A predictor–corrector method for structural nonlinear analysis

Abstract

A predictor–corrector method is presented for the efficient and reliable analysis of structural nonlinear behaviors. The key idea lies on modifying the starting point of iterations of the Newton iterative method. The conventional Newton method starts iterations at the previously converged solution point. However, in the present predictor–corrector method, a point close to the converged solution of the current step is predicted first, and then the Newton method starts iterative procedure at the predicted point. The predictor, the neural network in the present study, recognizes the pattern of the previously converged solutions to predict the starting point of the current step. Then the corrector, the standard Newton method in the present study, is used to obtain the converged solution by iterative computation starting at the predicted point. Numerical tests are conducted to demonstrate the effectiveness and reliability of the present predictor–corrector method. The performance of the present method is compared with the conventional Newton method and Riks' continuation method. The present predictor–corrector method saves computational cost significantly and yields stable results without diverging, for the nonlinear analysis with monotonous deformation path as well as complicated deformation path including buckling and post-buckling behaviors.