Application of the method of fundamental solutions for inverse problems related to the determination of elasto-plastic properties of prizmatic bar

Abstract

The problem of determining the elastoplastic properties of a prismatic bar from the given relation from experiment between torsional moment MT and angle of twist per unit of rod’s length θ is investigated as inverse problem. Proposed method of solution of inverse problem is based on solution of some sequences of direct problem with application of the Levenberg-Marquardt iteration method. In direct problem these properties are known and torsional moment as a function of angle of twist is calculated form solution of some non-linear boundary value problem. For solution of direct problem on each iteration step the method of fundamental solutions and method of particular solutions is used for prismatic cross section of rod. The non-linear torsion problem in plastic region is solved by means of the Picard iteration.