Pseudoforce method for nonlinear analysis and reanalysis of structural systems

This paper develops a new solver to enhance the computational efficiency of finite-element programs far the nonlinear analysis and reanalysis of struc tural systems. The proposed solver does not require the reassembly of the g lobal 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 uf members are changed tit each step of an iterative optim ization algorithm or reliability analysis. It is also applicable to a nonli near analysis where the plastic zone spreads throughout the structure due t o incremental loading. This solver is based on an extension of the Sherman- Morrison-Woodburg formula and is applicable to a variety of structural syst ems including 2D and SE) trusses, frames, grids, plates, and shells. The so lver defines the response of the modified structure as the difference betwe en the response of the original structure to a set of applied lends and the response of the original structure to a set of pseudoforces. The proposed algorithm requires O(mm) operations, as compared with traditional solvers t hat need O(m(2)n) operations, where m = bandwidth of the global stiffness m atrix and n = number of degrees of freedom. Thus, the pseudoforce method pr ovides a dramatic improvement of computational efficiency for structural re design sind optimization problems, since it can perform a nonlinear increme ntal analysis nea harder than the inversion of the global stiffness matrix. The proposed method's efficiency and accuracy ale demonstrated in this pap er through the nonlinear analysis of an example bridge and a frame redesign problem.