Modal analysis of laminates by a mixed assumed-strain finite element model

Abstract

Fibre-reinforced plates and shells are finding an increasing interest in engineering applications; in most cases dynamic phenomena need to be taken into account. Consequently, effective and robust computational tools are sought in order to provide reliable results for the analysis of such structural models. In this paper the mixed assumed-strain laminated plate element, previously used for static analyses, has been extended to the dynamic realm. This model is derived within the framework of the so-called First-order Shear Deformation Theory (FSDT). What is peculiar in this assumed-strain finite element is that in-plane strain components are modeled directly; the corresponding stress components are deduced via constitutive law. By enforcing the equilibrium equations for each lamina, and taking continuity requirements into account, the out-of-plane shear stresses are computed and, finally, constitutive law provides the corresponding strains. The resulting global strain field depends only on a fixed number of parameters, regardless of the total number of layers. Since the proposed element is not locking-prone, even in the thin plate limit, and provides an accurate description of inter-laminar stresses, an extension to the dynamic range seems to be particularly attractive. The same kinematic assumptions will lead to the formulation of a consistent mass matrix. The element, developed in this way, has been extensively tested for several symmetric lamination sequences; comparison with available analytical solutions and with numerical results obtained by refined 3-D models are also presented.