Free vibration analysis of laminated composite shell structures using hybrid strain based layerwise finite elements

Abstract

The essential objective of the investigation reported in this paper was to extend the previously developed hybrid strain based layerwise shell elements to the free vibration analysis of laminated composite plate and shell structures. The hybrid strain based layerwise shell elements are proposed as viable alternatives to the conventional solid elements for the modeling and analysis of laminated composite shell structures. Several lower order hybrid strain based triangular shell elements for the general non-linear analysis of isotropic shell structures, developed earlier by the authors, are employed as the basic building block of the layerwise elements. The latter are formed by stacking the aforementioned lower order isotropic triangular shell elements. The investigation exploits ways of transforming element matrices from a layer to the mid-surface of the shell structure. The symbolic algebraic package MAPLE V is used for the derivation of the explicit consistent element stiffness and consistent element mass matrices. Thus, no numerical matrix inversion and integration are required in the derivation of element matrices. The numerical studies examine effects of several parameters to identify the “region of satisfactory performance” of the proposed layerwise elements. Also examined is the convergence pattern of the elements.