A boundary element method for plate bending problems

An indirect boundary element formulation is constructed by using a fundamental solution of the biharmonic operator. It is shown that the fundamental solution and its derivatives can be represented by four functions with two integers. The new representation is not only a simpler representation but also reveals a structure that is exploited in the development of an algorithm based on the analytical integration of line and area integrals. The analytical integral values are used to establish continuity requirements on the unknown fictitious densities. Numerical examples consider the consequences of satisfying and violating the continuity requirements by the unknown fictitious densities. It is also shown that if the fictitious density distributions do not satisfy certain conditions then (he solution can be affected by the choice of the non-dimensionalizing variables. Numerical examples with a variety of boundary conditions demonstrate the effectiveness and limitations of the proposed algorithm. © 1991