AN APPROACH TO THE INCLUSION OF TRANSVERSE SHEAR DEFORMATION IN FINITE ELEMENT ANALYSIS.

Abstract

A finite element formulation for the shear-deformable analysis of beams, plates and shells, based on a strain energy expression defined in terms of total and flexural displacement components, is presented. The effects of transverse shear deformation are considered while the normal strain is neglected. The finite element representation requires independent descriptions of total and flexural displacement components. The flexural strain energy term involves second derivatives of flexural displacement component and thereby necessitates slope-compatible shape functions. This requirement is relaxed by adopting the 'discrete Kirchhoff' hypothesis for the flexural displacement component. An element of triangular shape is formulated for the analysis of laminated composite plates and shallow shells. Numerically exact integration is employed in the calculation of element stiffness matrix and corresponding load vectors. The resulting finite element possesses twelve degrees of freedom at each corner node of the triangle. Numerical results obtained for an extensive range of thickness and planform aspect ratios, laminate configurations, mesh sizes, edge conditions, types of loading and geometry of the structure demonstrate the efficacy of the finite element formulation. The element is applicable to a full range of thicknesss ratios. The present formulation is employed for dynamic and stability analysis of beams, as a precursor to the inclusion of these effects in the analysis of plates and shells.