考虑热对材料参数影响的FGM梁热后屈曲特性研究

功能梯度梁热后屈曲特性研究对于推进功能梯度材料在航天器热防护设计中的应用有着重要意义。基于经典梁的几何非线性理论和物理中面的概念，建立了热载荷作用下功能梯度梁的运动微分方程，通过化简得到一个仅关于挠度的四阶微分-积分方程，并与固支边界条件构成特征值问题，分析研究了功能梯度梁的热后屈曲及在此基础上的振动问题。首先证明了通过哈密顿原理推导的运动方程是轴线可伸长理论的近似形式。接着考虑热对材料物性参数的影响，并对梁的长细比、功能梯度指数和温度比作了详细分析，研究了这些参数对热后屈曲路径和后屈曲振动的影响规律。结果表明:只有在长细比较大时才可以不考虑温度对材料物性参数的影响，否则误差较大；长细比、功能梯度指数和温度比的增大会增大无量纲热屈曲载荷，同时使屈曲路径和频率-载荷曲线向热载荷增大的方向移动。

THERMAL POST-BUCKLING ANALYSIS OF FGM BEAMS CONSIDERING THE HEAT EFFECT ON MATERIALS

Thermal post-buckling analysis of functionally graded beams is of great significance for the practical implementation of functionally graded materials for the thermal insulation of spacecrafts. The governing equations of the functionally graded beam in thermal environment are obtained based on the geometrical nonlinear theory and the introduction of the physical neutral surface. By simplification, a fourth-order integral-differential equation with respect to transverse deformation is obtained, and the eigenvalue problem is solved with the clamped boundary condition. The thermal post-buckling and the vibration on the basis of the buckled configuration are investigated. Firstly, the governing equations obtained by the Hamilton's principle are proved to be approximate equations obtained by the axial extension theory. Then, considering the heat effect on the properties of the material, the influence of the slenderness ratio, functionally gradient index and temperature ratio on post-buckling vibration is analyzed in detail. The heat effect on the properties of the material can be neglected when the slenderness is large enough. Increasing the slenderness ratio, functionally gradient index or temperature ratio will increase the non-dimensional thermal buckling load.