On a regular boundary integral equation and a modified Trefftz method in Reissner's plate theory

Abstract

If fundamental solutions are known it is convenient to formulate boundary value problems as boundary integral equations, usually locating the source points of the fundamental solutions on the deal boundary. This paper deals with Reissner's plate theory and presents ttwo solution techniques which avoid some inherent difficulties of the conventional approach, such as the need for accurate evaluation of singular integrals. If the points of source of the fundamental solutions are moved outside the domain of the problem they will never coincide with field points; this results in regular kernels and, thus, in regular integral equations. Use of the fundamental solutions as expansion functions, where the free expansion coefficients are determined by satisfying the prescribed conditions, permits integration to the avoided totally; this is a special formulation, a modification of the well-known Trefftz method. Several examples are presented to illustrate the merits and disadvantages of these two procedures.