Second-order two-scale finite element algorithm for dynamic thermo-mechanical coupling problem in symmetric structure

The new second-order two-scale (SOTS) finite element algorithm is developed for the dynamic thermo-mechanical coupling problems in axisymmetric and spherical symmetric structures made of composite materials. The axisymmetric structure considered is periodic in both radial and axial directions and homogeneous in circumferential direction. The spherical symmetric structure is only periodic in radial direction. The dynamic thermo-mechanical coupling model is presented and the equivalent compact form is derived. Then, the cell problems, effective material coefficients and the homogenized thermo-mechanical coupling problem are obtained successively by the second-order asymptotic expansion of the temperature increment and displacement. The homogenized material obtained is manifested with the anisotropic property in the circumferential direction. The explicit expressions of the homogenized coefficients in the plane axisymmetric and spherical symmetric cases are given and both the derivation of the analytical solutions of the cell functions and the quasi-static thermoelasticity problems are discussed. Based on the SOTS method, the corresponding finite-element procedure is presented and the unconditionally stable implicit algorithm is established. Some numerical examples are solved and the mutual interaction between the temperature and displacement field is studied under the condition of structural vibration. The computational results demonstrate that the second-order asymptotic analysis finite-element algorithm is feasible and effective in simulating and predicting the dynamic thermo-mechanical behaviors of the composite materials with small periodic configurations in axisymmetric and spherical symmetric structures. This may provide a vital computational tool for analyzing composite material internal temperature distribution and structural deformation induced by the dynamic thermo-mechanical coupling response under strong aerothermodynamic environment.