Plate bending by a boundary point method

Abstract

The problem of linear elastic plate bending is solved by a boundary point method. Four fundamental homogeneous solutions for each of a number of sources, which are situated outside the plate, are superimposed and combined with appropriate particular solutions. Each source point is associated with a boundary point, which may be clamped or simply supported. At each boundary point, four edge conditions are enforced which allow the scalar coefficients, introduced in the superposition process, to be determined, and, hence, the plate displacement and stress solution to be obtained. Four non-rectangular example plates are considered, under uniform and hydrostatic loading, for which no internal sub-division is required, and it is demonstrated that accurate solutions may be obtained with 10–14 boundary points.