Linear elasticity

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

The simulation of dynamic crack propagation using the cohesive segments method

Abstract: The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.

Free vibration analysis of functionally graded panels and shells of revolution

Abstract: The aim of this paper is to study the dynamic behaviour of functionally graded parabolic and circular panels and shells of revolution. The First-order Shear Deformation Theory (FSDT) is used to study these moderately thick structural elements. The treatment is developed within the theory of linear elasticity, when the materials are assumed to be isotropic and inhomogeneous through the thickness direction. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. Two different power-law distributions are considered for the ceramic volume fraction. For the first power-law distribution, the bottom surface of the structure is ceramic rich, whereas the top surface is metal rich and on the contrary for the second one.

Micromechanical analysis of quasi-brittle materials using fracture-based interface elements

Abstract: A microstructural model for the mechanical behaviour of quasi-brittle materials is developed and verified for concrete and bone specimens. The model is based on interface elements equipped with a constitutive law representing non-linear fracture, while continuum elements remain linear elastic. The interface constitutive model is implemented with a sub-stepping scheme. Non-linear geometric effects due to large displacements are included in the model by means of an incremental Lagrangian formulation, although strains in the continuum and relative displacements in the interfaces are assumed to remain small. An arc-length procedure is used to ensure convergence during the highly non-linear behaviour in the post-peak regime. Concrete and bone specimens are idealized as two-phase particle composites and are discretized into finite elements, including interface elements along the main potential crack paths. The numerical results in tension and compression are described and compared with experimental observations. The need of considering non-linear geometric effects in this type of calculations is also discussed. Copyright © 2001 John Wiley & Sons, Ltd.

Nonlinear theory for plates and shells including the effects of transverse shearing

Abstract: Nonlinear strain displacement relations for three-dimensional elasticity are determined in orthogonal curvilinear coordinates. To develop a two-dimensiona l theory, the displacements are expressed by trigonometric series representation through the thickness. The nonlinear strain-displacement relations are expanded into a series that contains all first- and second-degree terms. In the series for the displacements only the first few terms are retained. Insertion of the expansions into the three-dimensional virtual work expression leads to nonlinear equations of equilibrium for laminated and thick plates and shells that include the effects of transverse shearing. Equations of equilibrium and buckling equations are derived for flat plates and cylindrical shells. The shell equations reduce to conventional transverse shearing shell equations when the effects of the trigonometric terms are omitted and to classical shell equations when the trigonometric terms are omitted and the shell is assumed to be thin. Numerical results are presented for the buckling of a thick simply supported flat rectangular plate in longitudinal compression.

Elasticity: Theory and Applications

Abstract: Mathematical Preliminaries Stress Deformation and Strain Elasticity and its Limits Formulation and ''Exact'' Solutions of some Linear Elasticity Problems Structural Mechanics Energy Principles Numerical Methods The Initially Stressed Solid-Elastic Instability References Index