Static analysis using flexibility disassembly perturbation for material nonlinear problem with uncertainty

Nonlinear finite element analysis of large-scale structures usually requires a lot of calculation cost, because it is necessary to repeatedly inverse the modified stiffness matrix caused by nonlinearity in the calculation process. When considering the uncertainty in materials, the calculation of the nonlinear analysis will be more unbearable. To improve the computational efficiency, this work develops a new method for nonlinear analysis with material uncertainty based on flexibility disassembly perturbation (FDP) approach. The FDP is an algorithm that can quickly calculate the inverse of a stiffness matrix. The basic idea of the proposed method is to introduce the FDP formula into Newton-Raphson iteration method to accelerate the nonlinear iterative calculation. Three numerical examples, one statically determinate structure and two statically indeterminate structures, are used to verify the accuracy and efficiency of the proposed method. The results show that the calculation time of the proposed method is far less than that of the existing complete analysis and combined approximation algorithms. In terms of computational accuracy, for statically determinate structures, the proposed algorithm can obtain exact solutions that are identical to the complete analysis results, while for statically indeterminate structures, the proposed algorithm can obtain approximate solutions that are very close to the complete analysis results.