Problems with Some Common Plate Bending Elements and the Development of a Pseudo-higher Order Plate Bending Element

摘要

Anomalous results from a number of raft foundation and pile cap designs in Hong Kong employing the finite element analytical method have revealed the shortcomings of some popular plate elements. For simple cases with these problematic plate elements, this paper proposes to use simple interpolation functions to overcome the abnormalities. For more general cases, an improved pseudo-higher order rectangular plate element has been developed in this paper. The element possesses nine number of nodes which include the four corner nodes, four mid-side nodes and one centre node in the formulation of its shape functions. Such high order polynomials can simulate the structural behaviour much better than the classical plate element for both thin and thick plate configurations. In the formulation, the four mid-side nodes and the centre node are turned 'pseudo' by having their displacements incorporated into that of the four corner nodes. Such static condensation can reduce the required computer capacities as well as provide greater convenience for simulation of the structure and the boundary conditions. Comparisons with the former eight node plate element by the authors and the analytical solution by series have shown that this nine node element can perform well even when the mesh is coarse. The merits of the proposed nine node element over other popular plate elements are further illustrated by cross-comparison on a simple cantilever slab problem.