Quasi-3D analysis of free vibration of anisotropic plates

Abstract

The subject of the present work is multilayered finite elements that are able to furnish an accurate description of both strain and stress fields. The formulation of the finite elements is based upon Reissner’s mixed variational theorem (RMVT), which allows one to assume two independent fields for displacements and transverse stress variables. The resulting advanced finite elements can describe, a priori, the interlaminar continuous transverse shear and normal stress fields, and the so called C z 0 - requirements can be satisfied. This paper is mainly concerned about the vibrations of multilayered plates. The present FEM formulation is validated by comparing the results with both the literature and the commercial code NASTRAN. To conduct the assessment, five challenging benchmarks with different boundary conditions and lamination schemes are considered. For each benchmark, the first four non-dimensional frequencies are calculated and a few modes are presented. It can be concluded that the present quasi-3D layer-wise formulation has a very good agreement with respect to the more computationally expensive three-dimensional FEM formulations. Moreover, the displacement and transverse stresses are computed a priori without any operation of post-processing. Therefore, the present results can be used as reference numbers for testing other new FEM models.