Showing papers on "Linear elasticity published in 1988"
Book•
01 Jan 1988
TL;DR: In this article, the equations of equilibrium and the principle of virtual work for three-dimensional elasticity have been discussed and the boundary value problems of 3D elasticity has been studied.
Abstract: Part A Description of Three-Dimensional Elasticity 1 Geometrical and other preliminaries 2 The equations of equilibrium and the principle of virtual work 3 Elastic materials and their constitutive equations 4 Hyperelasticity 5 The boundary value problems of three-dimensional elasticity Part B Mathematical Methods in Three-Dimensional Elasticity 6 Existence theory based on the implicit function theorem 7 Existence theory based on the minimization of the Energy Bibliography Index
475 citations
TL;DR: Finite element methods are constructed by adding to the classical Galerkin method various least-squares like terms as mentioned in this paper, which involve integrals over element interiors, and include mesh-parameter dependent coefficients.
Abstract: Finite element methods are presented in an abstract settings for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations. Applied to various problems, simple finite element interpolations are rendered convergent, including convenient equal-order interpolations which are generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: 1. (1) Circumventing Babuska-Brezzi condition methods. 2. (2) Satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to compressible and incompressible elasticity problems.
289 citations
TL;DR: In this article, a new mixed finite element formulation for the equations of linear elasticity is considered, where the variables approximated are the displacement, the unsymmetric stress tensor and the rotation.
Abstract: A new mixed finite element formulation for the equations of linear elasticity is considered. In the formulation the variables approximated are the displacement, the unsymmetric stress tensor and the rotation. The rotation act as a Lagrange multiplier introduced in order to enforce the symmetry of the stress tensor. Based on this formulation a new family of both two-and three-dimensional mixed methods is defined. Optimal error estimates, which are valid uniformly with respect to the Poisson ratio, are derived. Finally, a new postprocessing scheme for improving the displacement is introduced and analyzed.
286 citations
TL;DR: In this article, the vritional inequalities of Hashin and Shtrikman are transformed to a simple and concise form, which are used to bound the effective conductivity tensor σ ∗ of an anisotropic composite made from an arbitrary number of possibly anisotropic phases.
Abstract: The vritional inequalities of Hashin and Shtrikman are transformed to a simple and concise form. They are used to bound the effective conductivity tensor σ∗ of an anisotropic composite made from an arbitrary number of possibly anisotropic phases, and to bound the effective elasticity tensor C ∗ of an anisotropic mixture of two well-ordered isotropic materials. The bounds depend on the conductivities and elastic moduli of the components and their respective volume fractions. When the components are isotropic the conductivity bounds, which constrain the eigenvalues of σ∗, include those previously obtained by Hashin and Shtrikman, Murat and Tartar, and Lurie and Cherkaev. Our approach can also be used in the context of linear elasticity to derive bounds on C ∗ for composites comprised of an arbitrary number of anisotropic phases. For two-component composites our bounds are tighter than those obtained by Kantor and Bergman and by Francfort and Murat, and are attained by sequentially layered laminate materials.
283 citations
256 citations
TL;DR: In this paper, the singular stresses at interface corners in bonded lap joints were examined and a generalized stress intensity factor was defined and used for the prediction of failure in some single-lap joint geometries.
161 citations
Book•
01 Oct 1988
TL;DR: Alfrey and Love as discussed by the authors used the term "Viscoelasticity" to describe the properties of real materials under the action of external forces in the context of polymers.
Abstract: The classical theories of Linear Elasticity and Newtonian Fluids, though trium phantly elegant as mathematical structures, do not adequately describe the defor mation and flow of most real materials Attempts to characterize the behaviour of real materials under the action of external forces gave rise to the science of Rheology Early rheological studies isolated the phenomena now labelled as viscoelastic Weber (1835, 1841), researching the behaviour of silk threats under load, noted an instantaneous extension, followed by a further extension over a long period of time On removal of the load, the original length was eventually recovered He also deduced that the phenomena of stress relaxation and damping of vibrations should occur Later investigators showed that similar effects may be observed in other materials The German school referred to these as "Elastische Nachwirkung" or "the elastic aftereffect" while the British school, including Lord Kelvin, spoke ofthe "viscosityofsolids" The universal adoption of the term "Viscoelasticity," intended to convey behaviour combining proper ties both of a viscous liquid and an elastic solid, is of recent origin, not being used for example by Love (1934), though Alfrey (1948) uses it in the context of polymers The earliest attempts at mathematically modelling viscoelastic behaviour were those of Maxwell (1867) (actually in the context of his work on gases; he used this model for calculating the viscosity of a gas) and Meyer (1874)"
151 citations
TL;DR: In this paper, a flexible multibody synthesis formulation for structural geometric non-linear effects is presented, where the theory of linear elasticity relative to a body reference frame is used to describe deformation and its coupling with system motion.
Abstract: A substructure synthesis formulation is presented that permits use of established flexible multibody dynamic analysis computer codes to account for structural geometric non-linear effects. Large relative displacement is permitted between points within bodies that undergo small strain elastic deformation. Components are divided into substructures, on each of which the theory of linear elasticity relative to a body reference frame is adequate to describe deformation and its coupling with system motion. Normal vibration and static correction deformation modes are used to account for elastic deformation within each substructure. Compatibility conditions are derived and imposed as constraint equations at boundary points between substructures. System equations of motion that include geometric non-linear effects of large rotation, in terms of generalized co-ordinates of a reference frame for each substructure and a set of deformation modes that are defined within the substructure, are assembled. The method is implemented in an industry standard flexible multibody dynamics code, with minimal modification. Use of the formulation is illustrated on the classical problem of a spinning beam with geometric stiffening and on a space structure that experiences large deformation.
144 citations
TL;DR: In this article, the numerical treatment of contact problems with friction is considered, starting from the algebraic stiffness equation of two discretized linear elastic bodies and taking the contact and friction laws into account, a new type of Linear Complementarity Problem (LCP) is suggested.
126 citations
TL;DR: In this paper, the authors considered the linear elasticity problem for an interface crack between two bonded half planes and showed that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip.
121 citations
TL;DR: In this paper, a new mixed variational formulation for linear elasticity was proposed, which does not require symmetric tensors and therefore is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.
Abstract: We propose a new mixed variational formulation for the equations of linear elasticity. It does not require symmetric tensors and consequently is easy to discretize by adapting mixed finite elements developed for scalar second order elliptic equations.
TL;DR: In this article, the authors considered the case of a negative Poisson's ratio and showed that the static definition of the shear factor in Timoshenko beam theory may not be satisfactory in all cases.
Abstract: Recently, isotropic elastic materials with a negative Poisson’s ratio have been manufactured. Since most of the theoretical results of linear elasticity focus on a positive Poisson’s ratio, the need arises for their extension and reexamination. The above materials may have a variety of technological applications so the motivation for this study is not purely academic. The article deals first with some of the limit cases arising when Poisson’s ratio takes on an extreme value. For models represented by these limit cases, the material and structure responses may not be treated independently from each other. Then such basic dynamic elasticity problems as reflection from a free surface, propagation of Rayleigh waves, and lateral vibrations of beams and plates are reconsidered for the case of a negative Poisson’s ratio. It is shown, in particular, that the static definition of the shear factor in Timoshenko beam theory may not be satisfactory in all cases. Extensive numerical results are also given.
TL;DR: In this paper, a crack rail shear (CRS) specimen is used to characterize the Mode III interlaminar fracture toughness of continuous-fiber-reinforced composite materials and an analytical expression for the strain energy release rate is developed based on a strength of materials approach.
Book•
31 Dec 1988TL;DR: In this paper, the authors derived the governing equation for a plate with moment-curvature relations and integrated stress resultant-displacement relations and derived the equilibrium equation for the plate.
Abstract: 1. Equations of Linear Elasticity in Cartesian Coordinates.- 1.1 Stresses.- 1.2 Displacements.- 1.3 Strains.- 1.4 Isotropy and Its Elastic Constants.- 1.5 Equilibrium Equations.- 1.6 Stress-Strain Relations.- 1.7 Linear Strain-Displacement Relations.- 1.8 Compatibility Equations.- 1.9 Summary.- 1.10 References.- 1.11 Problems.- 2. Derivation of the Governing Equations for Beams and Rectangular Plates.- 2.1 Assumptions of Plate Theory.- 2.2 Derivation of the Equilibrium Equations for a Plate.- 2.3 Derivation of Plate Moment-Curvature Relations and Integrated Stress Resultant- Displacement Relations.- 2.4 Derivation of the Governing Equations for a Plate.- 2.5 Boundary Conditions.- 2.6 Stress Distribution within a Plate.- 2.7 References.- 2.8 Problems.- 3. Beams and Rods.- 3.1 General Remarks.- 3.2 Development of the Governing Equations.- 3.3 Solutions for the Beam Equation.- 3.4 Stresses in Beams - Rods - Columns.- 3.5 Example: Clamped-Clamped Beam with a Constant Lateral Load, q(x) = -q0.- 3.6 Example: Cantilevered Beam with a Uniform Lateral Load, q(x) = -q0.- 3.7 Example: Simply Supported Beam with a Uniform Load over Part of Its Length.- 3.8 Beam with an Abrupt Change in Stiffness.- 3.9 Beam Subjected to Concentrated Loads.- 3.10 Solutions by Green's Functions.- 3.11 Tapered Beam Solution Using Galerkin's Method.- 3.12 Problems.- 4. Solutions to Problems of Rectangular Plates.- 4.1 Some General Solutions to the Biharmonic Equation.- 4.2 Double Series Solution (Navier Solution).- 4.3 Single Series Solution (Method of M. Levy).- 4.4 Example of Plate with Edges Supported by Beams.- 4.5 Summary.- 4.6 References.- 4.7 Problems.- 5. Thermal Stresses in Plates.- 5.1 General Considerations.- 5.2 Derivation of the Governing Equations for a Thermoelastic Plate.- 5.3 Boundary Conditions.- 5.4 General Treatment of Plate Nonhomogeneous Boundary Conditions.- 5.5 Thermoelastic Effects on Beams.- 5.6 Self-Equilibration of Thermal Stresses.- 5.7 References.- 5.8 Problems.- 6. Circular Plates.- 6.1 Introduction.- 6.2 Derivation of the Governing Equations.- 6.3 Axially Symmetric Circular Plates.- 6.4 Solutions for Axially Symmetric Circular Plates.- 6.5 Circular Plate, Simply Supported at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.6 Circular Plate, Clamped at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.7 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Stress Couple, M, at the Inner Boundary.- 6.8 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Shear Resultant, Q0, at the Inner Boundary.- 6.9 General Remarks.- 6.10 Problems.- 7. Buckling of Columns and Plates.- 7.1 Derivation of the Plate Governing Equations for Buckling.- 7.2 Buckling of Columns Simply Supported at Each End.- 7.3 Column Buckling with Other Boundary Conditions.- 7.4 Buckling of Plates Simply Supported on All Four Edges.- 7.5 Buckling of Plates with Other Loads and Boundary Conditions.- 7.6 References.- 7.7 Problems.- 8. The Vibrations of Beams and Plates.- 8.1 Introduction.- 8.2 Natural Vibrations of Beams.- 8.3 Natural Vibrations of Plates.- 8.4 Forced Vibrations of Beams and Plates.- 8.5 References.- 8.6 Problems.- 9. Energy Methods in Beams, Columns and Plates.- 9.1 Introduction.- 9.2 Theorem of Minimum Potential Energy.- 9.3 Analysis of Beams Subjected to a Lateral Load.- 9.4 The Buckling of Columns.- 9.5 Vibration of Beams.- 9.6 Minimum Potential Energy for Rectangular Plates.- 9.7 The Buckling of a Plate under Uniaxial Load, Simply Supported on Three Sides, and Free on an Unloaded Edge.- 9.8 Functions to Assume in the Use of Minimum Potential Energy for Solving Beam, Column, and Plate Problems.- 9.9 Problems.- 10. Cylindrical Shells.- 10.1 Cylindrical Shells under General Loads.- 10.2 Circular Cylindrical Shells under Axially Symmetric Loads.- 10.3 Edge Load Solutions.- 10.4 A General Solution for Cylindrical Shells under Axially Symmetric Loads.- 10.5 Sample Solutions.- 10.6 Circular Cylindrical Shells under Asymmetric Loads.- 10.7 Shallow Shell Theory (Donnell'1. Equations of Linear Elasticity in Cartesian Coordinates.- 1.1 Stresses.- 1.2 Displacements.- 1.3 Strains.- 1.4 Isotropy and Its Elastic Constants.- 1.5 Equilibrium Equations.- 1.6 Stress-Strain Relations.- 1.7 Linear Strain-Displacement Relations.- 1.8 Compatibility Equations.- 1.9 Summary.- 1.10 References.- 1.11 Problems.- 2. Derivation of the Governing Equations for Beams and Rectangular Plates.- 2.1 Assumptions of Plate Theory.- 2.2 Derivation of the Equilibrium Equations for a Plate.- 2.3 Derivation of Plate Moment-Curvature Relations and Integrated Stress Resultant- Displacement Relations.- 2.4 Derivation of the Governing Equations for a Plate.- 2.5 Boundary Conditions.- 2.6 Stress Distribution within a Plate.- 2.7 References.- 2.8 Problems.- 3. Beams and Rods.- 3.1 General Remarks.- 3.2 Development of the Governing Equations.- 3.3 Solutions for the Beam Equation.- 3.4 Stresses in Beams - Rods - Columns.- 3.5 Example: Clamped-Clamped Beam with a Constant Lateral Load, q(x) = -q0.- 3.6 Example: Cantilevered Beam with a Uniform Lateral Load, q(x) = -q0.- 3.7 Example: Simply Supported Beam with a Uniform Load over Part of Its Length.- 3.8 Beam with an Abrupt Change in Stiffness.- 3.9 Beam Subjected to Concentrated Loads.- 3.10 Solutions by Green's Functions.- 3.11 Tapered Beam Solution Using Galerkin's Method.- 3.12 Problems.- 4. Solutions to Problems of Rectangular Plates.- 4.1 Some General Solutions to the Biharmonic Equation.- 4.2 Double Series Solution (Navier Solution).- 4.3 Single Series Solution (Method of M. Levy).- 4.4 Example of Plate with Edges Supported by Beams.- 4.5 Summary.- 4.6 References.- 4.7 Problems.- 5. Thermal Stresses in Plates.- 5.1 General Considerations.- 5.2 Derivation of the Governing Equations for a Thermoelastic Plate.- 5.3 Boundary Conditions.- 5.4 General Treatment of Plate Nonhomogeneous Boundary Conditions.- 5.5 Thermoelastic Effects on Beams.- 5.6 Self-Equilibration of Thermal Stresses.- 5.7 References.- 5.8 Problems.- 6. Circular Plates.- 6.1 Introduction.- 6.2 Derivation of the Governing Equations.- 6.3 Axially Symmetric Circular Plates.- 6.4 Solutions for Axially Symmetric Circular Plates.- 6.5 Circular Plate, Simply Supported at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.6 Circular Plate, Clamped at the Outer Edge, Subjected to a Uniform Lateral Loading, p0.- 6.7 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Stress Couple, M, at the Inner Boundary.- 6.8 Annular Plate, Simply Supported at the Outer Edge, Subjected to a Shear Resultant, Q0, at the Inner Boundary.- 6.9 General Remarks.- 6.10 Problems.- 7. Buckling of Columns and Plates.- 7.1 Derivation of the Plate Governing Equations for Buckling.- 7.2 Buckling of Columns Simply Supported at Each End.- 7.3 Column Buckling with Other Boundary Conditions.- 7.4 Buckling of Plates Simply Supported on All Four Edges.- 7.5 Buckling of Plates with Other Loads and Boundary Conditions.- 7.6 References.- 7.7 Problems.- 8. The Vibrations of Beams and Plates.- 8.1 Introduction.- 8.2 Natural Vibrations of Beams.- 8.3 Natural Vibrations of Plates.- 8.4 Forced Vibrations of Beams and Plates.- 8.5 References.- 8.6 Problems.- 9. Energy Methods in Beams, Columns and Plates.- 9.1 Introduction.- 9.2 Theorem of Minimum Potential Energy.- 9.3 Analysis of Beams Subjected to a Lateral Load.- 9.4 The Buckling of Columns.- 9.5 Vibration of Beams.- 9.6 Minimum Potential Energy for Rectangular Plates.- 9.7 The Buckling of a Plate under Uniaxial Load, Simply Supported on Three Sides, and Free on an Unloaded Edge.- 9.8 Functions to Assume in the Use of Minimum Potential Energy for Solving Beam, Column, and Plate Problems.- 9.9 Problems.- 10. Cylindrical Shells.- 10.1 Cylindrical Shells under General Loads.- 10.2 Circular Cylindrical Shells under Axially Symmetric Loads.- 10.3 Edge Load Solutions.- 10.4 A General Solution for Cylindrical Shells under Axially Symmetric Loads.- 10.5 Sample Solutions.- 10.6 Circular Cylindrical Shells under Asymmetric Loads.- 10.7 Shallow Shell Theory (Donnell's Equations).- 10.8 Inextensional Shell Theory.- 10.9 Membrane Shell Theory.- 10.10 Examples of Membrane Theory.- 10.11 References.- 10.12 Problems.- 11. Elastic Stability of Shells.- 11.1 Buckling of Isotropic Circular Cylindrical Shells under Axially Symmetric Axial Loads.- 11.2 Buckling of Isotropic Circular Cylindrical Shells under Axially Symmetric Axial Loads and an Internal Pressure.- 11.3 Buckling of Isotropic Circular Cylindrical Shells under Bending.- 11.4 Buckling of Isotropic Circular Cylindrical Shells under Lateral Pressures.- 11.5 Buckling of Isotropic Circular Cylindrical Shells in Torsion.- 11.6 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Loads and Bending Loads.- 11.7 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Load and Torsion.- 11.8 Buckling of Isotropic Circular Cylindrical Shells under Combined Bending and Torsion.- 11.9 Buckling of Isotropic Circular Cylindrical Shells under Combined Bending and Transverse Shear.- 11.10 Buckling of Isotropic Circular Cylindrical Shells under Combined Axial Compression, Bending and Torsion.- 11.11 Buckling of Isotropic Spherical Shells under External Pressure.- 11.12 Buckling of Anisotropic and Sandwich Cylindrical Shells.- 11.13 References.- 11.14 Problems.- 12. The Vibration of Cylindrical Shells.- 12.1 Governing Differential Equations for Natural Vibrations.- 12.2 Hamilton's Principle for Determining the Natural Vibrations of Cylindrical Shells.- 12.3 Reference.- Appendix 1. Properties of Useful Engineering Materials.- Appendix 2. Answers to Selected Problems.
TL;DR: In this article, a simple constitutive model for nonsmared cracking nonlinear finite element analysis of reinforced concrete structures is described, and the effect of biaxial stress conditions on peak strengths is represented by a variation of the Kupfer-Hilsdorf failure curve in stress space, where the compressive and tensile envelopes are separately specified.
Abstract: A simple constitutive model for ‘smeared cracking’ nonlinear finite element analysis of reinforced concrete structures is described. The model divides the uniaxial response curve for concrete into fivedamage regions, described as linear elastic; compressive strain hardening; compressive strain softening; tensile strain softening; and tensile stiffening regions. Recommendations for incorporating strain localization effects into homogenized material properties in the softening regions are given. The effect of biaxial stress conditions on peak strengths is represented by a variation of the Kupfer‐Hilsdorf failure curve in stress space, in which the compressive and tensile envelopes are separately specified. Recommendations for the effects of tensile cracking and confinement on the shear modulus and the compressivesoftening modulus, respectively, are included. The central thrust of the paper is to incorporate those attributes of the constitutive model which affect the prediction of structural failure modes as...
TL;DR: In this article, a numerical method is presented to carry out sizing design sensitivity calculations outside established finite element analysis codes, using postprocessing data only, using a distributed parameter approach to structural design sensitivity analysis.
Abstract: A numerical method is presented to carry out sizing design sensitivity calculations outside established finite element analysis codes, using postprocessing data only. Geometric as well as material non-linearities are treated. To demonstrate the accuracy of the proposed method, numerical results are presented for structural systems with linear elastic material, large displacements, large rotations and small strains. A distributed parameter approach to structural design sensitivity analysis is used to retain the continuum elasticity formulation throughout the derivation of design sensitivity results. Using this approach and an adjoint variable method, design sensitivity computations are carried out. For structural performance functionals stress and displacement are considered.
It is shown that computations can be performed with the same computational effort as for sizing design sensitivity analysis of linear structural systems. Accurate design sensitivity results are obtained for both linear and non-linear structural systems without the uncertainty of numerical accuracy and high cost associated with the selection of finite difference perturbations. Also, the method does not require differentiation of element stiffness and mass matrices in conventional finite element models.
TL;DR: The analogous theory, linear dielectric-breakdown electrostatics, is developed, based on a Griffith-like energy-balance calculation applied to a single conducting crack in an isotropic dielectrics medium, and the development of the critical field-intensity factor and a contour-independent line integral are introduced.
Abstract: The dielectric breakdown of solids is a problem of great practical and theoretical interest. It is the electrical analog of the fracture of solids under applied loads. In the case of fracture, the reigning theory for linear elastic materials is linear elastic fracture mechanics. This paper develops the analogous theory, linear dielectric-breakdown electrostatics, based on a Griffith-like energy-balance calculation applied to a single conducting crack in an isotropic dielectric medium. Results include the development of the critical field-intensity factor, ${K}_{c}^{e}$, and the introduction of a contour-independent line integral, ${J}^{e}$, which is analogous to the J integral of linear and nonlinear elastic fracture mechanics. Some discussion of the relation between these results and recent lattice models of dielectric breakdown is given.
TL;DR: In this article, a method for predicting the stress-strain and volumetric behavior of particulate composites from constituent properties has been developed for large values of strain, which allows a simple model for systems in which damage occurs without resorting to complicated constitutive equations.
Abstract: A method for predicting the stress-strain and volumetric behavior of particulate composites from constituent properties has been developed for large values of strain. This approach allows a simple model for systems in which damage occurs without resorting to complicated constitutive equations. An energy balance derived from the first law of thermodynamics and the equations of linear elasticity calculates critical strain values at which filler particles will dewet when subjected to uniaxial tension and superimposed pressure. Calculations of critical strains over the entire strain history using reevaluated material properties accounting for the damage yield highly nonlinear stress-strain and volumetric curves. Experimentally observed dependences on particle size, filler concentration, matrix and filler properties, and superimposed pressure are correctly predicted. The method has no adjustable parameters, and allows several idealized models of the dewetting process to be examined. Comparisons of model predictions to experimental data show good agreement.
TL;DR: In this article, a plane strain model for dynamic soil-structure interaction problems under harmonic state is presented, where the boundary element method is used to study the response of a homogeneous isotropic linear elastic soil.
Abstract: A plane strain model for dynamic soil-structure interaction problems under harmonic state is presented. The boundary element method is used to study the response of a homogeneous isotropic linear elastic soil. The far field displacement at the free surface is approximated by an outgoing Rayleigh wave. The finite element method is used to describe the response of the building, of the foundation and possibly of a finite part of the inhomogeneous non-linear soil. Two coupling procedures are described. The model is applied to a problem previously studied in the antiplane case. Incident P, SV and Rayleigh waves are considered. The results show an amplification and an attenuation of the structure motion with frequency when incident Rayleigh waves and P, SV body waves are respectively considered.
TL;DR: In this article, the existence and partial regularity of an inverse function were proved for nonlinear 3D elasticity problems with Claret-Necas injectivity, and it was shown that this relation is maintained under the weak convergence of minimising sequences for non-linear elasticity problem.
Abstract: This paper gives a sufficient condition for almost-everywhere injectivity for nonlinear three dimensional elasticity similar to that of Claret-Necas [8], namely.We prove that this relation is maintained under the weak convergence of minimising sequences for nonlinear elasticity problems. The existence and partial regularity of an “inverse” function are proved.
TL;DR: In this paper, the influence of material anisotropy and test specimen geometry on the data reduction scheme used to characterize the axial compressive modulus and ultimate strength is examined.
TL;DR: In this article, a study on the dynamic response of three-dimensional flexible foundations of arbitrary shape, embedded in a homogenous, isotropic and linear elastic half-space is presented.
Abstract: A study on the dynamic response of three-dimensional flexible foundations of arbitrary shape, embedded in a homogenous, isotropic and linear elastic half-space is presented. Both massive and massless foundations are considered. The soil-foundation system is subjected to externally applied forces, and/or to obliquely incident seismic waves. The numerical method employed is a combination of the frequency domain Boundary Element Method, which is used to simulate the elastic soil medium, and the Finite Element Method, on the basis of which the stiffness matrix of the foundation is obtained. The foundation and soil media are combined by enforcing compatibility and equilibrium conditions at their common interface. Both relaxed and completely bonded boundary conditions are considered. The accuracy of the proposed methodology is partially verified through comparison studies with results reported in the literature for rigid embedded foundations.
TL;DR: In this paper, the authors deal with the two-dimensional static problems of the interface crack in a periodically layered space, and the exact solutions of the considered problems are obtained within the framework of the homogenized model of the linear elasticity with microlocal parameters.
Abstract: This paper deals with the two-dimensional static problems of the interface crack in a periodically layered space. Within the framework of the homogenized model of the linear elasticity with microlocal parameters [19, 20] the exact solutions of the considered problems are obtained. The stress singularities at the crack tips are discussed in detail from the viewpoint of the fracture theory.
TL;DR: In this article, the ground-state linear elastic constants for Ni3Al and Pt3Al were derived and the anomalous (positive) temperature dependence of flow stress in Ni3A and its absence in Pt3A were discussed.
Abstract: First-principles calculations of the ground-state linear elastic constants for Ni3Al and Pt3Al are presented. It is found that, while the bulk modulus of Pt3Al (B = 292 GPa) is larger than that of Ni3Al (B = 175 GPa), a far smaller shear-anisotropy factor for Pt3Al is predicted (A = 1·3 and A = 2·9 for Pt3Al and Ni3Al respectively). The anomalous (positive) temperature dependence of flow stress in Ni3Al and its absence in Pt3Al are discussed in terms of the present results.
TL;DR: In this article, a 2D triangular solid with atoms interacting via the Johnson potential was used to investigate static and dynamic aspects of crack extension, and the results for the energy balance during dynamic crack extension were presented for various sample sizes.
TL;DR: In this article, a lattice model for the rotational stiffness of molecular crystals is presented, and it is shown that dislocations and disclinations are independent in the model.
TL;DR: In this paper, a multidomain approach is adopted to treat cracks in an infinite body, where the body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion.
Abstract: General two-dimensional linear elastic fracture problems are investigated using the boundary element method. The √r displacement and 1/√r traction behaviour near a crack tip are incorporated in special crack elements. Stress intensity factors of both modes I and II are obtained directly from crack-tip nodal values for a variety of crack problems, including straight and curved cracks in finite and infinite bodies. A multidomain approach is adopted to treat cracks in an infinite body. The body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion. Numerical results, compared with exact solution whenever possible, are accurate even with a coarse discretization.
TL;DR: In this paper, an extension of the two-dimensional weight function theory in linear elastic crack mechanics is introduced for piecewise homogeneous isotropic notched structures under antipiane strain conditions.
Abstract: An extension of the two-dimensional weight-function theory in linear elastic crack mechanics is introduced for piecewise homogeneous isotropic notched structures under antipiane strain conditions. Using the concepts of fundamental fields and elastic reciprocity, we show that the notch-interface stress-intensity factor for a notch with the tip situated at the material interface can be computed for any antiplane strain loading through the notch-interface weight function by quadrature. Closed-form notch-interface weight functions are given for some simple geometries.
TL;DR: In this article, the dynamic equations of motion for one-dimensional wave propagation in a fluid-saturated linear elastic isotropic soil are solved using Laplace transformation followed by numerical inversion and the results compared with a direct finite element formulation.
Abstract: Biot's dynamic equations of motion for one-dimensional wave propagation in a fluid-saturated linear elastic isotropic soil are solved using Laplace transformation followed by numerical inversion and the results compared with a direct finite element formulation. A soil column of finite dimension subjected to velocity boundary conditions is analysed, allowing for reflection of waves from boundaries. Comparison of time histories at given points along the column shows that the finite element solution gives good agreement with the Laplace transform solution for low as well as high drag.
TL;DR: In this article, the authors developed a variational formulation and a procedure for the computational solution for the shape optimal design of a two-dimensional linear elastic body, subject to an isoperimetric constraint on the area.
Abstract: This study is concerned with the development of a variational formulation and a procedure for the computational solution for the shape optimal design of a two-dimensional linear elastic body. The objective is to minimize the maximum value of the Von Mises equivalent stress in the body, subject to an isoperimetric constraint on the area. The optimality conditions for this problem are derived using a mixed variational formulation, where the equations defining the elastostatics problem are dealt with as additional constraints for the optimization. The results of the analysis are implemented via a finite element discretization. The discretized model is tested in two numerical examples, the shape optimization of a hole in a biaxially loaded sheet, and of the design of a fillet.