An algorithm for the analysis of problems with combined material and geometric nonlinearities

Abstract

A solution procedure which combines the first-order self-correcting technique with linear iterations and equilibrium corrections is presented. Both geometric and material nonlinearities are considered. However, in order to describe geometric nonlinearities, large displacements but small strains are considered. The procedure presented requires only a single inversion of the linear elastic stiffness matrix and the iterations are required to be performed on the equilibrium equations without altering the nonlinear matrices. First the analytical formulation for the incremental plasticity equations theory used is presented. Then, a description of the solution algorithm is presented. Finally, the solution algorithm is demonstrated for a simply supported circular plate problem subjected separately to monotonic loading and cyclic loading, and the numerical results obtained are compared with those reported in the literature for similar problems. For problems with combined nonlinearities, the procedure has been found to be numerically stable, accurate and efficient for relatively large load increments.