Some Computational Aspects of the Stability Analysis of Nonlinear Structures

摘要

The perturbation method and the continuation method for the solution of finite element equations that describe instability phenomena are discussed. The discrete analog of Koiter's perturbation method and modifications proposed for use in nonlinear finite element codes are assessed. Continuation strategies for the computation of equilibrium paths along equilibrium surfaces are considered. The importance of adaptive parametrization is stressed. Problems related to the evaluation of the stability properties of the solutions, including determination of critical points along the solution curves and a strategy for branch switching at bifurcation points, are treated.