Three-dimensional thermo-mechanical solutions of cross-ply laminated plates and shells by a differential quadrature hierarchical finite element method

The thermo-elastic behaviour induced by temperature in composite structures has become a significant factor in structural design. In this paper, a three-dimensional thermo-elastic theory for composite cross-ply laminated plates was discretized by a differential quadrature hierarchical finite element method (DQHFEM). The DQHFEM is a weak-form differential quadrature method using hierarchical bases that can provide highly accurate results using only a few sampling points. Flexible and efficient wedge (triangular prism) and hexahedron elements were constructed and applied to three-dimensional (3D) analyses of cross-ply laminated plates and shells for the first time. Compared with various models in literatures, the DQHFEM showed very good agreements with exact solutions based on 3D elastic theory. The thermo-mechanical analyses of cross-ply laminated plates and shells based on 3D theory indicate that the DQHFEM is an effective method for high accuracy analyses with low computational costs, because the DQHFEM can provide results with high accuracy by using only several nodes on the thickness direction.