Development of higher-order triangular elements for better prediction of stress-resultants in plate
This paper is concerned with the development of a higher-order triangular plate finite element based on the third order shear deformation theory as well as a layerwise plate theory for bending analysis of laminated composite plates. This development is motivated by the fact that conventional lower order finite elements do not yield accurate or even correct stress resultants in plates with free edges. In fact the transverse shear forces, twisting moments and the transverse shear stresses across the thickness of a laminated plate, obtained using lower order finite elements fail to satisfy the natural (or force) boundary conditions and yield incorrect variation of stresses through the thickness. It will be shown herein that the proposed element that is constructed based on the nodal basis approach is able to handle complex problems involving stress singularities more efficiently as opposed to some widely used lower order finite elements. In this approach, we establish both the number of nodes and the degree of polynomial basis functions using the peak values of stress resultants rather than deflections as the criterion for converged bending results.