A boundary integral method applied to plates of arbitrary plan form

Abstract An integral equation method for the solution of thin elastic plates of arbitrary plan form has been presented. The method involves embedding the real plate in a fictitious plate for which the Green's function is known. An unknown load vector is then introduced on the boundary of the real plate (line load and line normal moment). The deflection field due to both known transverse and unknown boundary loads can then be found everywhere by superposition. Satisfaction of the boundary conditions on the real plate results in a vector integral equation in the unknown boundary vector. In concept, any consistent set of boundary conditions will yield a solution. Practically, boundary conditions requiring higher derivatives of the deflection are both very cumbersome and yield singularities in the integral equations which cause numerical difficulties. For these reasons only clamped boundary conditions are treated numerically in the present paper. For interior bending moments and deflections (greater than distances of the order of one boundary subdivision from the boundary) the method is both highly accurate and inexpensive. Errors right on the boundary, e.g. the clamping moment in the clamped boundary condition case, can be appreciable, however. While this can be improved by a more sophisticated treatment of the unknown boundary vector in the numerical solution (increased expense) it is shown in the paper that a simple boundary extrapolation procedure gives excellent accuracy there.