A higher order shear deformable finite element for homogeneous plates

A C0 finite element is introduced for the analysis of thick plates with transverse shear and normal strain and nonlinear in-plane displacement distribution with respect to the plate thickness. The warping theory proposed by Hassis [1] is used for the equations governing the plate deformation. The analytical solutions of the plate deformation theory were compared with other higher-order theories and found to be predicting the thick plate behavior reasonably well. Based on this higher order shear deformation theory, an eight-node finite element is introduced for thick plates, and a computer program is developed. The warping functions used in the formulations presented simpler equations than the other higher order homogeneous models. The proposed element incorporates bending–stretching coupling via the additional terms introduced in the displacement field. Some example problems are solved and the results are compared with the exact and other mathematical solutions available in the literature. For comparison, both stress and displacement results are investigated. The results of the proposed element are found to be in good agreement with the literature.