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2019•Unpublished venueRequires access

Study of Boundary Element Method for Lamb Wave Propagation and Defect Interaction Problems

Xianhui Wang, Yujian Liu, Jiangong Yu, Hui Min Qiao

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Abstract

The governing equation of Lamb wave propagation and defect interaction is the wave equation in elastodynamics. The boundary element method (BEM) is suitable choice to solve scattering problems in infinite domain. Based on the Contour integral theorem, analytical expressions of singular integral were obtained in in finite part. In this paper, analytical integration of strongly singular boundary integrals equations with constant element for 2D elastodynamics BEM with constant elements. All the singular and strongly integrals can be analytical evaluation in finite part sense when the constant elements are applied to discretize the boundary. The contour integral is used to solve the singular and strongly integrals. The validity of the presented formulas has been demonstrated by the numerical examples.

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What this paper is about

The governing equation of Lamb wave propagation and defect interaction is the wave equation in elastodynamics. The boundary element method (BEM) is suitable choice to solve scattering problems in infinite domain. Based on the Contour integral theorem, analytical expressions of singular integral were obtained in in finite part. In this paper, analytical integration of strongly singular boundary integrals equations with constant element for 2D elastodynamics BEM with constant elements. All the singular and strongly integrals can be analytical evaluation in finite part sense when the constant elements are applied to discretize the boundary. The contour integral is used to solve the singular and strongly integrals. The validity of the presented formulas has been demonstrated by the numerical examples.

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Available abstract

The governing equation of Lamb wave propagation and defect interaction is the wave equation in elastodynamics. The boundary element method (BEM) is suitable choice to solve scattering problems in infinite domain. Based on the Contour integral theorem, analytical expressions of singular integral were obtained in in finite part. In this paper, analytical integration of strongly singular boundary integrals equations with constant element for 2D elastodynamics BEM with constant elements. All the singular and strongly integrals can be analytical evaluation in finite part sense when the constant elements are applied to discretize the boundary. The contour integral is used to solve the singular and strongly integrals. The validity of the presented formulas has been demonstrated by the numerical examples.

Key concepts: Boundary element method, Mathematical analysis, Discretization, Singular integral, Boundary knot method, Mathematics, Boundary (topology), Method of fundamental solutions

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