Numerical solution of the nonlinear evolutional inverse problem related to elastoplastic torsional problem

Abstract

This paper is devoted to the determination of an unknown function that describes elastoplastic properties of a bar under torsion. The mathematical (evolution) model leads to an inverse problem that consists of determining the unknown coefficient , in the nonlinear parabolic equation , , , using measured output data given in the integral form. Existence of a quasi-solution of the considered inverse problem is obtained in the appropriate class of admissible coefficients. The direct problem is solved using a semi-implicit finite difference scheme. The inverse problem is solved using the semi-analytic inversion method (also known the fast algorithm). Finally, some examples are presented related to direct and inverse problems.

Keywords:

• evolutional problem
• torque
• power-law material
• difference scheme
• parametrization
• semi-analytic inversion method

AMS Subject Classifications:

• 35R30
• 73K05
• 35J60

Acknowledgments

The research has been partially supported by the Scientific and Technological Research Council of Turkey (TUBITAK), also by Zirve University Research Fund. The authors thank the reviewers for their very careful reading and for pointing out several mistakes as well as for their useful comments and suggestions. The first author also thanks to S. Ulusoy and R. Tınaztepe for fruitful discussions.