Open Access

ARTICLE

Are Higher-Order Theories and Layer-wise Zig-Zag Theories Necessary for N-Layer Composite Laminates?

by Qifeng Fan¹, Yaping Zhang², Leiting Dong¹, Shu Li¹, Satya N. Atluri⁴

1 School of Aeronautic Science and Engineering, Beihang University, China
2 Taizhou Polytechnic College, China
3 Corresponding Author, Email: dong.leiting@gmail.com
4 Department of Mechanical Engineering, Texas Tech University, USA

Computer Modeling in Engineering & Sciences 2015, 107(2), 155-186. https://doi.org/10.3970/cmes.2015.107.155

Abstract

Although “higher-order” and layer-wise “higher-order” plate and shell theories for composite laminates are widely popularized in the current literature, they involve (1) postulating very complex assumptions of plate/shell kinematics in the thickness direction, (2) defining generalized variables of displacements, strains, and stresses, and (3) developing very complex governing equilibrium, compatibility, and constitutive equations in terms of newly-defined generalized kinemaic and generalized kinetic variables. Their industrial applications are thus hindered by their inherent complexity, and the fact that it is difficult for end-users (front-line structural engineers) to completely understand all the newly-defined FEM DOFs in higher-order and layer-wise theories. In an entirely different way, the authors developed very simple lowest-order (8-node hexahedral), and higher-order (32-node hexahedral) 3-D continuum solid-shell elements, based on the theory of 3D solid mechanics, for static and dynamic analyses of composite laminates. The shear-locking of the lower-order 8-node hexahedral element is alleviated by independently assuming locking-free strain fields for each element. Over-integration is used to evaluate the element stiffness matrices of laminated structures with an arbitrary number of laminae, while only one element is used in the thickness direction without increasing the number of degrees of freedom. A stress-recovery approach is used to compute the distribution of transverse stresses by considering the equations of 3D elasticity. Comprehensive numerical results are presented for static, free vibration, and transient analyses of different laminated plates and shells, which agree well with existing solutions in the published literature, or solutions of very-expensive 3D models (where 3D elements are used to model each layer) by using commercial FEM codes. Because the proposed methodology merely involves simple displacement DOFs at each node, relies only on the simple theory of solid mechanics, and is capable of accurately and efficiently predicting the static and dynamical behavior of composite laminates in a very simple and cost-effective manner, it is thus believed by the authors that the development of “higher-order” or “layer-wise higher-order” theories are not entirely necessary for analyses of laminated plates and shells.

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