An incremental-iterative scheme for solving structures with highly nonlinear postbuckling responses

Most incremental-iterative schemes for tracing the postbuckling response of structures have failed to achieve convergent solutions when the load-deflection curves make sharp turns in regions where nearby equilibrium paths exist, due to the fact that iterations are not performed along a correct direction. This problem can be overcome by introducing two parameters for detecting the change in loading direction and for guiding the direction of iteration, and a unit conversion factor in the constraint equation to make it physically consistent. The reliability of the present method has been demonstrated in the solution of a benchmark problem, which is characterized by the occurrence of multi winding loops in the load-deflection curves.