Multilayered Finite Element Formulation for Vibration and Stability Analysis of Plates

Abstract

A finite element formulation for multilayered and thick plates, based on a multilayered theory, which was previously applied to a static analysis is extended to include vibration and stability analyses. First, a mass matrix formulation is presented which is consistent with the stiffness coefficient derivation, namely a virtual work expression is obtained which is then evaluated through numerical differentiation. This is followed by a more general discussion of a geometric stiffness derivation which is seen within the concept of linear elastic stability. The geometric stiffness itself, in this context is the difference between the linear stiffness and the tangent stiffness where the tangent stiffness is evaluated, within the general nonlinear theory, usually at a unit load stress state. In both cases vibration and stability analysis, the usual generalized eigenvalue problem follows. In some applications for layered beams and plates the vibration and stability analysis presented is compared with exact solutions.