Thin plates by the boundary element method by means of two Poisson equations

Abstract

The problem of thin plates according to Kirchhoff's theory is formulated by means of two coupled Poisson equations, which are expressed in integral form using the second theorem of Green in the classical way. The domain integrals are evaluated approximating the integrands by a series of simple domain functions whose coefficients are calculated by a collocation procedure at points placed along the boundary and domain, which originates a certain extra number of unknowns. The approximated domain integrals are then expressed by equivalent boundary integrals, the extra unknowns requiring the use of integral equations associated to the internal points used to approximate the domain integrals. This formulation avoids the problems associated with the singular character of the fundamental solution of the biharmonic equation.