Fibre reinforced plates and shells are funding 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 laminate hybrid assumed-strain plate element presented in [1], and used there in a static analysis, has been extended to the dynamic realm. This model is derived within the framework of the so called First-order Shear Deformation Theory (FSDT) [2], [3]. What is peculiar in this assumed strain finite element is the direct modelling of the in-plane strain components; the corresponding stress components are deduced via constitutive law. By enforcing the equilibrium equations for each lamina, account taken of continuity requirements, the out-of-plane shear stresses are computed and, finally, constitutive law provides the corresponding strains. The resulting global strain field depends 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 lamination sequences and comparison with analytical solutions are presented.
Modal analysis of laminated composite plates by a new hybrid assumed strain finite element
STOCHINO, FLAVIO;CAZZANI, ANTONIO MARIA
2013-01-01
Abstract
Fibre reinforced plates and shells are funding 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 laminate hybrid assumed-strain plate element presented in [1], and used there in a static analysis, has been extended to the dynamic realm. This model is derived within the framework of the so called First-order Shear Deformation Theory (FSDT) [2], [3]. What is peculiar in this assumed strain finite element is the direct modelling of the in-plane strain components; the corresponding stress components are deduced via constitutive law. By enforcing the equilibrium equations for each lamina, account taken of continuity requirements, the out-of-plane shear stresses are computed and, finally, constitutive law provides the corresponding strains. The resulting global strain field depends 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 lamination sequences and comparison with analytical solutions are presented.
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