Nonlinear solution method for fiber beam element based on the hybrid approximations method
Li Gang1 Jin Yongqiang1 Dong Zhiqian1 Li Hongnan1,2
1. State Key Laboratory of Costal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China;
2. Shenyang Jianzhu University, Shenyang 110168, China
Abstract：Nonlinearity problems in civil engineering structures mainly involve the material nonlinearity and geometric nonlinearity (i.e., hybrid nonlinearities) under environmental loads. Because the computational cost is high, great attentions have been paid to the numerical solution of hybrid nonlinearity problem. The inelasticity-separated finite element method (IS FEM) is an efficient nonlinear solution method, and based on the concept, the strain of a nonlinear material can be decomposed into the linear-elastic and inelastic components. Consequently, the elastic and plastic components in the stiffness matrices from the governing equation can be separated, such that the Woodbury formula can be used to solve local material nonlinearity problems. In this study, the governing equation of the fiber beam element considering hybrid nonlinear behaviors is derived using the IS FEM. In order to efficiently solve the governing equation, the efficient hybrid approximations method is proposed based on the Woodbury formula and the combined approximations (CA) method. In addition, the time complexity theory is used to evaluate the calculation efficiency of the present method, and the results show that it is obviously superior to the conventional finite element method. Finally, based on a numerical example, it is proved that the proposed method can produce accurate results efficiently, and thus, appear to be appealing in solving hybrid nonlinear problems of the fiber beam element.
李 钢 靳永强 董志骞 李宏男. 基于混合近似法的纤维梁单元非线性求解方法#br#[J]. 土木工程学报, 2019, 52(6): 81-91.
Li Gang Jin Yongqiang Dong Zhiqian Li Hongnan. Nonlinear solution method for fiber beam element based on the hybrid approximations method. 土木工程学报, 2019, 52(6): 81-91.
