Inverse heat conduction problem solutions via second-order design sensitivities and newton's method

Abstract

Analytical first- and second-order design sensitivities are derived and for a general nonlinear system. These analytical techniques as well as approximate techniques are then discussed and illustrated via a two degree-of-freedom nonlinear spring system. The design sensitivity concepts are next applied to a nonlinear steady-state conduction system. The first- and second-order design sensitivities are used in conjunction with Newton's method to solve an inverse heat conduction problem. These results are compared to results obtained from the first-order Broyton-Fletcher-Goldfarb-Shanno (BFGS) variable metric method. Analyses are first performed for materials with constant thermal conductivity since an exact solution is known. Subsequent analyses are then performed for materials with temperature dependent thermal conductivity. The second-order sensitivity based method is shown to be superior to the first-order method due to its faster convergence rates, more stable solutions, and limited dependence on regularization. In addition, the second-order method obtained solutions in cases where the first-order technique failed.

Also, Department of Theoretical and Applied Mechanics.

Also, Department of Theoretical and Applied Mechanics.

Notes

Also, Department of Theoretical and Applied Mechanics.