A new method for simultaneous identification of thermal-mechanical loading and thermophysical properties in dynamic coupled thermoelasticity problems based on Levenberg-Marquardt method

To solve inverse dynamic coupled thermoelasticity problems, a new method is proposed to identify thermal-mechanical loading and material properties of the coupled problems. In this paper, the complex variable element differential method (EDM) element for direct dynamic coupled thermoelasticity problems is constructed for the first time through the element differential method and complex variable derivative method (CVDM). The complex variable EDM element demonstrates significant advantages in calculation of sensitivity matrix. Furthermore, the new method has been established by combining complex variable EDM elements with the Levenberg Marquardt (L-M) algorithm, enabling simultaneous identification of mechanical loading and heat flux. Finally, the numerical examples achieved simultaneous identification of thermal-mechanical properties and thermal-mechanical loadings, including an analysis of the influence of guess values and measurement errors. The proposed method demonstrates good stability, accuracy, and robustness.