Geometrically nonlinear analysis of plates and cylindrical shells by a predictor–corrector method

The main aspects of a predictor–corrector algorithm for tracing the equilibrium path of geometrically nonlinear plates and cylindrical shells are discussed. The predictor step is carried out by an asymptotic extrapolation that exploits a parametrization equation based on residual error minimization. The constraint equation in the Newton like corrector step is defined imposing the minimum distance between the approximate solution point and the solution curve. For the range of applications considered here the efficiency of the extrapolation is not problem dependent. Furthermore, residual based steplength adaptation and an appropriate direction of traversing selection permit us to locate the predictor point on the asymptotic approximation in such a way as to prevent sudden changes of direction of the path, as in axially compressed cylindrical shells analysis.