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research-article

A new rotation-free shell formulation using exact corotational frame for dynamic analysis and applications

[+] Author and Article Information
Jiabei Shi

P.hD Student, School of Naval, Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China
sjbnust@163.com

Zhuyong Liu

Assistant Professor, School of Naval, Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China
zhuyongliu@sjtu.edu.cn

Jiazhen Hong

Professor, School of Naval, Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, P.R.China
jzhong@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4039129 History: Received September 01, 2017; Revised January 12, 2018

Abstract

Rotation-free shell formulations were proved to be an effective approach to speed up solving large scaled problems. It reduces systems' degrees of freedom and avoids shortages of using rotational degrees of freedom, such as singular problem and rotational interpolation. The rotation-free element can be extended for solving geometrically nonlinear problems using a corotational frame. However, its accuracy may be lost if the approach is used directly. Therefore, a new nonlinear rotation-free shell element is formulated to improve the accuracy of the local bending strain energy using a corotational frame. The linear strain for bending is obtained by combining two re-derived elements, while the nonlinear part is deduced with the side rotation concept. Furthermore, a local frame is presented to correct the conventional local corotational frame. An explicit tangential stiffness matrix is derived based on plane polar decomposition local frame. Simple elemental rotation tests show that the stiffness matrix and the proposed local frame are both correct. Several numerical examples and the application of drape simulations are given to verify the accuracy of nonlinear behavior of the presented element, and some of the results show that the presented method only requires few elements to obtain an accurate solution to the problem studied.

Copyright (c) 2018 by ASME
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