New Domain Integral Transformation in Boundary Element Analysis for 2D Anisotropic Thermoelasticity

Abstract

As is well known in the boundary element method (BEM), thermal effect reveals itself as an additional volume integral in the associated boundary integral equation. Any attempt to directly integrate it shall require domain discretization that will destroy the BEM’s most distinctive notion of boundary discretization. For anisotropic elastostatics, this additional volume integral can be exactly transformed onto the boundary; however, additional line integrals intersecting the domain are invoked in such a transformation. For simply connected domains, evaluation of the extra line integrals can be avoided by simply employing branch-cut redefinitions; however, the evaluation is inevitable for multiply connected domains. This paper presents a new approach to validate the exact transformation yet without invoking extra line integrals. For the two-dimensional thermoelastic analysis of anisotropic bodies, the present approach has completely restored the BEM’s feature of boundary discretization without extra line integrals involved. In the end, a few typical examples are presented to illustrate the veracity of the formulation and its applicability to engineering practice.