Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Semigroups Associated with Dissipative Systems

Abstract: Preliminaries Some Definitions C0-Semigroup Generated by Dissipative Operator Exponential Stability and Analyticity The Sobolev Spaces and Elliptic Boundary Value Problems Linear Thermoelastic Systems The Setting of Problems for the One-Dimensional Thermoelastic System The Exponential Stability for the Dirichlet Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at Both Ends The Exponential Stability for the Stress-Free Boundary Conditions at One End The Thermoelastic Kirchhoff Plate Equations Linear Viscoelastic System Linear Viscoelastic System Wave Equation with Locally Distributed Damping Linear Viscoelastic System with Memory The Linear Viscoelastic Kirchoff Plate with Memory Linear Thermoviscoelastic Systems Linear One-Dimensional Thermoviscoelastic System Linear Three-Dimensional Thermoviscoelastic System with Memory Elastic Systems with Shear Damping Shear Diffusion Equations Laminated Beam with Shear Damping Linear Elastic Systems with Boundary Damping Second-Order Hyperbolic Equation Euler-Bernoulli Beam Equation Uniformly Stable Approximations Main Theorem Approximations of the Thermoelastic System Approximation of the Viscoelastic System Bibliography

Existence Theorems in Elasticity

Abstract: The subject to be developed in this article covers a very large field of existence theory for linear and nonlinear partial differential equations. Indeed, problems of static elasticity, of the propagation of waves in elastic media, and of the thermodynamics of continua require existence theorems for elliptic, hyperbolic and parabolic equations both linear and nonlinear. Even if one restricts oneself to linear elasticity, there are several kinds of partial differential equations to be considered. In static problems we encounter second order systems, either with constant or with variable coefficients (homogeneous and non-homogeneous bodies), scalar second order equations (for instance either in the St. Venant torsion problems or in the membrane theory), fourth order equations (equilibrium of thin plates), eighth order equations (equilibrium of shells). Each case must be considered with several kinds of boundary conditions, corresponding to different physical situations. On the other hand, to every problem of static elasticity corresponds a dynamical one, connected with the study of vibrations in the elastic system under consideration. Moreover, problems of thermodynamics require the study of certain diffusion problems of parabolic type. In addition to that, the study of materials with memory requires existence theorems for certain integro-differential equations, first considered by Volterra.

The role of T-stress in brittle fracture for linear elastic materials under mixed-mode loading

Abstract: The purpose of this paper is to revisit the maximum tensile stress (MTS) criterion to predict brittle fracture for mixed mode conditions. Earlier experimental results for brittle fracture of polymethylmethacrylate (PMMA) using angled cracked plates are also re-examined. The role of the T-stress in brittle fracture for linear elastic materials is emphasized. The generalized MTS criterion is described in terms of mode I and II stress intensity factors, K I and K II and the T-stress (the stress parallel to the crack), and a fracture process zone, r c . The generalized MTS criterion is then compared with the earlier experimental results for PMMA subjected to mixed mode conditions. It is shown that brittle fracture can be controlled by a combination of singular stresses (characterized by K) or non-singular stress (T-stress). The T-stress is also shown to have an influence on brittle fracture when the singular stress field is a result of mode II loading.

Classical and Computational Solid Mechanics

Abstract: Tensor analysis stress tensor analysis of strain conservation laws elastic and plastic behaviour of materials linearized theory of elasticity solutions of problems in linearized theory of elasticity by potentials two-dimensional problems in linearized theory of elasticity variational calculus, energy theorems, Saint-Venant's principle Hamilton's principle, wave propagation, applications of generalized co-ordinates elasticity and thermodynamics irreversible thermodynamics and viscoelasticity thermoelasticity viscoelasticity large deformation incremental approach to solving some nonlinear problems finite element methods mixed and hybrid formulations finite element methods for plates and shells finite element modelling of nonlinear elasticity, viscoelasticity, plasticity, viscoplasticity and creep.