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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 9/10
Edited by: B.H.V. Topping
Paper IX.2

General Eigenvalue Test for Nonlinear Finite Elements

W. Liu* and Y-B. Yang+

*Chung=Cheng Institute of Technology, Taoyuan, Taiwan
+National Taiwan University, Taipei, Taiwan

Full Bibliographic Reference for this paper
W. Liu, Y-B. Yang, "General Eigenvalue Test for Nonlinear Finite Elements", in B.H.V. Topping, (Editor), "Proceedings of the Fourth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Edinburgh, UK, pp 345-350, 1989. doi:10.4203/ccp.9.9.2
An eigenvalue procedure is described for detecting the legitimacy of a non linear finite element. A non linear (linearized) finite element differs from the linear finite element in that the effect of change in geometry has to be considered. This will result in a geometric stiffness matrix in addition to the elastic stiffness matrix for the finite element. By decomposing the element deformations into natural and rigid body deformations, the geometric stiffness matrix can be divided into the internal and external stiffness matrices in accordance. The external stiffness matrix can be obtained as the difference of the initial nodal forces before and after the rigid body movements, while the internal stiffness matrix can be computed by deducting the external stiffness matrix from the geometric stiffness matrix. Only the elastic stiffness matrix and the internal stiffness matrix need to be considered in the eigenvalue test for non linear finite elements.

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