Nonlinear transient heat conduction problems for a class of inhomogeneous anisotropic materials by BEM

A dual-reciprocity boundary element approach for axisymmetric nonlinear time-dependent heat conduction in a nonhomogeneous solid

“…Earlier works on boundary element methods, such as Kikuta et al [12] and Goto and Suzuki [9], assume that the solids are thermally isotropic and have density, specific heat capacity and thermal conductivity which are functions of temperature alone. Clements and Budhi [8], Azis and Clements [5] and, more recently, Ang and Clements [2] have proposed boundary element procedures for thermally anisotropic solids with material properties that vary with temperature and spatial coordinates.…”

“…The works in [2,5] are also applicable to linear heat conduction in nonhomogeneous media such as functionally graded materials. The analysis of functionally graded materials is a topic of special interest in boundary element methods.…”

“…Such a problem is of practical interest as axisymmetric structures can be found in many engineering applications (such as pressure vessels and piping components). The analyses in Ang and Clements [2], Azis and Clements [5] and Brebbia et al [6] are used as a guide to convert the nonlinear partial differential equation governing the axisymmetric heat conduction into a suitable integro-differential equation. In addition to a boundary integral over a curve on an appropriate coordinate plane, the integrodifferential equation also contains a domain integral.…”

Nonlinear heat equation for nonhomogeneous anisotropic materials: A dual‐reciprocity boundary element solution

“…In earlier works on boundary element techniques for solving the nonlinear heat conduction problem, such as Kikuta et al [6] and Goto and Suzuki [7], the solids are assumed to be thermally isotropic with material properties (density, specific heat capacity and thermal conductivity) which are functions of temperature alone. Extensions to thermally anisotropic solids with material properties that vary with temperature and spatial coordinates are given by Clements and Budhi [8] and Azis and Clements [9].…”

A boundary element method with analytical integration for deformation of inhomogeneous elastic materials

“…The use of BEM has also been applied to homogeneous as well as to inhomogeneous materials, and not only to isotropic but also to anisotropic materials. For example, [1] used the BEM for solving infiltration problems of isotropic homogeneous media, [2] derived a fundamental solution, [3] considered diffusionconvection problems for anisotropic homogeneous materials, [4] solved elasticity problems for isotropic inhomogeneous materials and [5] studied elasticity problems, [6] worked on elliptic boundary value problems, [7] solved heat conduction problems, [8] worked on elasticity problems and [9] considered transient heat conduction problems for anisotropic inhomogeneous materials.…”