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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 Laplace and linear elasticity operators in two-and three-dimensional nonsmooth domains were investigated and the results for the singular exponents in the asymptotic expansion were derived.
Abstract: This paper is devoted to some transmission problems for the Laplace and linear elasticity operators in two- and three-dimensional nonsmooth domains. We investigate the behaviour of harmonic and linear elastic fields near geometrical singularities, especially near corner points or edges where the interface intersects with the boundaries. We give a short overview about the known results for 2-D problems and add new results for 3-D problems. Numerical results for the calculation of the singular exponents in the asymptotic expansion are presented for both two- and three-dimensional problems. Some spectral properties of the corresponding parameter depending operator bundles are also given. Furthermore, we derive boundary integral equations for the solution of the transmission problems, which lead finally to "local" pseudo-differential operator equations with corresponding Steklov–Poincare operators on the interface. We discuss their solvability and uniqueness. The above regularity results are used in order to characterize the regularity of the solutions of these integral equations.
60 citations
TL;DR: The method described here is a useful alternative to time-temperature superposition requiring a limited number of adjustable parameters, and Tschoegl's formulation affords a better description of this material than Friedrich's approach.
60 citations
TL;DR: In this article, exact solutions within the framework of linear elasticity theory were developed and compared to the respective solutions governed by CPT, and numerical data calculated based on simple harmonic load distributions have indicated rather wide discrepancy between the two solutions for laminates having low span to depth ratios.
Abstract: In a series of three papers [1,2,3], the range of applicability of classical laminated plate theory (CPT) in describing the response of composite laminates under static bending has been examined. Briefly, exact solutions within the framework of linear elasticity theory were developed and compared to the respective solutions governed by CPT [4,5,6]. Numerical data calculated based on simple harmonic load distributions have indicated rather wide discrepancy between the two solutions for laminates having low span-to-depth ratios. At high aspect ratios however, the CPT solution is in good agreement with the elasticity solution.
60 citations
TL;DR: In this paper, the authors considered linear and nonlinear infinitesimal elasticity with mixed boundary conditions and proved W 1, p regularity for the displacements and L p norm for the stresses for some p > 2.
60 citations
TL;DR: In this paper, the authors applied the dual boundary element method and the path independent integral for the evaluation of dynamic stress intensity factors of stationary cracks in a linear elastic material and compared the results with solutions obtained by using other methods.
Abstract: The application of the dual boundary element method and the path independentĴ-integral for the evaluation of dynamic stress intensity factors of stationary cracks in a linear elastic material is presented. The distinct set of boundary equations of elastodynamics is obtained by using the dual boundary element method and the dual reciprocity approach. Numerical implementation of the path-independentĴ-integral and the decomposition technique is presented. The method is applied for several cracked structures and the results are compared with solutions obtained by using other methods.
60 citations