Fixed Point Formulation and Accelation Iterative Algorithm for Thermal Buckling Analysis of Structures with Temperature-Dependent Material Properties

For the temperature-dependent thermal structure problem of material properties, temperature not only affects the thermal structure response as a load term, but also affects the structural response through the temperature-dependent material properties. Therefore, for the problem of critical thermal buckling temperature analysis for material property temperature-dependent problems, the change of temperature affects both the geometric stiffness and the global stiffness of the structure, which leads to the nonlinear eigenvalue buckling problem. In this paper, the structural critical thermal buckling analysis for temperature-dependent problems of materials is mathematically reduced to a fixed point problem. By using the fixed point theory, the existence and uniqueness of the solution to the thermal buckling problem are discussed. On this basis, an Aitken accelerated iterative algorithm is proposed to solve the critical temperature of thermal buckling, which significantly improves the efficiency of the algorithm. Based on the proposed algorithm, the function of existing CAE software which can only solve the thermal structure buckling problem independent of material properties is extended by means of secondary development, and the effectiveness of the proposed method is verified through a circular ring example.