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This paper treats a united-form solution for a point force applied at the interior of an infinite transversely isotropic solid. Several heuristic functions are adopted to obtain the expressions of the solution based on the general solution. To exclude some indeterminate attributes, the expressions are rewritten. In the final expressions, unlike previous publications where the solutions are expressed in different forms, or when some individual constants have different definitions depending on the conditions satisfied by the elastic constants, we provide united solutions which are suitable for all stable transversely isotropic materials and isotropic materials. Thus accurate numerical evaluation of the boundary element method can be performed directly without the need to resolve the singularity algebraically. Some numerical examples with BEM are also presented in this paper. © 1997 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well. [ABSTRACT FROM AUTHOR]