A faster modified newton-raphson iteration

Abstract The paper describes an accelerated modified Newton-Raphson iteration in which the iterative deflection change is a scalar times the previous iterative change plus a further scalar times the usual unaccelerated change. These scalars are automatically recalculated at each iteration. They are related to inner products involving the iterative deflections and the present and past out-of-balance force vectors. The extra computation for each iteration is negligble, the only penalty being the storage of two extra vectors. The method is based on a secant approach and leads to a significant reduction in the required number of iterations. Examples are presented in which the method is applied to the nonlinear analysis of thin plates and shells. The technique is used in conjunction with the finite element method.

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