Computation of stress resultants in plate bending problems using higher-order triangular elements

This paper is concerned with the development of a higher-order triangular plate element based on the first-order shear deformation plate theory. The present study brings out the shortcomings of conventional lower-order finite element interpolation when applied for the bending analysis of plates with free edges. The stress resultants, especially the transverse shear forces and twisting moments, obtained using the lower-order displacement finite elements fail to satisfy the natural (or force) boundary conditions accurately. On the other hand, the plate element with higher-order interpolation of the field variables enables the accurate prediction of stress resultants for plates. The superior performance of the higher-order plate bending element is demonstrated through bending analyses of plates of various shapes and free edges and examining the distribution of the stress resultants and the satisfaction of the natural boundary conditions.