ANALYTICAL TREATMENT OF BOUNDARY INTEGRALS IN DIRECT BOUNDARY-ELEMENTANALYSIS OF PLATE-BENDING PROBLEMS

A direct-type Boundary Element Method (BEM) for the analysis of simply supported and built-in plates is employed. The integral equations due to a combined biharmonic and harmonic governing equations are first e stablished. The boundary integrals developed are then evaluated analyt ically. The domain integrals due to external body forces are also tran sformed over the boundary and subsequently evaluated analytically. Thu s, it needs only the boundary to be discretized. Without loss of gener ality, the exact expression for the integrals would enhance the soluti on accuracy of the BEM. This is due to the fact that at locations wher e the fundamental solutions approach their singular points the value d etermined by numerical quadrature may be inconsistent and inaccurate. Also, another major advantage of the exact expressions for integration s is the insensitivity to the geometrical location of the source point on the boundary. The distribution of boundary quantities is approxima ted either over linear or quadratic boundary elements. General type of plate bending problems, with plates of different geometrical shapes s upported simply or fixed can be handled. Loading may be applied point concentrated, uniformly distributed within the domain or over the boun dary. Also, hydrostatic pressure can be applied. The results obtained by BEM in comparison with those obtained by analytical or other approx imate solutions are found to be very accurate and the solution method is efficient.