A complex variable boundary element method for a class of boundary value problems in anisotropic thermoelasticity

Abstract

A boundary element method based on the Cauchy's integral formulae, called the complex variable boundary element method (CVBEM), is proposed for the numerical solution of boundary value problems governing plane thermoelastic deformations of anisotropic elastic bodies. The method is applicable for a wide class of problems which do not involve inertia or coupling effects and can be easily and efficiently implemented on the computer. It is applied to solve specific test problems.

Development and implementation of some BEM variants—A critical review

“…In their report, computational results of CVBEM on several different structures (i.e., circular disk, cantilever beam, simply supported square plate) under external concentrated forces or uniform loads show good agreement with the exact solution. The CVBEM was later imposed into other elasticity problem including thermoelasticity [13,141], poroelasticity [108] and viscoelasticity [109]. In spite of all those improvements mentioned above, before 21th century, the CVBEM only concentrated in the 2D problem and the lack of multi-dimensional application feature was realized and recently, the problem is solved and the upgraded CVBEM can be applied for three-dimensional analysis [103].…”

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

“…The approach adopted in the present paper is to generalize the numerical solution of Ang et al [7], where they applied the Cauchy's integral formulae to construct approximately holomorphic functions which satisfy the boundary conditions of the problem under consideration. We characterize the elastic constants C pjkr , initial stress P and the density ρ of non-homogeneous material by C pjkr = C pjkr x 2 m , P = Px 2 m and ρ = ρx 2 m…”

“…In the present paper, we have investigated the generation of the thermal stresses in a non-homogeneous anisotropic solid rotating about z-axis with a constant angular velocity under compressive initial stress, through generalization of the numerical solution of Ang et al [7] in solving displacement equation, where they proved that their boundary element solution agrees quite well with the exact solution.…”

A complex variable boundary element method for antiplane stress analysis around a crack in some nonhomogeneous bodies

“…Notice that (6) implies that µ 1/2 satisfies the two-dimensional Laplace's equation in R ∪ C. Although this places some restriction on the choice of µ, it does allow for rather general multiparameter forms like the one in (1). In some other work on cracks in nonhomogeneous bodies, investigators assume even more restrictive form on the shear modulus, e.g.…”

“…Ang and Park [8] extended the approach to a generalized system of secondorder elliptic partial differential equations. Application of the CVBEM for the numerical solution of an anisotropic thermoelastic problem was carried out by Ang, Clements and Cooke [6].…”