Analysis of skew and triangular plates in bending

Abstract

The objective of this paper is to develop fast converging series solutions for rectangular, parallelogram and triangular plate bending elements with arbitrary boundary conditions and arbitrary shapes, and subjected to generalized normal loading. Solutions to parallelogram and rectangular plates are obtained by representing the deformed shape of a structure by a sequence of functions that are complete and satisfy the natural and forced boundary conditions. These consist of a combination of trigonometric and ploynomial functions with undetermined coefficients. The undetermined coefficients are determined by using modified Galerkin technique, and satisfying the boundary conditions. After necessary simplifications, this leads to a set of summation equations in terms of the undetermined coefficients. The summation equations are solved by using special techniques or by resorting to standard elimination procedures. Solutions of triangular plates for simply supported and clamped boundary conditions are obained in a similar manner by selecting appropriate shape functions that satisfy the natural and forced boundary conditions. Study of the numerical results for the rectangular, parallelogram and triangular plates indicates that the deflection functions developed for these shapes are fast converging, and results of reasonable accuracy can be obtained by considering only the first two or three harmonics.