Reissner’s mixed variational theorem toward MITC finite elements for multilayered plates

Abstract

In this paper, we analyze a two dimensional model of multilayered plates for which the main interest is to study the mechanical and physical properties, that may change in the thickness direction. The finite element method showed successful performances to approximate the solutions of the advanced structures. In this regard, two variational formulations are available to reach the stiffness matrices, the principle of virtual displacement (PVD) and the Reissner mixed variational theorem (RMVT). Here we introduce a strategy similar to Mixed Interpolated of Tensorial Components (MITC) approach, in the RMVT formulation, in order to construct an advanced locking-free finite element. Assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. It is known that unless the combination of finite element spaces for displacement and stresses is chosen carefully, the problem of locking is likely to occur. Following this suggestion, we propose a finite element scheme that it is known to be robust with respect to the locking phenomenon in the classical PVD approach. We show that in the RMVT context, the element exhibits both properties of convergence and robustness when comparing the numerical results with benchmark solutions from literature.