Multiple pole residue approach for 3D BEM analysis of mathematical degenerate and non‐degenerate materials

In this paper we develop an alternative boundary element method (BEM) formulation for the analysis of anisotropic three‐dimensional (3D) elastic solids. Our implementation is based on the derivation of explicit expressions for the fundamental solution displacements and tractions, of general validity for any class of anisotropic materials, by means of Stroh formalism and Cauchy's residue theory. The resulting fundamental solution remains valid for mathematical degenerate cases when Stroh's eigenvalues are coincident, meanwhile it does not exhibit numerical instabilities for quasi‐degenerate cases when Stroh's eigenvalues are nearly equal. A multiple pole residue approach is followed, leading to general explicit expressions to evaluate the traction fundamental solution for poles of m‐multiplicity. Despite the existence of general displacement solutions in the literature, and for the sake of completeness, the same approach as for the traction solution is considered to derive the displacement fundamental solution as well. Based on these solutions, an explicit BEM approach for the numerical solution of 3D linear elastic problems for solids with general anisotropic behavior is presented. The analysis of cracked anisotropic solids is also considered. Details on the numerical implementation and its validation for degenerate cases are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of gravity field and moving internal heat source on a 2-D problem of thermoelastic fiber-reinforced medium: Comparison of different theories

A new fiber-reinforced model has been constructed by taking into account the deformation of a generalized thermoelastic medium with internal heat source. A general model of the equations of the formulation in the context of the Lord–Shulman theory that includes one relaxation time and Green–Lindsay theory with two relaxation times, as well as the classical dynamical coupled theory, is applied to study the influence of gravity and reinforcement on the total deformation of a thermoelastic medium. The normal mode analysis is used to obtain the exact expressions for the physical quantities. The variations of the considered variables with the horizontal distance are illustrated graphically. Comparisons are made with the results in the three theories in the presence and absence of reinforcement, gravity, and moving internal heat source.     

Three-dimensional Green’s functions for a steady point heat source in a functionally graded half-space and some related problems

Three-dimensional Green’s functions are derived for a steady point heat source in a functionally graded half-space where the thermal conductivity varies exponentially along an arbitrary direction. We first introduce an auxiliary function which satisfies an inhomogeneous Helmholtz equation. Then by virtue of the image method which was first proposed by Sommerfeld for the homogeneous half-space Green’s function of a steady point heat source, we arrive at an explicit expression for this function. Finally with this auxiliary function, we derive the three-dimensional Green’s functions due to a steady point heat source in a functionally graded half-space. Also investigated in this paper are the temperature field induced by a point heat source moving at a constant speed in a functionally graded full-space; the electric potential due to a static point electric charge in a dielectric full-space with electric field gradient effects; and the two-dimensional time-harmonic dynamic Green’s function for homogeneous and functionally graded materials with strain gradient effects.