Inversing heat flux boundary conditions based on precise integration FEM without iteration and estimation of thermal stress in FGMs

In this article, based on the precise integration finite element method, a non-iterative inverse method is proposed to inverse the heat flux boundary conditions for the thermo-mechanical problem in functionally graded materials. Comparing with general iterative inverse methods, the novel inverse method can directly obtain accurate inversed results by least square method without iteration. Furthermore, the precise integration method is utilized to obtain a stable and accurate solution. On the other hand, in order to improve the adaptability of the inverse method, the unknown heat flux boundary conditions are expanded by a series of compactly supported radial basis functions. Once the unknown heat flux boundary conditions are determined, the temperature and thermal stress distributions can be estimated as well. Several examples are discussed to investigate some factors such as the random measurement error, the position and number of measurement points and the bias on measurement points' position and thermophysical parameters. Numerical results show that the proposed method has excellent efficiency and accuracy.