Special Methods for Plate Analysis

Abstract

Special boundary element methods for the solution of plate bending problems are presented in this chapter. Some of these methods have been developed during the first efforts to apply the boundary integral equation method to the plate bending problem and before the appearance of general direct BEM formulations in the literature. Other special BEM’s have been developed later in order to overcome certain shortcomings and computational difficulties in the general direct BEM formulations or in order to solve problems for which the fundamental solution can not be established or is difficult to treat numerically. On the basis of common characteristics the special methods are classified in five groups: (a) Methods based on the biharmonic analysis, (b) Indirect boundary element methods (IBEM’s) (c) Boundary differential — integral equation methods (BDIEM’s) (d) Green’s function methods (GFM’s), (e) Other methods which lack common characteristics. For each group of special methods a separate section is devoted. The special methods are described by the most representative methods of each group. The description of each special method is supplemented by several numerical results which are compared with those obtained by analytical or other numerical methods in order to illustrate the versatility, the effectiveness and the accuracy of the special BEM’s. Concluding remarks are presented in the last section.