# Regularization of Divergent Integrals in Boundary Integral Equations for Elastostatics

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## Abstract

Let consider a homogeneous, linearly elastic body, which in three-dimensional (3-D) Euclidean space ℝ
where λ and μ are Lamé constants,μ > 0 and λ > –μ, and δ

^{3}occupies volume*V*with smooth boundary ∂*V*The region*V*is an open bounded subset of the 3-D Euclidean space ℝ^{3}with a C^{0,1}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$$A_{ij} u_j + b_i = 0, \quad A_{ij} = \mu\delta_{ij}\partial_k \partial_k + (\Lambda + \mu) \partial_i \partial_j \quad \forall{\rm x} \in V,$$

_{ 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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