Showing papers by "Vladimir Sladek published in 1992"

Non‐singular boundary integral representation of stresses

Abstract: This paper presents the derivation of the non-singular integral representation of stresses in two- and three-dimensional elastostatics. In contrast to the strongly singular and weakly singular integral representations, the numerical computation of the nearly singular integrals is eliminated because all the integrands are made finite in this new formulation even if the internal point approaches the boundary. Thus the method gives accurate numerical results even in that portion of a solid which is very close to a discretized boundary. Three test problems are analysed in which we present a comparison of the accuracies achieved by the numerical computations based on the use of strongly singular, weakly singular and non-singular integral representations of stresses.

Non‐singular boundary integral representation of potential field gradients

Abstract: In this paper we derive the non-singular boundary integral representation of the field gradients for two-dimensional problems of classical potential field theory. Numerical implementation of this representation is developed too. The proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary. Since the integrands in this new method are finite at any internal point, accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary. Two test problems are analysed in which the numerical results computed by strongly singular, weakly singular and non-singular integral representations are compared mutually and with exact solutions.