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Showing papers on "Linear elasticity published in 1984"


Book
01 Jan 1984
TL;DR: In this paper, the influence of non-linear elastic systems on a simple geometric model for elastic deformations is discussed, and the authors propose a planar and spatial euler introduction to nonlinear analysis.
Abstract: non linear elastic deformations iwsun non linear elastic deformations erpd non linear elastic deformations hneun non-linear elastic deformations (dover civil and non-linear elastic deformations of multi-phase fluid systems non linear elastic deformations dover civil and mechanical ogden nonlinear elastic deformations pdf wordpress non-linear, elastic researchgate chapter 6 non linear material models international journal of nonlinear mechanics nonlinear elastic deformations ogden pdfslibforme international journal of non-linear mechanics 1 rubber elasticity: basic concepts and behavior non linear elastic deformations dover civil and mechanical on a non-linear wave equation in elasticity non linear elastic deformations (pdf) by r. w. ogden (ebook) exact formulations of non-linear planar and spatial euler introduction to nonlinear analysis mit opencourseware manual for the calculation of elastic-plastic materials non linear elastic axisymmetric deformation of membranes types of analysis: linear static, linear dynamic and non fracture mechanics, damage and fatigue non linear fracture chapter 2 linear elasticity freie universität the influence of non-linear elastic systems on the a simple geometric model for elastic deformations

3,871 citations


Journal ArticleDOI
TL;DR: In this article, a mixed finite element procedure for plane elasticity is introduced and analyzed, and the symmetry of the stress tensor is enforced through the introduction of a Lagrange multiplier.
Abstract: A mixed finite element procedure for plane elasticity is introduced and analyzed. The symmetry of the stress tensor is enforced through the introduction of a Lagrange multiplier. An additional Lagrange multiplier is introduced to simplify the linear algebraic system. Applications are made to incompressible elastic problems and to plasticity problems.

360 citations


Journal ArticleDOI
TL;DR: In this article, a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small is studied and convergence proof is carried out.
Abstract: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e 0 then ω 0), (ω 0 then e 0) and lately (e and ω 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.

332 citations


Journal ArticleDOI
TL;DR: In this paper, the bending of a thin plate with rapidly varying thickness was studied and a fourth-order equation for the midplanc displacement was derived using an asymptotic analysis based on 3D linear elasticity.

276 citations


Journal ArticleDOI
TL;DR: In this article, the Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation.
Abstract: The Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation. Estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inL 2(Ω), and optimal order negative norm estimates are obtained inH s (Ω)? for a range ofs depending on the index of the finite element space. An optimal order estimate inL ?(Ω) for the displacement error is given. Also, a quasioptimal estimate is derived in an appropriate space. All estimates are valid uniformly with respect to the compressibility and apply in the incompressible case. The formulation of the elements is presented in detail.

238 citations


01 Jan 1984
TL;DR: In this article, a discrete crack is considered with softening zones at the crack tips, and closed stresses are applied to the crack faces in the softening zone, described by a power function.
Abstract: Concrete is modelled as a linear elastic softening material and introduced into fracture mechanics. A discrete crack is considered with softening zones at the crack tips. Following the approach of Dugdale/Barenblatt, closing stresses are applied to the crack faces in the softening zone. The stresses are described by a power function. Relations are worked out between the remote stress on a cracked plate, the tensile strength of the material and the size of the softening zone. The finite width of a plate is considered and so are various stress distributions of the softening zone. Experiments were performed to estabilish the stress-strain behaviour of concrete in deformation-controlled uniaxial tensile loading. Furthermore, it was investigated whether cyclic loading affects the static envelope curve. A qualitative model is presented which illustrates the effect of prepeak cyclic loading on deformation and stress distribution in a specimen. The results show that nonlinear fracture mechanics can be applied to concrete. The loadbearing capacity of a cracked plate can be predicted with reasonable accuracy. As appears from the experiments, the application of this approach to cyclic loading is very promising.

215 citations


Journal ArticleDOI
TL;DR: For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems as discussed by the authors.

214 citations


Journal ArticleDOI
TL;DR: In this paper, the dynamic response of three-dimensional rigid surface foundations of arbitrary shape is numerically obtained by placing the foundations on a linear elastic, isotropic and homogeneous half-space representing the soil medium and are subjected to either external dynamic forces or seismic waves of various kinds and directions.
Abstract: The dynamic response of three-dimensional rigid surface foundations of arbitrary shape is numerically obtained. The foundations are placed on a linear elastic, isotropic and homogeneous half-space representing the soil medium and are subjected to either external dynamic forces or seismic waves of various kinds and directions, with a general transient time variation. The problem is formulated in the time domain by the boundary element method and the response is obtained by a time step-by-step integration. Two examples dealing with three-dimensional rectangular foundations are presented in detail, together with comparisons with other methods, in order to document the accuracy of the method. The main advantages of the proposed method are that, unlike frequency domain techniques, it provides directly the transient response and forms the basis for extension to the case of non-linear behaviour.

177 citations


Journal ArticleDOI
TL;DR: In this paper, the total potential energy for a body composed of an anisotropic micropolar linear elastic material is developed and used to formulate a displacement type finite element method of analysis.

97 citations


Journal ArticleDOI
TL;DR: In this article, a l'elasticite statique lineaire, homogene isotrope, and homogene homogenized isotropes are applied to determine lois de conservation tridimensionnelles and bidimensionnelses.
Abstract: Application a l'elasticite statique lineaire, homogene isotrope. Determination des lois de conservation tridimensionnelles et bidimensionnelles

76 citations


Journal ArticleDOI
TL;DR: In this article, the eight noded quarter-point Serendipity quadrilateral isoparametric element is reexamined and the stresses are proven to be square-root singular on all rays in a small region adjacent to the crack tip and, as was previously shown, along the element sides.
Abstract: The eight noded quarter-point Serendipity quadrilateral isoparametric element is reexamined. The stresses are proven to be square-root singular on all rays in a small region adjacent to the crack tip and, as was previously shown, along the element sides. It is demonstrated that the element strain energy, and hence its stiffness, is bounded. The effect of element size in characterizing the square-root singular behavior is investigated through stress intensity factor calculations in the case of two geometries with crack tip elements of various dimensions. Workers in the field of fracture mechanics may now, without hesitation, employ this element for modeling crack tip singularities in linear elastic material.

Journal ArticleDOI
TL;DR: In this article, a finite element mesh is used for the linear elastic fracture analysis of cracked structure and the results are analyzed by the finite element method using the isoparametric quadratic singular element.
Abstract: This paper attempts to answer two commonly raised questions during the preparation of a finite element mesh, for the linear elastic fracture analysis of cracked structure: how to set up the finite element mesh around the crack tip, and what level of accuracy is to be expected from such a modelling. Two test problems, with known analytical expressions for their stress intensity factors, are analysed by the finite element method using the isoparametric quadratic singular element. The modified parameters were the order of integration, aspect ratio, number of elements surrounding the crack tip, use of transition elements, the singular element length over the total crack length, the symmetry of the mesh around the crack tip. Based on these analyses, a data base is created and various plots produced. The results are interpreted, the accuracy evaluated and recommendations drawn. Contrary to previous reports, it is found that the computed stress intensity factor (SIF) remains within engineering accuracy (10 per cent) throughout a large range of l/a (singular element length over crack length) for problems with a uniform non-singular stress distribution ahead of the crack tip (i.e. double edge notch), and l/a should be less than 0·1 for problems with a non-singular stress gradient (i.e three-point bend). Also, it is found that the best results are achieved by using at least four singular elements around the crack tip, with their internal angles around 45 degrees, and a reduced (2 × 2) numerical integration.

Journal ArticleDOI
TL;DR: In this article, the stability of multilayer elastomeric bearings is considered within the framework of two-dimensional finite elasticity, and simple constitutive equations which generalize those of a transversally isotropic linear elastic solid are considered.

Journal ArticleDOI
TL;DR: In this article, the authors studied boundary-value problems in a theory recently proposed to model linear elastic materials with voids, and they showed that the model exhibits stress relaxation, hysteresis, and failure.
Abstract: I study several specific boundary-value problems in a theory recently proposed to model linear elastic materials with voids. I show that, in addition to the known fact that the model exhibits stress relaxation, it also exhibits creep, hysteresis, and a phenomenon which can be interpreted as failure. In order to maintain plausible physical behavior, I suggest an a priori inequality not contained in the original theory.

Journal ArticleDOI
TL;DR: In this article, the effective linear elastic behavior of random media subjected to inhomogeneous mean fields is studied and the authors show that the effective elastic moduli show dispersion, i.e., they depend on the wave vector of the mean field.
Abstract: The paper deals with the effective linear elastic behaviour of random media subjected to inhomogeneous mean fields. The effective constitutive laws are known to be non-local. Therefore, the effective elastic moduli show dispersion, i.e∗ they depend on the “wave vector” k of the mean field. In this paper the well-known Hashin-Shtrikman bounds (1962) for the Lame parameters of isotropic multi-phase mixtures are generalized to inhomogeneous mean fields k ≠ 0. The bounds involve two-point correlations of random elastic moduli. In the limit k → ∞ the bounds converge to the exact result. The interest is focussed on composites with cell structures and on binary mixtures. To illustrate the results, numerical evaluations are carried out for a binary cell material composed of nearly spherical grains of equal size.

Journal ArticleDOI
TL;DR: In this paper, an observational procedure for predicting multi-dimensional consolidation behavior is proposed, in which the observations of deformations and/or excess pore water pressures raised in the early stages of consolidation are used for the prediction of those behavior in the successive future stage.

Journal ArticleDOI
TL;DR: In this article, the authors used linear elastic fracture analysis to calculate the energy consumed per unit length of fracture fracture energy, as described by the resistance curve Rcurve, and found that the energy consumption varies with the crack length.
Abstract: Using linear elastic fracture analysis, the energy consumed per unit length of fracture fracture energy varies with the crack length, as described by the resistance curve Rcurve. This concept, orig...

Journal ArticleDOI
TL;DR: In this article, the problem of quasi-static pure bending of a beam in the context of the complete theory of linear elastic materials with voids presented in [1] was studied.
Abstract: This note concerns the problem of quasi-static pure bending of a beam in the context of the complete theory of linear elastic materials with voids presented in [1]. It is shown here that the solution in the context of the complete theory of [1] is coincident with the pure bending solution of classical elasticity for small time, and that the solution for large time is the bending solution given in [1], a solution which neglected the rate effect in the complete theory of [1]. In between these two limit solutions the rate effect moderates a monotonic transition.

Book ChapterDOI
01 Jan 1984
TL;DR: In the theory of linearized elasticity, the authors of as discussed by the authors show that the predictions of these analyses cannot possibly be uniformly valid in the immediate vicinity of the crack-tips, no matter how small the loads.
Abstract: Crack problems within the theory of linearized elasticity give rise to strain fields which are locally unbounded, even at small values of the applied load. This is, of course, a violation of the approximative assumptions upon which the theory rests. Most early extensions of such studies to beyond the scope of the classical theory of elasticity continue to retain the kinematic assumption of infinitesimal deformations but replace the linear stress-strain law by a nonlinear constitutive relation of some sort. (See for example, the monograph by Hutchinson [1].) The predictions of these analyses cannot possibly be uniformly valid in the immediate vicinity of the crack-tips, no matter how small the loads. It is natural therefore to examine such problems within the setting of a finite theory, which allows for both large deformations and constitutive nonlinearities.

Journal Article
TL;DR: In this paper, a one-dimensional combo viscoelastic-plastic constitutive model composed of Burger-type mechanical elements connected in series with a friction slider is used.
Abstract: Constitutive equations used in solving the boundary value problem of flexible pavements employ linear elastic or viscoelastic theory. Accordingly, permanent deformations are calculated based on elastic or viscoelastic deformation laws. Advances in the field of constitutive modeling of materials indicated the need to develop a constitutive relationship that better replicates asphaltic mixture responses under various loading and environmental conditions. In this paper a one-dimensional combo viscoelastic-plastic constitutive model composed of Burger-type mechanical elements connected in series with a friction slider is used. The friction slider is the mechanical representation of plasticity with a DruckerPrager yield criterion. This model is solved under creep phase loading conditions, and the solution is used to develop a rutting model that incorporates a densification phase represented by a relaxing spring. Within the verification of the constitutive model a true yield line has been identified and used instead of the Mohr-Coloumb failure line. The two developed models are supplemented by appropriate experimentation phases to identify and numerically evaluate the relevant parameters. Experimentation is based on actual existing routine methods, with proper adjustments, modifications, or extensions to comply with proper evaluation of the model parameters, and kept as simple as possible to encourage wider user acceptance. An example using actual data is worked out and compared with results obtained from the VESYS III structural subsystem program.

Journal ArticleDOI
TL;DR: In this paper, the authors present a modelle d'elements finis d'une structure and un systeme de charges externes for the analysis of elasticite lineaires.
Abstract: En analyse d'elasticite lineaire un probleme consiste a trouver les vecteurs de contraintes et de deformations etant donnes un modele d'elements finis d'une structure et un systeme de charges externes. On montre que ce probleme est un cas particulier du probleme de norme minimum pour des systemes indetermines d'equations lineaires

Journal ArticleDOI
TL;DR: In this article, a linear elastic, plane stress finite element investigation of the stress distribution around pin-loaded holes is presented for isotropic as well as several fiber reinforced plastic (FRP) composite materials.
Abstract: Results of a linear elastic, plane stress finite element investigation of the stress distribution around pin-loaded holes are presented for isotropic as well as several fibre reinforced plastic (FRP) composite materials. The case of full contact (contact angle = 180°) and that of partial contact (contact angle < 180°) between the pin and the hole have been considered. Important conclusions regarding the peak stress distribution around the pin-loaded hole are made specially with respect to the anisotropy (axial to transverse elastic stiffness ratio, E1/E2) introduced in the materials by way of fibre reinforcements and laminating schemes, geometrical parameters (hole diameter to plate width ratio) and the contact angle between the pin and hole.

Book ChapterDOI
01 Jan 1984
TL;DR: In this paper, three approaches to bond strength analysis are discussed: linear elastic stresses, linear fracture mechanics parameters, and those based upon nonlinear analyses, and the first two approaches are then discussed with respect to standard adhesion test methods.
Abstract: Three approaches to bond strength analysis are discussed in this article: those based upon linear elastic stresses, those based upon linear fracture mechanics parameters, and those based upon nonlinear analyses. The first two approaches are then discussed with respect to standard adhesion test methods. The stresses in linear lap shear test specimens are shown analytically and experimentally to be concentrated at the bond termination and to be strongly dependent upon adherend thickness for standard tests. The bond stress intensity factors and energy release rates near the bond termination are given and discussed. Adherend thickness should be at least 4 times larger than that recommended by standard test techniques. The stresses in butt tensile tests are also discussed. It is shown that test specimen alignment problems can lead to low debond forces and excessively large data scatter. Stress intensity factors are also determined for butt tensile tests.


Journal ArticleDOI
TL;DR: In this article, a finite deformation formulation for dynamic analysis of cable nets is presented, under assumption of straight cable elements and a displacement field varying linearly along the element, global equations of motion are established by referring the displacements to an initial configuration.
Abstract: A finite deformation formulation for dynamic analysis of cable nets is presented. Lagrangian coordinates and Piola‐Kirchhoff stresses are used and elasto‐plastic material behavior is considered. Under assumption of straight cable elements and a displacement field varying linearly along the element, global equations of motion are established by referring the displacements to an initial configuration. These equations are linearized for iterative computation of the equilibrium configuration and for determining the eigenfrequencies and mode shapes of the linear vibration of the net about its equilibrium configuration. This analysis is performed by means of a computer program that can analyze nets anchored in fixed points. Slackness of cable elements is allowed. Three application examples are presented for linear elastic material behavior, showing a good agreement with experimental and computed published data.

Journal ArticleDOI
TL;DR: In this article, the elastic properties of rectangular twist and wedge disclination loops in an infinite isotropic medium are examined in terms of linear elasticity, based on the representation of the initial loop in the form of a continuous distribution of infinitesimal disclinations, their rotation axes being displaced with respect to the centres.
Abstract: The elastic properties of rectangular disclination loops in an infinite isotropic medium are examined in terms of linear elasticity. For the calculation of the disclination stress tensor, an effective method is proposed which is based on the representation of the initial loop in the form of a continuous distribution of infinitesimal disclination loops, their rotation axes being displaced with respect to the centres. The stresses and self-energies of rectangular twist and wedge disclination loops are obtained in an analytical form. To calculate the elastic fields of the disclination and dislocation defects constructed by some mutually perpendicular segments, a mathematical technique for transforming the rectangular-loop solutions is developed. The stress fields of angular disclinations are studied by considering the defect to be a superposition of U-shaped disclinations with infinitesimal arms.

Journal ArticleDOI
TL;DR: The effect of the application of an incremental method is the approximation of the three-dimensional nonlinear equations of finite elasticity by a sequence of linear problems as mentioned in this paper, and sufficient conditions which guarantee the convergence of such a method are given here.
Abstract: The effect of the application of an incremental method is the approximation of the three-dimensional nonlinear equations of finite elasticity by a sequence of linear problems. We give here sufficient conditions which guarantee the convergence of such a method.

Journal ArticleDOI
TL;DR: In this paper, the wave propagation in a fluid line consisting of a circular tube, initially stressed, viscoelastic, orthotropic, surrounded by external materials, containing a compressible linear elastic fluid was considered under isentropic conditions.
Abstract: The wave propagation in a fluid line consisting of a circular tube, initially stressed, viscoelastic, orthotropic, surrounded by external materials, containing a compressible linear elastic fluid is considered under isentropic conditions. The dispersion equation is derived and a number of simplifications are discussed. The impedances of the line and the transfer matrix are given.

Book ChapterDOI
01 Jan 1984
TL;DR: In this article, a review of the recent developments in structural mechanics, which are used to extract fracture parameters for linear elastic, nonlinear and dynamic fracture mechanics, are reviewed. But the focus is on the finite element methods for determining two-and three-dimensional (2-D and 3-D) stress intensity factors in linear elastic fracture mechanics.
Abstract: Recent developments in four numerical techniques in structural mechanics, which are used to extract fracture parameters for linear elastic, nonlinear and dynamic fracture mechanics, are reviewed. Primary emphasis is placed on the finite element methods for determining two- and three-dimensional (2-D and 3-D) stress intensity factors in linear elastic fracture mechanics. Crack opening displacements (COD) and J-integrals for 2-D, stable crack growth, ductile fracture, and use of elastic finite element method in its generation mode for obtaining dynamic elastic fracture parameters are discussed. The second topic is the finite difference method for analyzing the elasto-dynamic and elastic-plastic dynamic states in fracturing 2-D and 3-D problems. The third topic is the boundary element method which has evolved into a practical tool for numerical analysis in 3-D linear elastic fracture mechanics. The final topic is the updated alternating technique, which was merged with a 3-D finite element code and together with a break-through in its analytical formulation, has become a cost-effective numerical technique in solving part and complete elliptical crack problems in 3-D linear elastic fracture mechanics. Comparisons between the J-integral of a 3-point bend specimen, the stress intensity factor for a surface flaw specimen and the dynamic stress intensity factor of a fracturing dynamic tear test specimen obtained by various investigators are made.

Journal ArticleDOI
TL;DR: In this article, the nonlinear transient response for stresses and deflection of thin linear elastic circular plates subjected to different time-dependent loads was investigated and several new useful results were reported.