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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, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity, which does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.
Abstract: Applying the uniform-approximation technique, consistent plate theories of different orders are derived from the basic equations of the three-dimensional linear theory of elasticity. The zeroth-order approximation allows only for rigid-body motions of the plate. The first-order approximation is identical to the classical Poisson-Kirchhoff plate theory, whereas the second-order approximation leads to a Reissner-type theory. The proposed analysis does not require any a priori assumptions regarding the distribution of either displacements or stresses in thickness direction.
83 citations
01 Jan 2000
TL;DR: In this article, the rolling contact phenomena of linear elasticity is treated, with special emphasis on the elastic half-space, and a special case of the elastic contact is considered.
Abstract: In this paper, we treat the rolling contact phenomena of linear elasticity, with special emphasis on the elastic half-space.
83 citations
TL;DR: In this article, a modification of this approach makes it possible to calculate singular fields also in the interior of the structural domain, which can be significantly enhanced by using these approximations in the extended finite element method (X-FEM).
Abstract: Strain singularities appear in many linear elasticity problems. A very fine mesh has to be used in the vicinity of the singularity in order to obtain acceptable numerical solutions with the finite element method (FEM). Special enrichment functions describing this singular behavior can be used in the extended finite element method (X-FEM) to circumvent this problem. These functions have to be known in advance, but their analytical form is unknown in many cases. Li et al. described a method to calculate singular strain fields at the tip of a notch numerically. A slight modification of this approach makes it possible to calculate singular fields also in the interior of the structural domain. We will show in numerical experiments that convergence rates can be significantly enhanced by using these approximations in the X-FEM. The convergence rates have been compared with the ones obtained by the FEM. This was done for a series of problems including a polycrystalline structure. Copyright © 2010 John Wiley & Sons, Ltd.
83 citations
TL;DR: In this article, a micromechanics-based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented.
83 citations
TL;DR: In this paper, large deflections of thin cantilever beams of non-linear materials of the Ludwick type were studied and a closed-form solution was presented for the resulting second-order nonlinear differential equation.
Abstract: This paper deals with the large deflections (finite) of thin cantilever beams of non-linear materials of the Ludwick type. The beam is subjected to an end constant moment. Large deflections of beams induce geometrical non-linearity. Therefore, in formulating the analysis, the exact expression of the curvature is used in the Euler-Bernoulli law. A closed-form solution is presented for the resulting second-order non-linear differential equation. This solution is compared to previous results assuming linear elastic materials. Deflections at the free end of beams of aluminum alloy and annealed copper are obtained.
82 citations