots are currently polar and mountain areas. Temperature rise, precipitation and land ice conditions change, early springs occur more often. The big linear infrastructure objects cross the territories with different permafrost conditions which are sensitive to the changes in air temperature, hydrology, and snow accumulation which are connected to climatic dynamics. One of the most extensive linear structures built on permafrost worldwide are Trans Alaskan Pipeline (USA), Alaska Highway (Canada), Qinghai-Xizang Railway (China) and Eastern Siberia - Pacific Ocean Oil Pipeline (Russia). Those are currently being influenced by the regional climate change and permafrost impact which may act differently from place to place. Thermokarst is deemed to be the most dangerous process for linear engineering structures. Its formation and development depend on the linear structure type: road or pipeline, elevated or buried one. Zonal climate and geocryological conditions are also of the determining importance here. All the projects are of the different age and some of them were implemented under different climatic conditions. The effects of permafrost thawing have been recorded every year since then. The exploration and transportation companies from different countries maintain the linear infrastructure from permafrost degradation in different ways. The highways in Alaska are in a good condition due to governmental expenses on annual reconstructions. The Chara-China Railroad in Russia is under non-standard condition due to intensive permafrost response. Standards for engineering and construction should be reviewed and updated to account for permafrost hazards caused by the
A Linear Electromagnetic Piston Pump
Hogan, Paul H.
Advancements in mobile hydraulics for human-scale applications have increased demand for a compact hydraulic power supply. Conventional designs couple a rotating electric motor to a hydraulic pump, which increases the package volume and requires several energy conversions. This thesis investigates the use of a free piston as the moving element in a linear motor to eliminate multiple energy conversions and decrease the overall package volume. A coupled model used a quasi-static magnetic equivalent circuit to calculate the motor inductance and the electromagnetic force acting on the piston. The force was an input to a time domain model to evaluate the mechanical and pressure dynamics. The magnetic circuit model was validated with finite element analysis and an experimental prototype linear motor. The coupled model was optimized using a multi-objective genetic algorithm to explore the parameter space and maximize power density and efficiency. An experimental prototype linear pump coupled pistons to an off-the-shelf linear motor to validate the mechanical and pressure dynamics models. The magnetic circuit force calculation agreed within 3% of finite element analysis, and within 8% of experimental data from the unoptimized prototype linear motor. The optimized motor geometry also had good agreement with FEA; at zero piston displacement, the magnetic circuit calculates optimized motor force within 10% of FEA in less than 1/1000 the computational time. This makes it well suited to genetic optimization algorithms. The mechanical model agrees very well with the experimental piston pump position data when tuned for additional unmodeled mechanical friction. Optimized results suggest that an improvement of 400% of the state of the art power density is attainable with as high as 85% net efficiency. This demonstrates that a linear electromagnetic piston pump has potential to serve as a more compact and efficient supply of fluid power for the human scale.
Sparse Linear Identifiable Multivariate Modeling
Henao, Ricardo; Winther, Ole
2011-01-01
and bench-marked on artificial and real biological data sets. SLIM is closest in spirit to LiNGAM (Shimizu et al., 2006), but differs substantially in inference, Bayesian network structure learning and model comparison. Experimentally, SLIM performs equally well or better than LiNGAM with comparable......In this paper we consider sparse and identifiable linear latent variable (factor) and linear Bayesian network models for parsimonious analysis of multivariate data. We propose a computationally efficient method for joint parameter and model inference, and model comparison. It consists of a fully...
Quantized, piecewise linear filter network
Sørensen, John Aasted
1993-01-01
A quantization based piecewise linear filter network is defined. A method for the training of this network based on local approximation in the input space is devised. The training is carried out by repeatedly alternating between vector quantization of the training set into quantization classes...... and equalization of the quantization classes linear filter mean square training errors. The equalization of the mean square training errors is carried out by adapting the boundaries between neighbor quantization classes such that the differences in mean square training errors are reduced...
Correct Linearization of Einstein's Equations
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Introduction to computational linear algebra
Nassif, Nabil; Erhel, Jocelyne
2015-01-01
Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s
Linear feedback controls the essentials
Haidekker, Mark A
2013-01-01
The design of control systems is at the very core of engineering. Feedback controls are ubiquitous, ranging from simple room thermostats to airplane engine control. Helping to make sense of this wide-ranging field, this book provides a new approach by keeping a tight focus on the essentials with a limited, yet consistent set of examples. Analysis and design methods are explained in terms of theory and practice. The book covers classical, linear feedback controls, and linear approximations are used when needed. In parallel, the book covers time-discrete (digital) control systems and juxtapos
Passive longitudinal phase space linearizer
P. Craievich
2010-03-01
Full Text Available We report on the possibility to passively linearize the bunch compression process in electron linacs for the next generation x-ray free electron lasers. This can be done by using the monopole wakefields in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order rf time curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.
Generalized, Linear, and Mixed Models
McCulloch, Charles E; Neuhaus, John M
2011-01-01
An accessible and self-contained introduction to statistical models-now in a modernized new editionGeneralized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects.A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed m
Emittance control in linear colliders
Ruth, R.D.
1991-01-01
Before completing a realistic design of a next-generation linear collider, the authors must first learn the lessons taught by the first generation, the SLC. Given that, they must make designs fault tolerant by including correction and compensation in the basic design. They must also try to eliminate these faults by improved alignment and stability of components. When these two efforts cross, they have a realistic design. The techniques of generation and control of emittance reviewed here provide a foundation for a design which can obtain the necessary luminosity in a next-generation linear collider
Linear contextual modal type theory
Schack-Nielsen, Anders; Schürmann, Carsten
Abstract. When one implements a logical framework based on linear type theory, for example the Celf system [?], one is immediately con- fronted with questions about their equational theory and how to deal with logic variables. In this paper, we propose linear contextual modal type theory that gives...... a mathematical account of the nature of logic variables. Our type theory is conservative over intuitionistic contextual modal type theory proposed by Nanevski, Pfenning, and Pientka. Our main contributions include a mechanically checked proof of soundness and a working implementation....
Vanilla Technicolor at Linear Colliders
T. Frandsen, Mads; Jarvinen, Matti; Sannino, Francesco
2011-01-01
We analyze the reach of Linear Colliders (LC)s for models of dynamical electroweak symmetry breaking. We show that LCs can efficiently test the compositeness scale, identified with the mass of the new spin-one resonances, till the maximum energy in the center-of-mass of the colliding leptons. In ...
Variational linear algebraic equations method
Moiseiwitsch, B.L.
1982-01-01
A modification of the linear algebraic equations method is described which ensures a variational bound on the phaseshifts for potentials having a definite sign at all points. The method is illustrated by the elastic scattering of s-wave electrons by the static field of atomic hydrogen. (author)
Feedback Systems for Linear Colliders
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an integral part of the design. Feedback requirements for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at high bandwidth and fast response. To correct for the motion of individual bunches within a train, both feedforward and feedback systems are planned. SLC experience has shown that feedback systems are an invaluable operational tool for decoupling systems, allowing precision tuning, and providing pulse-to-pulse diagnostics. Feedback systems for the NLC will incorporate the key SLC features and the benefits of advancing technologies
Aspects of robust linear regression
Davies, P.L.
1993-01-01
Section 1 of the paper contains a general discussion of robustness. In Section 2 the influence function of the Hampel-Rousseeuw least median of squares estimator is derived. Linearly invariant weak metrics are constructed in Section 3. It is shown in Section 4 that $S$-estimators satisfy an exact
Periodic linear differential stochastic processes
Kwakernaak, H.
1975-01-01
Periodic linear differential processes are defined and their properties are analyzed. Equivalent representations are discussed, and the solutions of related optimal estimation problems are given. An extension is presented of Kailath and Geesey’s [1] results concerning the innovations representation
Linear colliders for photon collisions
Anon.
1994-01-01
The enthusiasm of the first international workshop on photonphoton colliders and associated physics, held at the Lawrence Berkeley Laboratory from 28 March - 1 April, could have set a ball rolling. According to proponents of this physics, the particle physics one can study with a high energy linear collider is special and complements that of a hadron supercollider
Saturation and linear transport equation
Kutak, K.
2009-03-01
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Parameterized Linear Longitudinal Airship Model
Kulczycki, Eric; Elfes, Alberto; Bayard, David; Quadrelli, Marco; Johnson, Joseph
2010-01-01
A parameterized linear mathematical model of the longitudinal dynamics of an airship is undergoing development. This model is intended to be used in designing control systems for future airships that would operate in the atmospheres of Earth and remote planets. Heretofore, the development of linearized models of the longitudinal dynamics of airships has been costly in that it has been necessary to perform extensive flight testing and to use system-identification techniques to construct models that fit the flight-test data. The present model is a generic one that can be relatively easily specialized to approximate the dynamics of specific airships at specific operating points, without need for further system identification, and with significantly less flight testing. The approach taken in the present development is to merge the linearized dynamical equations of an airship with techniques for estimation of aircraft stability derivatives, and to thereby make it possible to construct a linearized dynamical model of the longitudinal dynamics of a specific airship from geometric and aerodynamic data pertaining to that airship. (It is also planned to develop a model of the lateral dynamics by use of the same methods.) All of the aerodynamic data needed to construct the model of a specific airship can be obtained from wind-tunnel testing and computational fluid dynamics
Linear Methods for Image Interpolation
Pascal Getreuer
2011-09-01
Full Text Available We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Directivity of basic linear arrays
Bach, Henning
1970-01-01
For a linear uniform array ofnelements, an expression is derived for the directivity as a function of the spacing and the phase constants. The cases of isotropic elements, collinear short dipoles, and parallel short dipoles are included. The formula obtained is discussed in some detail and contour...
Data Compression with Linear Algebra
Etler, David
2015-01-01
A presentation on the applications of linear algebra to image compression. Covers entropy, the discrete cosine transform, thresholding, quantization, and examples of images compressed with DCT. Given in Spring 2015 at Ocean County College as part of the honors program.
175 Years of Linear Programming
polynomial-time solvability of linear programming, that is, testing if a polyhedron Q E ~ ... Q is rational, i.e. all extreme points and rays of Q are ra- tional vectors or ..... rithrll terminates with an interior solution, a post-processing step is usually ...
175 Years of Linear Programming
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. 175 Years of Linear Programming - Max Flow = Min Cut. Vijay Chandru M R Rao. Series Article Volume 4 Issue 10 October 1999 pp 22-39. Fulltext. Click here to view fulltext PDF. Permanent link:
Linear collider systems and costs
Loew, G.A.
1993-05-01
The purpose of this paper is to examine some of the systems and sub-systems involved in so-called ''conventional'' e + e - linear colliders and to study how their design affects the overall cost of these machines. There are presently a total of at least six 500 GeV c. of m. linear collider projects under study in the world. Aside from TESLA (superconducting linac at 1.3 GHz) and CLIC (two-beam accelerator with main linac at 30GHz), the other four proposed e + e - linear colliders can be considered ''conventional'' in that their main linacs use the proven technique of driving room temperature accelerator sections with pulsed klystrons and modulators. The centrally distinguishing feature between these projects is their main linac rf frequency: 3 GHz for the DESY machine, 11.424 GHz for the SLAC and JLC machines, and 14 GHz for the VLEPP machine. The other systems, namely the electron and positron sources, preaccelerators, compressors, damping rings and final foci, are fairly similar from project to project. Probably more than 80% of the cost of these linear colliders will be incurred in the two main linacs facing each other and it is therefore in their design and construction that major savings or extra costs may be found
Linear accelerators of the future
Loew, G.A.
1986-07-01
Some of the requirements imposed on future linear accelerators to be used in electron-positron colliders are reviewed, as well as some approaches presently being examined for meeting those requirements. RF sources for use in these linacs are described, as well as wakefields, single bunches, and multiple-bunch trains
175 Years of Linear Programming
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 5. 175 Years of Linear Programming - Pune's Gift. Vijay Chandru M R Rao. Series Article Volume 4 Issue 5 May ... Computer Science and Automation, IISc Bangalore 560012, India. Director, Indian Institute of Management, Bannerghatta Road, ...
Spaces of Piecewise Linear Manifolds
Gomez Lopez, Mauricio Esteban
Abstract In this thesis we introduce Δ-set ψPLd(RN) which we regard as the piecewise linear analogue of the space ψd(RN) of smooth d-dimensional submanifoldsin RN introduced by Galatius in [4]. Using ψPLd(RN) we define a bi-Δ-set Cd(RN)•,• ( whose geometric realization BCPLd(RN) = llCd(RN)•,•ll ......Abstract In this thesis we introduce Δ-set ψPLd(RN) which we regard as the piecewise linear analogue of the space ψd(RN) of smooth d-dimensional submanifoldsin RN introduced by Galatius in [4]. Using ψPLd(RN) we define a bi-Δ-set Cd(RN)•,• ( whose geometric realization BCPLd(RN) = ll...... BCPLd (RN) ≅ ΩN–1lψPLd (RN)•l when N — d ≥ 3. The proof of the main theorem relies on properties of ψPLd (RN) • which arise from the fact that this Δ-set can be obtained from a more general contravariant functor PL op → Sets defined on the category of finite dimensional polyhedraand piecewise linear...... maps, and on a fiberwise transversality result for piecewise linear submersions whose fibers are contained in R × (-1,1)N-1 ⊆ RN . For the proof of this transversality result we use a theorem of Hudson on extensions of piecewise linear isotopies which is why we need to include the condition N — d ≥ 3...
Linear fixed-field multipass arcs for recirculating linear accelerators
V. S. Morozov
2012-06-01
Full Text Available Recirculating linear accelerators (RLA’s provide a compact and efficient way of accelerating particle beams to medium and high energies by reusing the same linac for multiple passes. In the conventional scheme, after each pass, the different energy beams coming out of the linac are separated and directed into appropriate arcs for recirculation, with each pass requiring a separate fixed-energy arc. In this paper we present a concept of an RLA return arc based on linear combined-function magnets, in which two and potentially more consecutive passes with very different energies are transported through the same string of magnets. By adjusting the dipole and quadrupole components of the constituting linear combined-function magnets, the arc is designed to be achromatic and to have zero initial and final reference orbit offsets for all transported beam energies. We demonstrate the concept by developing a design for a droplet-shaped return arc for a dogbone RLA capable of transporting two beam passes with momenta different by a factor of 2. We present the results of tracking simulations of the two passes and lay out the path to end-to-end design and simulation of a complete dogbone RLA.
Multivariate covariance generalized linear models
Bonat, W. H.; Jørgensen, Bent
2016-01-01
are fitted by using an efficient Newton scoring algorithm based on quasi-likelihood and Pearson estimating functions, using only second-moment assumptions. This provides a unified approach to a wide variety of types of response variables and covariance structures, including multivariate extensions......We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models, designed to handle multivariate response variables, along with a wide range of temporal and spatial correlation structures defined in terms of a covariance link...... function combined with a matrix linear predictor involving known matrices. The method is motivated by three data examples that are not easily handled by existing methods. The first example concerns multivariate count data, the second involves response variables of mixed types, combined with repeated...
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
Linear accelerator for radioisotope production
Hansborough, L.D.; Hamm, R.W.; Stovall, J.E.
1982-02-01
A 200- to 500-μA source of 70- to 90-MeV protons would be a valuable asset to the nuclear medicine program. A linear accelerator (linac) can achieve this performance, and it can be extended to even higher energies and currents. Variable energy and current options are available. A 70-MeV linac is described, based on recent innovations in linear accelerator technology; it would be 27.3 m long and cost approx. $6 million. By operating the radio-frequency (rf) power system at a level necessary to produce a 500-μA beam current, the cost of power deposited in the radioisotope-production target is comparable with existing cyclotrons. If the rf-power system is operated at full power, the same accelerator is capable of producing an 1140-μA beam, and the cost per beam watt on the target is less than half that of comparable cyclotrons
Linear regression in astronomy. II
Feigelson, Eric D.; Babu, Gutti J.
1992-01-01
A wide variety of least-squares linear regression procedures used in observational astronomy, particularly investigations of the cosmic distance scale, are presented and discussed. The classes of linear models considered are (1) unweighted regression lines, with bootstrap and jackknife resampling; (2) regression solutions when measurement error, in one or both variables, dominates the scatter; (3) methods to apply a calibration line to new data; (4) truncated regression models, which apply to flux-limited data sets; and (5) censored regression models, which apply when nondetections are present. For the calibration problem we develop two new procedures: a formula for the intercept offset between two parallel data sets, which propagates slope errors from one regression to the other; and a generalization of the Working-Hotelling confidence bands to nonstandard least-squares lines. They can provide improved error analysis for Faber-Jackson, Tully-Fisher, and similar cosmic distance scale relations.
Squares of Random Linear Codes
Cascudo Pueyo, Ignacio; Cramer, Ronald; Mirandola, Diego
2015-01-01
a positive answer, for codes of dimension $k$ and length roughly $\\frac{1}{2}k^2$ or smaller. Moreover, the convergence speed is exponential if the difference $k(k+1)/2-n$ is at least linear in $k$. The proof uses random coding and combinatorial arguments, together with algebraic tools involving the precise......Given a linear code $C$, one can define the $d$-th power of $C$ as the span of all componentwise products of $d$ elements of $C$. A power of $C$ may quickly fill the whole space. Our purpose is to answer the following question: does the square of a code ``typically'' fill the whole space? We give...
Linear inflation from quartic potential
Kannike, Kristjan; Racioppi, Antonio [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia); Raidal, Martti [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia); Institute of Physics, University of Tartu,Tartu (Estonia)
2016-01-07
We show that if the inflaton has a non-minimal coupling to gravity and the Planck scale is dynamically generated, the results of Coleman-Weinberg inflation are confined in between two attractor solutions: quadratic inflation, which is ruled out by the recent measurements, and linear inflation which, instead, is in the experimental allowed region. The minimal scenario has only one free parameter — the inflaton’s non-minimal coupling to gravity — that determines all physical parameters such as the tensor-to-scalar ratio and the reheating temperature of the Universe. Should the more precise future measurements of inflationary parameters point towards linear inflation, further interest in scale-invariant scenarios would be motivated.
Computational linear and commutative algebra
Kreuzer, Martin
2016-01-01
This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...
Perspectives on large linear colliders
Richter, B.
1987-11-01
Three main items in the design of large linear colliders are presented. The first is the interrelation of energy and luminosity requirements. These two items impose severe constraints on the accelerator builder who must design a machine to meet the needs of experimentl high energy physics rather than designing a machine for its own sake. An introduction is also given for linear collider design, concentrating on what goes on at the collision point, for still another constraint comes here from the beam-beam interaction which further restricts the choices available to the accelerator builder. The author also gives his impressions of the state of the technology available for building these kinds of machines within the next decade. The paper concludes with a brief recommendation for how we can all get on with the work faster, and hope to realize these machines sooner by working together. 10 refs., 9 figs
Forms and Linear Network Codes
Hansen, Johan P.
We present a general theory to obtain linear network codes utilizing forms and obtain explicit families of equidimensional vector spaces, in which any pair of distinct vector spaces intersect in the same small dimension. The theory is inspired by the methods of the author utilizing the osculating...... spaces of Veronese varieties. Linear network coding transmits information in terms of a basis of a vector space and the information is received as a basis of a possibly altered vector space. Ralf Koetter and Frank R. Kschischang introduced a metric on the set af vector spaces and showed that a minimal...... distance decoder for this metric achieves correct decoding if the dimension of the intersection of the transmitted and received vector space is sufficiently large. The vector spaces in our construction are equidistant in the above metric and the distance between any pair of vector spaces is large making...
Perspectives on large Linear Colliders
Richter, B.
1987-01-01
The accelerator community now generally agrees that the Linear Collider is the most cost-effective technology for reaching much higher energies in the center-of-mass than can be attained in the largest of the e + e - storage rings, LEP. Indeed, even as the first linear collider, the SLC at SLAC, is getting ready to begin operations groups, at SLAC, Novosibirsk, CERN and KEK are doing R and D and conceptual design studies on a next generation machine in the 1 TeV energy region. In this perspectives talk I do not want to restrict my comments to any particular design, and so I will talk about a high-energy machine as the NLC, which is shorthand for the Next Linear Collider, and taken to mean a machine with a center-of-mass energy someplace in the 0.5 to 2 TeV energy range with sufficient luminosity to carry out a meaningful experimental program. I want to discuss three main items with you. The first is the interrelation of energy and luminosity requirements. These two items impose severe constraints on the accelerator builder. Next, I will give an introduction to linear collider design, concentrating on what goes on at the collision point, for still another constraint comes here from the beam-beam interaction which further restricts the choices available to the accelerator builder.Then, I want to give my impressions of the state of the technology available for building these kinds of machines within the next decade
Linear gate with prescaled window
Koch, J; Bissem, H H; Krause, H; Scobel, W [Hamburg Univ. (Germany, F.R.). 1. Inst. fuer Experimentalphysik
1978-07-15
An electronic circuit is described that combines the features of a linear gate, a single channel analyzer and a prescaler. It allows selection of a pulse height region between two adjustable thresholds and scales the intensity of the spectrum within this window down by a factor 2sup(N) (0<=N<=9), whereas the complementary part of the spectrum is transmitted without being affected.
Stanford Linear Collider magnet positioning
Wand, B.T.
1991-08-01
For the installation of the Stanford Linear Collider (SLC) the positioning and alignment of the beam line components was performed in several individual steps. In the following the general procedures for each step are outlined. The calculation of ideal coordinates for the magnets in the entire SLC will be discussed in detail. Special emphasis was given to the mathematical algorithms and geometry used in the programs to calculate these ideal positions. 35 refs., 21 figs
Linear positivity and virtual probability
Hartle, James B.
2004-01-01
We investigate the quantum theory of closed systems based on the linear positivity decoherence condition of Goldstein and Page. The objective of any quantum theory of a closed system, most generally the universe, is the prediction of probabilities for the individual members of sets of alternative coarse-grained histories of the system. Quantum interference between members of a set of alternative histories is an obstacle to assigning probabilities that are consistent with the rules of probability theory. A quantum theory of closed systems therefore requires two elements: (1) a condition specifying which sets of histories may be assigned probabilities and (2) a rule for those probabilities. The linear positivity condition of Goldstein and Page is the weakest of the general conditions proposed so far. Its general properties relating to exact probability sum rules, time neutrality, and conservation laws are explored. Its inconsistency with the usual notion of independent subsystems in quantum mechanics is reviewed. Its relation to the stronger condition of medium decoherence necessary for classicality is discussed. The linear positivity of histories in a number of simple model systems is investigated with the aim of exhibiting linearly positive sets of histories that are not decoherent. The utility of extending the notion of probability to include values outside the range of 0-1 is described. Alternatives with such virtual probabilities cannot be measured or recorded, but can be used in the intermediate steps of calculations of real probabilities. Extended probabilities give a simple and general way of formulating quantum theory. The various decoherence conditions are compared in terms of their utility for characterizing classicality and the role they might play in further generalizations of quantum mechanics
Order-constrained linear optimization.
Tidwell, Joe W; Dougherty, Michael R; Chrabaszcz, Jeffrey S; Thomas, Rick P
2017-11-01
Despite the fact that data and theories in the social, behavioural, and health sciences are often represented on an ordinal scale, there has been relatively little emphasis on modelling ordinal properties. The most common analytic framework used in psychological science is the general linear model, whose variants include ANOVA, MANOVA, and ordinary linear regression. While these methods are designed to provide the best fit to the metric properties of the data, they are not designed to maximally model ordinal properties. In this paper, we develop an order-constrained linear least-squares (OCLO) optimization algorithm that maximizes the linear least-squares fit to the data conditional on maximizing the ordinal fit based on Kendall's τ. The algorithm builds on the maximum rank correlation estimator (Han, 1987, Journal of Econometrics, 35, 303) and the general monotone model (Dougherty & Thomas, 2012, Psychological Review, 119, 321). Analyses of simulated data indicate that when modelling data that adhere to the assumptions of ordinary least squares, OCLO shows minimal bias, little increase in variance, and almost no loss in out-of-sample predictive accuracy. In contrast, under conditions in which data include a small number of extreme scores (fat-tailed distributions), OCLO shows less bias and variance, and substantially better out-of-sample predictive accuracy, even when the outliers are removed. We show that the advantages of OCLO over ordinary least squares in predicting new observations hold across a variety of scenarios in which researchers must decide to retain or eliminate extreme scores when fitting data. © 2017 The British Psychological Society.
Segmented rail linear induction motor
Cowan, Jr., Maynard; Marder, Barry M.
1996-01-01
A segmented rail linear induction motor has a segmented rail consisting of a plurality of nonferrous electrically conductive segments aligned along a guideway. The motor further includes a carriage including at least one pair of opposed coils fastened to the carriage for moving the carriage. A power source applies an electric current to the coils to induce currents in the conductive surfaces to repel the coils from adjacent edges of the conductive surfaces.
Linear polarization of BY Draconis
Koch, R.H.; Pfeiffer, R.J.
1976-01-01
Linear polarization measurements are reported in four bandpasses for the flare star BY Dra. The red polarization is intrinsically variable at a confidence level greater than 99 percent. On a time scale of many months, the variability is not phase-locked to either a rotational or a Keplerian ephemeris. The observations of the three other bandpasses are useful principally to indicate a polarization spectrum rising toward shorter wavelengths
Linear morphea with secondary mucinosis
Khandpur Sujay
2009-01-01
Full Text Available Secondary mucin deposition in the skin is a common feature of lupus erythematosus and dermatomyositis. In scleroderma, it occurs uncommonly or in small amount. We describe a 7-year-old boy with progressive, linear, bound-down plaques involving the thighs, lower abdomen and back with no systemic involvement. Histopathology showed features of scleroderma with abundant mucin deposition in the reticular dermis. This report highlights excessive mucin deposition in lesions of morphea.
Cast dielectric composite linear accelerator
Sanders, David M [Livermore, CA; Sampayan, Stephen [Manteca, CA; Slenes, Kirk [Albuquerque, NM; Stoller, H M [Albuquerque, NM
2009-11-10
A linear accelerator having cast dielectric composite layers integrally formed with conductor electrodes in a solventless fabrication process, with the cast dielectric composite preferably having a nanoparticle filler in an organic polymer such as a thermosetting resin. By incorporating this cast dielectric composite the dielectric constant of critical insulating layers of the transmission lines of the accelerator are increased while simultaneously maintaining high dielectric strengths for the accelerator.
Introduction to Microwave Linear [Accelerators
Whittum, David H
1999-01-04
The elements of microwave linear accelerators are introduced starting with the principles of acceleration and accelerating structures. Considerations for microwave structure modeling and design are developed from an elementary point of view. Basic elements of microwave electronics are described for application to the accelerator circuit and instrumentation. Concepts of beam physics are explored together with examples of common beamline instruments. Charged particle optics and lattice diagnostics are introduced. Considerations for fixed-target and colliding-beam experimentation are summarized.
Positive Quasi Linear Operator Formulation
Berry, L.A.; Jaeger, E.F.
2005-01-01
Expressions for the RF quasi-linear operator are biquadratic sums over the Fourier modes (or FLR equivalent) that describe the RF electric field with a kernel that is a function of the two wave vectors, k-vector L and k-vector R , in the sum. As a result of either an implicit or explicit average over field lines or flux surfaces, this kernel only depends on one parallel wave vector, conventionally k R -vector. When k-vector is an independent component of the representation for E, the sums are demonstrably positive. However, except for closed field line systems, k-vector is dependent on the local direction of the equilibrium magnetic field, and, empirically, the absorbed energy and quasi-linear diffusion coefficients are observed to have negative features. We have formally introduced an independent k-vector sum by Fourier transforming the RF electric field (assuming straight field lines) using a field-line-length coordinate. The resulting expression is positive. We have modeled this approach by calculating the quasi linear operator for 'modes' with fixed k-vector. We form these modes by discretizing k-vector and then assigning all of the Fourier components with k-vectorthat fall within a given k-vector bin to that k-vector mode. Results will be shown as a function of the number of bins. Future work will involve implementing the expressions derived from the Fourier transform and evaluating the dependence on field line length
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
Test accelerator for linear collider
Takeda, S.; Akai, K.; Akemoto, M.; Araki, S.; Hayano, H.; Hugo, T.; Ishihara, N.; Kawamoto, T.; Kimura, Y.; Kobayashi, H.; Kubo, T.; Kurokawa, S.; Matsumoto, H.; Mizuno, H.; Odagiri, J.; Otake, Y.; Sakai, H.; Shidara, T.; Shintake, T.; Suetake, M.; Takashima, T.; Takata, K.; Takeuchi, Y.; Urakawa, J.; Yamamoto, N.; Yokoya, K.; Yoshida, M.; Yoshioka, M.; Yamaoka, Y.
1989-01-01
KEK has proposed to build Test Accelerator Facility (TAF) capable of producing a 2.5 GeV electron beam for the purpose of stimulating R ampersand D for linear collider in TeV region. The TAF consists of a 1.5 GeV S-band linear accelerator, 1.5 GeV damping ring and 1.0 GeV X-band linear accelerator. The TAF project will be carried forward in three phases. Through Phase-I and Phase-II, the S-band and X-band linacs will be constructed, and in Phase-III, the damping ring will be completed. The construction of TAF Phase-I has started, and the 0.2 GeV S-band injector linac has been almost completed. The Phase-I linac is composed of a 240 keV electron gun, subharmonic bunchers, prebunchers and traveling buncher followed by high-gradient accelerating structures. The SLAC 5045 klystrons are driven at 450 kV in order to obtain the rf-power of 100 MW in a 1 μs pulse duration. The rf-power from a pair of klystrons are combined into an accelerating structure. The accelerating gradient up to 100 MeV/m will be obtained in a 0.6 m long structure. 5 refs., 3 figs., 2 tabs
Orthogonal sparse linear discriminant analysis
Liu, Zhonghua; Liu, Gang; Pu, Jiexin; Wang, Xiaohong; Wang, Haijun
2018-03-01
Linear discriminant analysis (LDA) is a linear feature extraction approach, and it has received much attention. On the basis of LDA, researchers have done a lot of research work on it, and many variant versions of LDA were proposed. However, the inherent problem of LDA cannot be solved very well by the variant methods. The major disadvantages of the classical LDA are as follows. First, it is sensitive to outliers and noises. Second, only the global discriminant structure is preserved, while the local discriminant information is ignored. In this paper, we present a new orthogonal sparse linear discriminant analysis (OSLDA) algorithm. The k nearest neighbour graph is first constructed to preserve the locality discriminant information of sample points. Then, L2,1-norm constraint on the projection matrix is used to act as loss function, which can make the proposed method robust to outliers in data points. Extensive experiments have been performed on several standard public image databases, and the experiment results demonstrate the performance of the proposed OSLDA algorithm.
Core seismic behaviour: linear and non-linear models
Bernard, M.; Van Dorsselaere, M.; Gauvain, M.; Jenapierre-Gantenbein, M.
1981-08-01
The usual methodology for the core seismic behaviour analysis leads to a double complementary approach: to define a core model to be included in the reactor-block seismic response analysis, simple enough but representative of basic movements (diagrid or slab), to define a finer core model, with basic data issued from the first model. This paper presents the history of the different models of both kinds. The inert mass model (IMM) yielded a first rough diagrid movement. The direct linear model (DLM), without shocks and with sodium as an added mass, let to two different ones: DLM 1 with independent movements of the fuel and radial blanket subassemblies, and DLM 2 with a core combined movement. The non-linear (NLM) ''CORALIE'' uses the same basic modelization (Finite Element Beams) but accounts for shocks. It studies the response of a diameter on flats and takes into account the fluid coupling and the wrapper tube flexibility at the pad level. Damping consists of one modal part of 2% and one part due to shocks. Finally, ''CORALIE'' yields the time-history of the displacements and efforts on the supports, but damping (probably greater than 2%) and fluid-structures interaction are still to be precised. The validation experiments were performed on a RAPSODIE core mock-up on scale 1, in similitude of 1/3 as to SPX 1. The equivalent linear model (ELM) was developed for the SPX 1 reactor-block response analysis and a specified seismic level (SB or SM). It is composed of several oscillators fixed to the diagrid and yields the same maximum displacements and efforts than the NLM. The SPX 1 core seismic analysis with a diagrid input spectrum which corresponds to a 0,1 g group acceleration, has been carried out with these models: some aspects of these calculations are presented here
A review of linear compressors for refrigeration
Liang, Kun
2017-01-01
Linear compressor has no crank mechanism compared with conventional reciprocating compressor. This allows higher efficiency, oil-free operation, lower cost and smaller size when linear compressors are used for vapour compression refrigeration (VCR) system. Typically, a linear compressor consists of a linear motor (connected to a piston) and suspension springs, operated at resonant frequency. This paper presents a review of linear compressors for refrigeration system. Different designs and mod...
A Trivial Linear Discriminant Function
Shuichi Shinmura
2015-11-01
Full Text Available In this paper, we focus on the new model selection procedure of the discriminant analysis. Combining re-sampling technique with k-fold cross validation, we develop a k-fold cross validation for small sample method. By this breakthrough, we obtain the mean error rate in the validation samples (M2 and the 95\\% confidence interval (CI of discriminant coefficient. Moreover, we propose the model selection procedure in which the model having a minimum M2 was chosen to the best model. We apply this new method and procedure to the pass/ fail determination of exam scores. In this case, we fix the constant =1 for seven linear discriminant functions (LDFs and several good results were obtained as follows: 1 M2 of Fisher's LDF are over 4.6\\% worse than Revised IP-OLDF. 2 A soft-margin SVM for penalty c=1 (SVM1 is worse than another mathematical programming (MP based LDFs and logistic regression . 3 The 95\\% CI of the best discriminant coefficients was obtained. Seven LDFs except for Fisher's LDF are almost the same as a trivial LDF for the linear separable model. Furthermore, if we choose the median of the coefficient of seven LDFs except for Fisher's LDF, those are almost the same as the trivial LDF for the linear separable model.
ESPRIT And Uniform Linear Arrays
Roy, R. H.; Goldburg, M.; Ottersten, B. E.; Swindlehurst, A. L.; Viberg, M.; Kailath, T.
1989-11-01
Abstract ¬â€?ESPRIT is a recently developed and patented technique for high-resolution estimation of signal parameters. It exploits an invariance structure designed into the sensor array to achieve a reduction in computational requirements of many orders of magnitude over previous techniques such as MUSIC, Burg's MEM, and Capon's ML, and in addition achieves performance improvement as measured by parameter estimate error variance. It is also manifestly more robust with respect to sensor errors (e.g. gain, phase, and location errors) than other methods as well. Whereas ESPRIT only requires that the sensor array possess a single invariance best visualized by considering two identical but other-wise arbitrary arrays of sensors displaced (but not rotated) with respect to each other, many arrays currently in use in various applications are uniform linear arrays of identical sensor elements. Phased array radars are commonplace in high-resolution direction finding systems, and uniform tapped delay lines (i.e., constant rate A/D converters) are the rule rather than the exception in digital signal processing systems. Such arrays possess many invariances, and are amenable to other types of analysis, which is one of the main reasons such structures are so prevalent. Recent developments in high-resolution algorithms of the signal/noise subspace genre including total least squares (TLS) ESPRIT applied to uniform linear arrays are summarized. ESPRIT is also shown to be a generalization of the root-MUSIC algorithm (applicable only to the case of uniform linear arrays of omni-directional sensors and unimodular cisoids). Comparisons with various estimator bounds, including CramerRao bounds, are presented.
Linearized gyro-kinetic equation
Catto, P.J.; Tsang, K.T.
1976-01-01
An ordering of the linearized Fokker-Planck equation is performed in which gyroradius corrections are retained to lowest order and the radial dependence appropriate for sheared magnetic fields is treated without resorting to a WKB technique. This description is shown to be necessary to obtain the proper radial dependence when the product of the poloidal wavenumber and the gyroradius is large (k rho much greater than 1). A like particle collision operator valid for arbitrary k rho also has been derived. In addition, neoclassical, drift, finite β (plasma pressure/magnetic pressure), and unperturbed toroidal electric field modifications are treated
Matrix algebra for linear models
Gruber, Marvin H J
2013-01-01
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f
Fast feedback for linear colliders
Hendrickson, L.; Adolphsen, C.; Allison, S.; Gromme, T.; Grossberg, P.; Himel, T.; Krauter, K.; MacKenzie, R.; Minty, M.; Sass, R.
1995-01-01
A fast feedback system provides beam stabilization for the SLC. As the SLC is in some sense a prototype for future linear colliders, this system may be a prototype for future feedbacks. The SLC provides a good base of experience for feedback requirements and capabilities as well as a testing ground for performance characteristics. The feedback system controls a wide variety of machine parameters throughout the SLC and associated experiments, including regulation of beam position, angle, energy, intensity and timing parameters. The design and applications of the system are described, in addition to results of recent performance studies
Cosmological perturbations beyond linear order
CERN. Geneva
2013-01-01
Cosmological perturbation theory is the standard tool to understand the formation of the large scale structure in the Universe. However, its degree of applicability is limited by the growth of the amplitude of the matter perturbations with time. This problem can be tackled with by using N-body simulations or analytical techniques that go beyond the linear calculation. In my talk, I'll summarise some recent efforts in the latter that ameliorate the bad convergence of the standard perturbative expansion. The new techniques allow better analytical control on observables (as the matter power spectrum) over scales very relevant to understand the expansion history and formation of structure in the Universe.
PIGMI linear-accelerator technology
Boyd, T.J.; Crandall, K.R.; Hamm, R.W.
1981-01-01
A new linear-accelerator technology has been developed that makes pi-meson (pion) generation possible for cancer therapy in the setting of a major hospital center. This technology uses several new major inventions in particle accelerator science-such as a new accelerator system called the radio-frequency quadrupole (RFQ), and permanent-magnet drift-tube focusing-to substantially reduce the size, cost, and complexity of a meson factory for this use. This paper describes this technology, discusses other possible uses for these new developments, and finally discusses possible costs for such installations
Beam dynamics in linear colliders
Ruth, R.D.
1990-09-01
In this paper, we discuss some basic beam dynamics issues related to obtaining and preserving the luminosity of a next generation linear collider. The beams are extracted from a damping ring and compressed in length by the first bunch compressor. They are then accelerated in a preaccelerator linac up to an energy appropriate for injection into a high gradient linac. In many designs this pre-acceleration is followed by another bunch compression to reach a short bunch. After acceleration in the linac, the bunches are finally focused transversely to a small spot. 27 refs., 1 fig
Modelling Loudspeaker Non-Linearities
Agerkvist, Finn T.
2007-01-01
This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...
Meromorphic functions and linear algebra
Nevanlinna, Olavi
2003-01-01
This volume describes for the first time in monograph form important applications in numerical methods of linear algebra. The author presents new material and extended results from recent papers in a very readable style. The main goal of the book is to study the behavior of the resolvent of a matrix under the perturbation by low rank matrices. Whereas the eigenvalues (the poles of the resolvent) and the pseudospectra (the sets where the resolvent takes large values) can move dramatically under such perturbations, the growth of the resolvent as a matrix-valued meromorphic function remains essen