Degenerated shell element with composite implicit time integration scheme for geometric nonlinear analysis |
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| Authors: | Jie Zhang Donghuan Liu Yinghua Liu |
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| Affiliation: | 1. Department of Engineering Mechanics, AML, Tsinghua University, Beijing, China;2. Department of Applied Mechanics, University of Science and Technology Beijing, Beijing, China |
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| Abstract: | A degenerated shell element with composite implicit time integration scheme is developed in the present paper to solve the geometric nonlinear large deformation and dynamics problems of shell structures. The degenerated shell element is established based on the eight‐node solid element, where the nodal forces, mass matrices, and stiffness matrices are firstly obtained upon virtual velocity principle and then translated to the shell element. The strain field is modified based on the mixed interpolation of tensorial components method to eliminate the shear locking, and the constitutive relation is modified to satisfy the shell assumptions. A simple and practical computational method for nonlinear dynamic response is developed by embedding the composite implicit time integration scheme into the degenerated shell element, where the composite scheme combines the trapezoidal rule with the three‐point backward Euler method. The developed approach can not only keep the momentum and energy conservation and decay the high frequency modes but also lead to a symmetrical stiffness matrix. Numerical results show that the developed degenerated shell element with the composite implicit time integration scheme is capable of solving the geometric nonlinear large deformation and dynamics problems of the shell structures with momentum and energy conservation and/or decay. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | finite elements time integrations large deformation nonlinear shell dynamics |
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