Unified formulation for finite element thermoelastic analysis of multilayered anisotropic composite plates

This article presents various finite plate elements for the thermal stress analysis of multi-layered anisotropic structures. Assumptions are made for the displacement fields in thickness direction and the principle of virtual displacements (PVD) is employed to derive finite element (FE) matrices. The unified formulation is employed so that these FE matrices have been derived in terms of a few fundamental nuclei whose form is not affected by number of the nodes of the elements or order of the expansion for the displacements-variable description (layer-wise (LW) and equivalent single layer (ESL) cases are both addressed). The Murakami zig-zag function is used to introduce zig-zag effects in the framework of ESL descriptions. The performances of the derived finite elements, in terms of displacement and stress fields, are shown by solving thermal stress problems related to cross-ply laminated plates for various thickness ratio values. Comparison to closed form solutions as well as to available 3-D exact analyses have shown the effectiveness of the proposed elements and their capability to trace quasi 3-D descriptions of thermal stresses in layered plates.