Mixed Finite Elements for Thermoelastic Analysis of Multilayered Anisotropic Plates

Abstract

This paper presents some finite elements for the thermoelastic analysis of multilayered plates which are based on unified formulation and the Reissner mixed variational theorem (RMVT). The pure mechanical statement of the theorem is herein extended to thermoelastic analysis and the related mixed constitutive equations have been derived. Assumptions are made for the displacement fields in thickness direction and the RMVT is employed to obtain finite element (FE) matrices. The unified formulation allows to easily derive the FE matrices in terms of a few fundamental nuclei whose form is not affected by: number of the nodes of the elements; 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. Comparisons to exact 3D solutions as well as to classical finite elements have proved the accuracy of the proposed elements and thier capability to accurately describe the stress field of layered plates subjected to thermal loadings.