填充点阵夹层结构由于其优异的承载能力与多功能一体化等特点，在航天、航空、交通运输等工程领域均有广阔的应用前景。近年来，关于填充点阵结构的研究工作主要针对其常温环境下的承载、冲击吸能等特性，关于复杂热-力载荷下填充点阵夹层结构失效行为的理论研究，例如热冲击、热屈曲等关键性能还缺乏系统的研究工作。因此，本文主要针对填充点阵夹层板热屈曲行为开展研究，通过理论分析获得不同材料与几何参数对结构热-力失效行为的影响规律。

首先，基于应变能守恒定律，通过细-宏观尺度分析杆件、填充物应变能与总应变能的关系，获得填充点阵夹芯等效刚度矩阵。在此基础上，分析混合填充点阵夹芯等效力学性能与杆件各参数（包括几何构型，截面，模量）和填充物各参数的关系，给结构设计提供提供理论指导。

其次，以填充点阵夹芯等效力学性能研究为基础，通过哈密顿原理获得了均匀温升条件下填充点阵夹层板结构热屈曲分析控制方程，基于Zig-Zag剪切模型获得了不同边界条件下结构的热屈曲临界失效温度。分析边界条件、剪切模型、材料参数、几何参数等对填充点阵夹层板临界屈曲温度的影响。

然后，给出了高温环境下填充点阵夹层结构不同失效模式下的临界载荷，包括整体屈曲、杆件屈曲、屈服等。通过比较不同失效模式的大小，获得了不同失效模式之间的临界转换关系，形成了无量纲几何参数下的失效图谱。分析了载荷参数、几何参数等对失效图谱的影响规律。

本文的理论推导结合有限元验证，将现有的均质刚度系数理论和夹层板屈曲理论进行改进，以适用于填充点阵夹层板，并在此过程中对原有理论进行简化，使得其适用性更广。最后，本文分析了影响填充点阵夹层板热屈曲临界失稳温度的热物性以及几何影响因素，提出了能够提升夹层板热防护能力的方法。

本文总结了三个公式，分别关于填充点阵夹层板的刚度和强度。关于填充点阵夹层的均质刚度公式，该公式建立了均值刚度与填充物和杆件的几何与物理参数的关系，可用于指导填充点阵夹芯的刚度设计；关于填充点阵夹层板的热屈曲公式，则建立了临界温度与填充点阵夹层板各项几何、物理参数之间的关系，可用于提升夹层板的抗热整体屈曲强度；最后是填充点阵夹层板的热失效公式，总结了填充点阵夹层板的各种失效行为，以及各种失效行为随物理、几何参数的变化规律，当填充点阵夹层板承受热-力载荷时，其热失效公式可用于指导其强度设计，填充点阵夹层板的轻量设计也根据热失效公式给出，该公式结合失效图谱，可指导对填充点阵夹层板的比强度设计。

Lattice sandwich structure with filler(LSSF) has a broad application prospect in aerospace, aviation, transportation and other engineering fields Because of its excellent bearing capacity and multi-function integration. In recent years, the research work on LSSF mainly focuses on its bearing capacity and impact energy absorption characteristics under normal temperature environment, and the theoretical research on the failure behavior of the LSSF under complex thermal-force load, such as thermal shock, thermal buckling and other key properties, is still lack of systematic research work.Therefore, this paper mainly studies the thermal buckling behavior of LSSF and obtains the influence law of different materials and geometric parameters on the thermal and mechanical failure behavior of this structure through theoretical analysis.

Firstly, based on the law of conservation of strain energy, the equivalent stiffness matrix of filling lattice sandwich was obtained by fine-macro scale analysis of the relationship between total strain energy and strain energy of truss and filler. On this basis, the relationship between the equivalent mechanical properties of LSSF and the parameters of truss (including geometric configuration, section, modulus) and the parameters of filler is analyzed, which provides theoretical guidance for the structural design.

Secondly, based on the study of equivalent mechanical properties of LSSF, the governing equations for thermal buckling analysis of sandwich plates with LSSF plate under uniform temperature rise were obtained by using Hamiltonian principle, and the critical failure temperatures of LSSF plates under different boundary conditions were obtained by using Zig-Zag shear theory. The influences of boundary conditions, shear model, material parameters and geometrical parameters on the critical buckling temperature of LSSF plate are analyzed.

Then, the critical loads under different failure modes of LSSF plate under high temperature are given, including overall buckling, bar buckling, yield, etc. By comparing the sizes of different failure modes, the critical transformation relationships among different failure modes are obtained, and the failure atlatures under dimensionless geometric parameters are formed. The influence of load parameters and geometric parameters on the failure graph was analyzed.

In summary, the theoretical derivation and finite element verification in this paper not only achieve the development of the homogeneous stiffness coefficient theory and plate buckling theory to be suitable for LSSF plates, but also simplify the original theory in the process, making its applicability wider and more concise. Finally, the physical and geometric factors that affect the strength of each component (including itself and the connection between them) are deeply analyzed, and the formula that can guide the heat resistance strength of the plate is put forward.

This paper has summarized three formulas about the stiffness and strength of the  lattice with filler sandwich plate respectively . As for the homogeneous stiffness of lattice with filler sandwich plate, the relationship between the homogeneous stiffness and the geometric and physical parameters of lattice with filler sandwich plate has been established, which can be used to guide the stiffness design of lattice with filler sandwich plate. As for the thermal buckling formula of lattice with filler sandwich plate, the relationship between the critical temperature and geometrical, physical factors of lattice with filler sandwich plates has been established, which can be used to improve the thermal resistance of sandwich plate. Finally thermal failure formula of lattice with filler sandwich plate summarized various failure behavior, and a variety of relation between failure behavior and physical and geometrical parameters of lattice with filler sandwich plate under thermal and mechanical load has been concluded, the formula can be used to guide the thermal failure strength design, lightweight design of lattice with filler sandwich plate is also based on the thermal  failure formula. Combined with the failure graph, the formula can be used to guide the specific strength design of lattice with filler sandwich plate