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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 article, the authors provide a formulation and proof of a version of Saint-Venant's principle appropriate to the plane strain and generalized plane stress solutions of the equations of the linear theory of elastic equilibrium.
Abstract: This paper presents results which provide a formulation and proof of a version of Saint-Venant's principle appropriate to the plane strain and generalized plane stress solutions of the equations of the linear theory of elastic equilibrium.
184 citations
TL;DR: In this paper, a least-squares functional for the generalized Stokes equations was developed by adding a pressure term in the continuity equation, which yields optimal discretization error estimates for finite element spaces in an H1 product norm appropriately weighted by the Reynolds number.
Abstract: Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H1 product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are naturally uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity, where we obtain the more substantive result that the estimates are uniform in the Poisson ratio.
183 citations
TL;DR: In this article, a generalized continuum representation of two-dimensional periodic cellular solids is obtained by treating these materials as micropolar continua, and the effects of shear deformation of the cell walls on the elastic constants are also discussed.
183 citations
TL;DR: In this paper, the authors describe the plane strain problem of a hydraulic fracture propagating in a permeable, linear elastic medium, and obtain the semi-analytic asymptotic solutions corresponding to small and large time, and compare them with the numerical solution.
181 citations
TL;DR: In this paper, the influence of surface tension and residual stress in the bulk induced by the surface tension on the elastic properties of nano structures was investigated. But the residual stress was neglected in the existing literatures.
181 citations