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Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics

  • V. V. Zozulya
Chapter

Abstract

Let consider a homogeneous, linearly elastic body, which in three-dimensional (3-D) Euclidean space ℝ3 occupies volume V with smooth boundary ∂V The region V is an open bounded subset of the 3-D Euclidean space ℝ3 with a C0,1 Lipschitzian regular boundary ∂V The boundary contains two parts \(\partial V_u\) and \(\partial V_p\) such that \(\partial V_u \cap \partial V_p = \emptyset \mbox{and} \partial V_u \cup \partial V_p = \partial V\) On the part \(\partial V_u\) are prescribed displacements u i (x) of the body points and on the part \(\partial V_p\) are prescribed tractions p i (x), respectively. The body may be affected by volume forces b i (x). We assume that displacements of the body points and their gradients are small, so its stress-strain state is described by the small strain deformation tensor ε ij (x) Then differential equations of equilibrium in the form of displacements may be presented in the form
$$A_{ij} u_j + b_i = 0, \quad A_{ij} = \mu\delta_{ij}\partial_k \partial_k + (\Lambda + \mu) \partial_i \partial_j \quad \forall{\rm x} \in V,$$
where λ and μ are Lamé constants,μ > 0 and λ > –μ, and δ ij is the Kronecker symbol.

Keywords

Brittle Balas Betti 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Centro de Investigación Cientifica de Yucatán A.C.MéridaMexico

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