热载荷作用下对称S型功能梯度圆板的非线性力学行为

本文研究了热环境中陶瓷-金属-陶瓷功能梯度圆板（S-FGM）的过屈曲和弯曲行为。圆板材料组分的体积分数符合Sigmoid定律，并承受沿圆板厚度方向变化的温度场作用。基于经典板理论，用能量法导出了对称S-FGM圆板静态问题的非线性平衡方程。用打靶法对所得方程进行了数值求解，并利用数值结果研究了不同边界条件、材料的组分、热载荷等因素对对称S-FGM圆板力学行为的影响。数值结果表明：对称S-FGM圆板相较于普通FGM圆板，其力学行为存在一些不同之处，且板的上下表面温升比对S型功能梯度圆板的力学行为有着显著的影响。

Nonlinear Mechanical Behavior of Symmetrical S-FGM Circular Plate under Thermal Load

In this paper, the post-buckling and bending behavior of ceramic-metal-ceramic functionally graded circular plates (S-FGM) in a thermal environment are studied. The volume fraction of the material components of the circular plate complies with Sigmoid law and bears the effect of the temperature field that changes along the thickness of the circular plate. Based on the classical plate theory, the nonlinear equilibrium equation of the static problem of the symmetric S-FGM circular plate is derived by the energy method. The equation is solved numerically by shooting method, and the influence of different boundary conditions, material composition, thermal load and other factors on the mechanical behavior of the symmetrical S-FGM circular plate is studied by using the numerical results. The numerical results show that the mechanical behavior of the symmetric S-FGM circular plate is different from that of the ordinary FGM circular plate, and the temperature rise ratio of the upper and lower surfaces of the S-FGM circular plate has a significant influence on its mechanical behavior.