Abstract：In general, material nonlinearity and geometric large deformation behaviors occur concurrently in engineering structures under external loads. Many numerical solution methods can successfully capture the response of structures, but they are time-consuming because of the requirement of repeatedly factorizing matrices. In this work, the governing equation of beam element involving the material nonlinearity and geometric large deformation behaviors is established by incorporating the inelasticity-separated finite element method (IS FEM) into the framework of the updated Lagrangian (UL) formulation. To efficiently solve the governing equation and overcome the limitations of Woodbury formula, a Woodbury approximation method (WAM) is presented as an efficient solver. The basic idea behind the developed WAM is that the changing global stiffness matrix is approximated as a constant matrix within a short time period, and a linear equation related to the Schur complement matrix is solved by the combined approximations (CA) method. To eliminate the additional error stemming from the approximation, an adaptive iteration strategy (AIS) based on the energy norm is adopted, in which the difference between the developed WAM solution and the exact solution is evaluated. Furthermore, time complexity analysis is used to verify the high-efficiency advantage of the proposed method. Finally, a reinforced concrete frame used as numerical example demonstrates that the proposed method can be implemented for nonlocal material nonlinearity and large deformation analyses of beam element.
李钢 靳永强. 基于近似Woodbury公式的梁单元几何大变形分析[J]. 土木工程学报, 2021, 54(11): 47-56.
Li Gang Jin Yongqiang. Geometric large deformation analysis for beam element based on the approximate Woodbury formula. 土木工程学报, 2021, 54(11): 47-56.
