关键词: 多宗量, 反问题, 热力耦合, 时域分析, 有限元

Abstract: Tikhonov’s regularization approach is used to solve inverse problem of thermo-mechanical coupling in transient state with multi-variables, using Bregman distances and weighted Bregman distances in the construction of regularization terms for the Tikhonov’s function. The inverse problem is formulated implicitly as an optimization problem by using the residual error between calculated and measured quantities to construct the least square function. A time stepping scheme is used for transient analysis and the eight-node isoparametric element model is given, facilitating sensitivity analysis of direct and inverse problems, and taking account of inhomogeneity and parameters distribution. Single and combined identifications can be carried out for thermal parameters and boundary conditions etc. Satisfactory numerical validation is given, including a preliminary investigation of effect of noise data on the results and the computational efficiency for different regularization terms. Results show that the proposed method can identify single and combined thermal parameters and boundary conditions for thermo-mechanical coupling problems with high computational precision, good stability and certain anti-noise capability.

Key words: Finite element method, Inverse problem, Multivariable, Thermomechanical coupling, Time domain analysis