Inverse Problem of Pure Bending of a Beam under Creep Conditions

Abstract

We propose an algorithm for solving the inverse problem of forming structural members under creep conditions using the Nelder–Mead algorithm. The initial problem of finding the forces that must be applied to obtain the desired curvature of a part is reduced to a sequence of auxiliary direct problems of modeling the stress-strain state of pure bending of rectangular beams. This model, taking into account the difference in the properties of the material in tension and compression as well as the presence of accumulated damage in the material during creep, was verified by numerical methods and implemented in the finite element program MSC Marc.