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Static and Dynamic Analysis of Laminated Thick and Thin Plates and Shells by a Very Simple Displacement-based 3-D Hexahedral Element with Over-Integration

Qifeng Fan1, Yaping Zhang2, Leiting Dong1,3, Shu Li1, Satya N. Atluri4
School of Aeronautic Science and Engineering, Beihang University, China
Taizhou Polytechnic College, China
Corresponding Author, Email:
Department of Mechanical Engineering, Texas Tech University, USA

Computers, Materials & Continua 2015, 47(2), 65-88.


A very simple displacement-based hexahedral 32-node element (denoted as DPH32), with over-integration in the thickness direction, is developed in this paper for static and dynamic analyses of laminated composite plates and shells. In contrast to higher-order or layer-wise higher-order plate and shell theories which are widely popularized in the current literature, the proposed method does not develop specific theories of plates and shells with postulated kinematic assumptions, but simply uses the theory of 3-D solid mechanics and the widely-available solid elements. 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 by commercial FEM codes. It is clearly shown that the proposed methodology can accurately and efficiently predict the structural and dynamical behavior of laminated composite plates and shells in a very simple and cost-effective manner.


laminated structure, plates and shells, hexahedral 32-node element, higher order theory, over-integration

Cite This Article

Q. . Fan, Y. . Zhang, L. . Dong, S. . Li and S. N. . Atluri, "Static and dynamic analysis of laminated thick and thin plates and shells by a very simple displacement-based 3-d hexahedral element with over-integration," Computers, Materials & Continua, vol. 47, no.2, pp. 65–88, 2015.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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