Approximation of anisotropic multilayered plates through RMVT and MITC elements

Abstract

This paper presents a mixed two dimensional model for the analysis of mechanical response in anisotropic multilayered plates, with particular attention to the behavior along the thickness of the plate. It is well known that the study of anisotropic material structures requires to take into account cross-elasticity effects that make the solution converge very slowly. The finite element method showed successful performances to approximate the solutions of these structures. In this regard, two variational formulations are available to calculate the stiffness matrix, the Principle of Virtual Displacement (PVD) and the Reissner Mixed Variational Theorem (RMVT). Here, a strategy similar to MITC (Mixed Interpolated of Tensorial Components) approach, in the RMVT formulation, is adopted to formulate advanced locking-free finite elements. Then, assuming the transverse stresses as independent variables, the continuity at the interfaces between layers is easily imposed. The displacement field is defined according to the Reissner–Mindlin theory and the shear stresses are assumed parabolic along the thickness by means of RMVT. The normal strain ∊zz and the normal stress σzz are discarded. The shear stresses σxz and σyz are interpolated in each element according to the MITC. By comparing the results with benchmark solutions from literature, it is shown that the element exhibits both properties of convergence and robustness and provides very accurate results in terms of transverse shear stresses of the anisotropic multilayered plate.