Laplace domain BEM for anisotropic transient elastodynamics. (October 2022)

• Record Type: Journal Article
• Authors: Markov, Ivan; Igumnov, Leonid; Belov, Aleksandr; Eremeyev, Victor
• Other Names: Bersani Alberto Maria guest-editor.; Cazzani Antonio M guest-editor.; Eremeyev Victor guest-editor.; Giorgio Ivan guest-editor.; Spagnuolo Mario guest-editor.
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 10(2022)
• Page Start: 2034
• Page End: 2045
• Publication Date: 2022-10
• Subjects: Anisotropic elasticity -- boundary element method -- dynamic analysis -- Laplace transform -- Durbin's method; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865221078202
• Languages: English
• ISSNs: 1081-2865

Abstract

In this paper, we describe Laplace domain boundary element method (BEM) for transient dynamic problems of three-dimensional finite homogeneous anisotropic linearly elastic solids. The employed boundary integral equations for displacements are regularized using the static traction fundamental solution. Modified integral expressions for the dynamic parts of anisotropic fundamental solutions and their first derivatives are obtained. Boundary elements with mixed approximation of geometry and field variables with the standard nodal collocation procedure are used for spatial discretization. In order to obtain time-domain solutions, the classic Durbin's method is applied for numerical inversion of Laplace transform. Problem of alleviating Gibbs oscillations is addressed. Dynamic boundary element analysis of the model problem involving trigonal material is performed to test presented formulation. Obtained results are compared with finite element solutions.