Pseudoforce Method for Nonlinear Analysis and Reanalysis of Structural Systems

Abstract

This paper develops a new solver to enhance the computational efficiency of finite-element programs for the nonlinear analysis and reanalysis of structural systems. The proposed solver does not require the reassembly of the global stiffness matrix and can be easily implemented in present-day finite-element packages. It is particularly well suited to those situations where a limited number of members are changed at each step of an iterative optimization algorithm or reliability analysis. It is also applicable to a nonlinear analysis where the plastic zone spreads throughout the structure due to incremental loading. This solver is based on an extension of the Sherman-Morrison-Woodburg formula and is applicable to a variety of structural systems including 2D and 3D trusses, frames, grids, plates, and shells. The solver defines the response of the modified structure as the difference between the response of the original structure to a set of applied loads and the response of the original structure to a set of pseudoforces. The proposed algorithm requires O(mn) operations, as compared with traditional solvers that need O(m2n) operations, where m = bandwidth of the global stiffness matrix and n = number of degrees of freedom. Thus, the pseudoforce method provides a dramatic improvement of computational efficiency for structural redesign and optimization problems, since it can perform a nonlinear incremental analysis no harder than the inversion of the global stiffness matrix. The proposed method's efficiency and accuracy are demonstrated in this paper through the nonlinear analysis of an example bridge and a frame redesign problem.