Abstract：Accurate geometry and stable computation are essential for heat conduction and thermo-mechanical analysis of complex three-dimensional structures. Traditional finite element methods often require laborious mesh generation for CAD models, which compromises both efficiency and accuracy. While classical Isogeometric analysis (IGA) offers advantages, it still struggles with the parameterization of complex boundary representation (B-Rep) models. In this paper, we develop an embedded domain IGA method for thermo-mechanical coupling problems. We present a unified solution framework for steady-state heat conduction and thermal stress analysis. The method utilizes NURBS as background basis functions and incorporates a virtual domain with an element classification strategy. This strategy effectively identifies the relationship between the background grid and the physical domain. To ensure accurate geometric representation, we employ adaptive Gaussian integration based on a recursive octree sub-cell scheme. This approach allows the method to capture the precise boundary of the B-Rep model without the need for boundary-fitted meshes. Based on this framework, the discrete forms of the steady-state heat conduction equation and thermal stress are derived. The coupling between temperature and displacement fields is considered in a consistent manner to handle thermal expansion effects and temperature-dependent responses. The proposed method can accurately capture temperature distribution and thermal stress in complex structures. Several numerical examples are presented to verify the performance of the proposed method. The results show that the method can achieve stable, accurate, and robust solutions. It avoids mesh generation and geometric reconstruction, significantly reducing the pre-processing time for complex CAD models. Compared with traditional methods, it shows good numerical accuracy and optimal convergence behavior. In addition, it has strong adaptability to complex geometries. The proposed method provides an effective and flexible approach for thermo-mechanical coupling analysis of complex engineering structures. It has significant potential applications in practical engineering analysis and design involving complex CAD models.
2026, Vol. 47 
