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Large Rotation Analyses of Plate/Shell Structures Based on the Primal Variational Principle and a Fully Nonlinear Theory in the Updated Lagrangian Co-Rotational Reference Frame

Y.C. Cai1, S.N. Atluri2
Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, P.R.China.
Center for Aerospace Research & Education, University of California, Irvine

Computer Modeling in Engineering & Sciences 2012, 83(3), 249-274. https://doi.org/10.3970/cmes.2012.083.249

Abstract

This paper presents a very simple finite element method for geometrically nonlinear large rotation analyses of plate/shell structures comprising of thin members. A fully nonlinear theory of deformation is employed in the updated Lagrangian reference frame of each plate element, to account for bending, stretching and torsion of each element. An assumed displacement approach, based on the Discrete Kirchhoff Theory (DKT) over each element, is employed to derive an explicit expression for the (18x18) symmetric tangent stiffness matrix of the plate element in the co-rotational reference frame. The finite rotation of the updated Lagrangian reference frame relative to a globally fixed Cartesian frame, is simply determined from the finite displacement vectors of the nodes of the 3-node element in the global reference frame. The element employed here is a 3-node plate element with 6 degrees of freedom per node, including 1 drilling degree of freedom and 5 degrees of freedom [3 displacements, and the derivatives of the transverse displacement around two independent axes]. The present (18×18) symmetric tangent stiffness matrices of the plate, based on the primal variational principle and the fully nonlinear plate theory in the updated Lagrangian reference frame, are much simpler than those of many others in the literature for large rotation/deformation analysis of plate/shell structures. Numerical examples demonstrate the accuracy and robustness of the present method.

Keywords

large deformation, thin plate/shell, Discrete Kirchhoff Theory (DKT), updated Lagrangian formulation, Primal principle.

Cite This Article

Cai, Y., Atluri, S. (2012). Large Rotation Analyses of Plate/Shell Structures Based on the Primal Variational Principle and a Fully Nonlinear Theory in the Updated Lagrangian Co-Rotational Reference Frame. CMES-Computer Modeling in Engineering & Sciences, 83(3), 249–274.



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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