利用周期结构设计具有优异散热、隔热性能的人工材料是近年来备受关注的一个前沿热点。由于周期结构的材料参数在空间频繁变化，因此其瞬态热传导的数值积分问题极具挑战性。本项目拟以周期结构瞬态热传导问题为背景，开展高性能数值积分方法研究。基于瞬态热传导问题的物理特性和结构的对称性，研究一般周期结构、单胞具有对称性周期结构瞬态热传导问题的高效率、高精度数值算法。建立含非线性缺陷和辐射边界条件周期结构瞬态热传导问题的拟叠加原理，在一个积分时间步长内将含非线性缺陷和辐射边界条件周期结构解耦为小规模非线性结构和一个大规模完美线性周期结构，从而避免求解大规模非线性瞬态热传导问题，建立含非线性缺陷和辐射边界条件周期结构的有效分析手段。项目成果不仅可以推进计算力学理论与方法研究的前沿进展，也可为周期结构的散热、隔热性能设计提供重要技术支撑。

Based on the periodic structures, the design of artificial materials with excellent heat dissipation or thermal insulation properties is a hot topic. The numerical integration of transient heat conduction for the periodic structures is actually very challenging due to the periodic changes of material parameters in the space domain. In this project, we intend to investigate the high-performance numerical integration method for transient heat conduction in periodic structures. Based on the physical properties of the transient heat conduction problem and the symmetry of structure, a high-efficiency and high-accuracy numerical algorithm would be investigated for the transient heat conduction of the periodic structures with general unit cell and symmetric unit cell. Furthermore, this project aims to develop a quasi-superposition principle of transient heat conduction problems for periodic structures with nonlinear defects and radiation boundary conditions. Based on the quasi-superposition principle, within a time step, the entire structure with nonlinear can be decoupled into a small-scale nonlinear structure and a large-scale perfect periodic structure, which would avoid the problem of solving large-scale nonlinear transient heat conduction and realize the effective analysis of the periodic structure with nonlinear defects. The achievements of this project can not only prompt the cutting edge research of computational mechanics, but also provide strong technical support for the design of periodic structures with excellent heat dissipation or thermal insulation properties.