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Linear elasticity
About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.
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TL;DR: In this paper, the authors studied the Brazilian disk test, where the diametric compression of a circular disk by radial loads that are uniformly distributed along two symmetric arcs of its periphery is studied using the method of complex potentials.
74 citations
73 citations
TL;DR: An adaptive discontinuous Galerkin finite element method for linear elasticity problems is presented and an a posteriori error estimate is developed and its robustness with respect to nearly incompressible materials is proved.
Abstract: An adaptive discontinuous Galerkin finite element method for linear elasticity problems is presented. We develop an a posteriori error estimate and prove its robustness with respect to nearly incompressible materials (absence of volume locking). Furthermore, we present some numerical experiments which illustrate the performance of the scheme on adaptively refined meshes.
73 citations
TL;DR: In this paper, an equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented.
Abstract: An equation solver for the large unsymmetric systems of linear equations arising in the application of the boundary integral equation method to problems of linear elasticity in homogeneous or piecewise homogeneous solids is presented. The solver uses Gaussian elimination. The advantages of the solver over many existing eliminational or iterational methods are that it ignores many of the large groups of zeros that occur in piecewise homogeneous work, and also restrains growth of the number of non-zero matrix entries. Memory requirements and computation times therefore are reduced for many piecewise homogeneous problems.
73 citations
TL;DR: In this article, the impact of plate/disc bending on three-dimensional stress fields is investigated, showing that it becomes non-negligible as the thickness of the component decreases.
Abstract: Three-dimensional effects near crack tips have been deeply investigated in the past, but the topic is still ongoing and under investigation. However, the understanding is in some cases limited, and the problem requires further attention. Three-dimensional effects are in fact neglected in situations where they may play an important role. The main aim of this review paper is to summarise some recent results of a study carried out on the coupled in-plane fracture mode induced by a nominal anti-plane (mode III) loading applied to plates and discs weakened by a straight crack. Only linear elastic conditions are considered herein. The results derived by a large bulk of finite element models allow a better understanding of coupled modes generated by anti-plane loading. The influence of plate/disc bending on three-dimensional stress fields is considered in the investigation, showing that it becomes non-negligible as the thickness decreases. Some considerations on the trend of KIII as the corner point is approached are also part of this paper. In addition, the trend of the strain energy density (SED) in a volume surrounding the crack tip is shown and commented on. This parameter allows the precise determination of the weakest point of the component through the thickness becoming a useful tool. Some new results for a disc under in-plane shear loading are included. These results clarify the influence of disc bending under anti-plane loading.
73 citations