The Dual Reciprocity Method For Solving Biharmonic Problems

The dual reciprocity method is now established as a suitable approach to the boundary element method solution of non-homogeneous field problems. The Poisson problem was probably the first such problem to be solved using dual reciprocity and has been the subject of much interest. By introducing a secondary dependent variable biharmonic problems may be written as a pair of coupled Poisson-type problems and as such are amenable to a dual reciprocity approach. The procedure is straightforward but some care is required when applying boundary conditions. If the boundary conditions can be expressed explicitly in terms of the primary variable and the secondary variable then the equations uncouple. If however, the boundary conditions are expressed in terms of the primary variable only then a fully coupled system must be solved. The process is well-suited to the analysis of the bending of a flatplate. Simply-supported and clamped boundary conditions correspond respectively to the two cases.