An improved rectangular element for plate bending analysis

Abstract This paper presents a new, simple, rectangular finite element with twelve degrees of freedom for the bending analysis of thin plates. Three interpolation functions corresponding to the normal deflections and tangential slopes at the nodal points are written in parametric form. Convergence requirements are then used to find relationships among the parameters included in these functions. To identify the optimal values of the still undetermined parameters extensive comparisons are carried out using plate problems with different loading and boundary conditions. Certain values of the unknown parameters are found to produce displacement results with faster rate of convergence than those of other simple elements. When comparisons are based on a measure representing the actual computational effort rather than the mesh size the proposed element is found to excell higher-order elements as well. Stress results are also calculated for the proposed element and found to be fairly close to the exact values.