Boundary element analysis of nonprismatic beams and plates

Abstract

Boundary element solutions for the bending of non-prismatic beams and plates are presented. The boundary integral formulation is developed for the analysis of non-prismatic beams. The required fundamental solutions for non-prismatic beams of linear and parabolic profiles are derived and exact relations are obtained among the variables over the nodes (beam supports). The method is then extended for the analysis of continuous beams with varying depth. The problem of a plate with linearly varying rigidity is solved by splitting the equation governing the transverse deflection of the plate into two Piosson's equations, for which, fundamental solutions are available. Finally, the proposed formulations for both beams and plates are tested through several numerical examples.