Peculiar Convergence and Accuracy for Laminated Moderately Thick Plates of Arbitrary Shape in Free Vibrations

As it is well known, engineering theories for plates and shells simplify the three-dimensional (3D) elasticity problem by introducing kinematic hypothesis which lead to simpler mathematical problems. Therefore, such simplified theories have limitations, which are strictly related to the initial hypotheses. The present work is based on the so-called Reissner-Mindlin theory or First-order Shear Deformation, which is used to study “moderately thick” plates. The term “moderately thick” refers to the fact that the plate is not “thin” as in the Classical Laminated Plate Theory (CLPT) or Kirchhoff-Love Theory and not “thick” as in the classical 3D theory of elasticity. Once the physical problem is mathematically well-posed, it is generally solved via numerical methods due to the complexity of finding analytical or semi-analytical solutions. The present work aims to show a peculiar behavior in the solution of such problems by comparing the results obtained using strong and weak form finite element methods when the plates are in free vibrations. In particular, the authors compare the results obtained with two- and three-dimensional theories as a function of the plate thickness.