Solution of Post-Buckling & Limit Load Problems, Without Inverting the Tangent Stiffness Matrix & Without Using Arc-Length Methods
T.A. Elgohary1, L. Dong2, J.L. Junkins3, S.N. Atluri4
CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.6, pp. 543-563, 2014, DOI:10.3970/cmes.2014.098.543
Abstract In this study, the Scalar Homotopy Methods are applied to the solution of post-buckling and limit load problems of solids and structures, as exemplified by simple plane elastic frames, considering only geometrical nonlinearities. Explicitly derived tangent stiffness matrices and nodal forces of large-deformation planar beam elements, with two translational and one rotational degrees of freedom at each node, are adopted following the work of [Kondoh and Atluri (1986)]. By using the Scalar Homotopy Methods, the displacements of the equilibrium state are iteratively solved for, without inverting the Jacobian (tangent stiffness) matrix. It is well-known that, the simple Newton’s method (and… More >
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