Geometrically nonlinear analysis of layerwise anisotropic shell structures by hybrid strain based lower order elements

Abstract

The objective of the investigation reported in this paper is to develop a hybrid-strain-based lower order shell element as a viable alternative to conventional solid elements for modeling and analysis of layerwise anisotropic shell structures undergoing large deformation of finite strains and finite rotations. Lower order hybrid-strain-based triangular shell elements for geometrically nonlinear analysis of isotropic shell structures, developed earlier by the authors, are employed as the basic building block of the layerwise element. Similar to the isotropic counterpart, the layerwise shell element has three nodes that are located on the mid-surface of the shell and eighteen degrees-of-freedom. The nodal degrees-of-freedom of each node include three translational and three rotational degrees-of-freedom. The latter includes the important drilling degree-of-freedom. The layerwise shell element is formed by stacking the aforementioned lower order triangular isotropic shell elements. The investigation exploits the use of symbolic algebraic package such as MAPLE V for the determination of explicit element stiffness matrix so that no numerical matrix inversion and integration are required in the computation. The investigation also explores strategies of effectively stacking layers by transferring nodal degrees-of-freedom of a layer to those of the element. The emphasis at this phase of the investigation, however, is large geometrically nonlinear analysis of layerwise laminated composite shell structures. Excellent agreement were observed between the results obtained by the present explicit expressions for the layerwise shell element and those available in the literature.