Transformed Newtons method with a fixed-point iteration for highly nonlinear problems in structural mechanics

In this paper, a nonlinear solver combining fixed-point iteration and transformed Newton’s method is first proposed. The transformed Newton’s method was recently introduced to decrease the degree of nonlinearity of problems in solid mechanics. The key contribution behind this work is to modify the starting point of each iteration of the transformed method. Specifically, the transformed method gets started with the previous converged solution while the proposed solver starts at an initial guess theoretically proved to be close to the converged root of the current step. The advantage of the proposed nonlinear solver lies in the simple implementation and the significant reduction in number of iterations compared with the purely transformed Newton’s method. Numerical results are presented to show the accuracy and efficiency of the proposed solver in dealing with highly nonlinear problems in structural mechanics.