Exact boundary integral transformation of the thermoelastic domain integral in BEM for general 2D anisotropic elasticity

Abstract

In the direct formulation of the boundary element method, body-force and thermal loads manifest themselves as additional volume integral terms in the boundary integral equation. The exact transformation of the volume integral associated with body-force loading into surface ones for two-dimensional elastostatics in general anisotropy, has only very recently been achieved. This paper extends the work to treat two-dimensional thermoelastic problems which, unlike in isotropic elasticity, pose additional complications in the formulation. The success of the exact volume-to-surface integral transformation and its implementation is illustrated with three examples. The present study restores the application of BEM to two-dimensional anisotropic elastostatics as a truly boundary solution technique even when thermal effects are involved.

Radial integration BEM for dynamic coupled thermoelastic analysis under thermal shock loading

“…Concerning the BEM solution to uncoupled problems, we can also refer to the works by Sladek and Sladek [12], Shiah and Tan [13], Park and Banerjee [14], and Gao [15]. The BEM has been successfully applied also to coupled thermoelasticity problems by Suh and Tosaka [16], Dargush [18], Chen and Dargush [19], Hosseini-Tehrani and Eslami [20].…”

Multiple reciprocity boundary element analysis of two-dimensional anisotropic thermoelasticity involving an internal arbitrary non-uniform volume heat source

“…This is not within the scope of the present study. By applying the principal of MRM, the process to successively convert the volume integral associated with the thermal loading follows the same vein as the procedures described in the work by Shiah and Tan (1999a). This scheme has been successfully implemented into BEM codes based on the quadratic isoparametric element formulation used in 2D anisotropic thermoelasticity.…”

“…This is because, unlike the potential function for bodyforce, the distribution of a temperature change in an anisotropic body, in the general case, does not satisfy the standard PoissonÕs equation. The difficulties arising from this were not overcome until very recently when Shiah and Tan (1999a) transformed the ''volume integral'', in the analytically exact sense, into a series of boundary ones. By removing the singularity at the source point for interior stress calculations, Shiah and Tan (1999b) also derived the SomiglianaÕs identity of the interior strain for 2D anisotropic thermoelasticity.…”

A boundary element method for analysis of thermoelastic deformations in materials with temperature dependent properties

“…Galerkin's tensor, or other thermoelastic potential functions, are related to particular solutions of the partial differential equation whose differential operator corresponds to the determinant of the original differential operator matrix. Such particular solutions can be (relatively) easily obtained for materials with constant isotropic and anisotropic properties [3]. In the latter the technique is limited to the plane problems as it fails for general three-dimensional cases.…”