Inverse Reconstruction of Thermal and Mechanical Boundary Conditions in Coupled Nonlinear Thermo-Elastic Problems

Abstract

A stable technique based on the finite element method for inverse analysis of coupled nonlinear thermo-elastic problems is presented. Not only the time-domain is divided into small intervals, but also the space-domain is divided into several sub-domains. The inverse problem is solved in each sub-domain subsequently. For the inverse analysis in each sub-domain, the unknown boundary conditions are found by using an optimization method and also by employing the information obtained in the previous sub-domain. The method is sufficiently stable to be used for inverse analysis of a thermo-elastic problem under a thermal shock. Three numerical examples are provided to demonstrate the efficiency of the proposed method. The effects of the number of sub-domains are investigated in the examples.

The method of fundamental solutions for problems in static thermo-elasticity with incomplete boundary data

“…equal to its value at average temperature. More general space or temperature variations of κ could also be considered, see the numerical implementations in [30] and [18], but for our theoretical study of uniqueness of a solution and for the MFS implementation these more complex cases are deferred to a future work.…”

“…For example, early studies by Noda [26] and Noda et al [27] investigated inverse transient thermo-elastic problems in an infinitely long cylinder and in a transversely-isotropic body, respectively. Later on, Lee and Yang [20] and Yang et al [31] investigated inverse problems predicting the heat flux and thermal stresses from strain measurements in an infinitely long annular cylinder, whilst Khajehpour and Hematiyan [18] presented a domain decomposition inverse analysis for solving a thermo-elastic problem under a thermal shock.…”

A novel inverse method for identification of 3D thermal conductivity coefficients of anisotropic media by the boundary element analysis

“…As reported by Liu [27], the stability of some inverse problems can be enhanced by increasing the number of measurements. Also, the domain decomposition method presented by Khajehpour et al [28,29] can be employed to convert an ill-posed inverse problem into several simpler inverse problems, which can be solved more efficiently.…”