Performance-based step-length adaptation laws for path-following methods

Abstract

A quasi-static problem is usually formulated by the equations of static equilibrium and a load parameterwhich shows the level of loading. Path-following methods are widely used to analyze these kinds of prob-lems. These methods add a constraint function to the equilibrium equations in order to determine theloading evolution. There is a parameter in the constraint function, the step-length, which should be pos-itive in each analysis step and which is determined by a step-length adaptation law. Different adaptationlaws control the step-length growth differently, and thus, they influence the performance of the solution.We propose two novel types of adaptation laws based on (a) a local degree of smoothness and (b) globalperformance measures of the solution. The former uses the angle between the linearized solution pathand the tangent to the analytical solution curve while the latter employs simple prediction models forthe future evolution of two performance measures. Moreover, appropriate constraint functions for thelatter are suggested. Example problems of structural damage are solved by path-following methods uti-lizing the proposed adaptation laws as well as a conventional one. Results show that the new laws raisedistinct possibilities to have solutions with an improved performance