Thermo-mechanical buckling of stepped circular bi-laminates subjected to a uniform temperature field is investigated analytically. The governing equations are derived via the Principal of Stationary Potential Energy, resulting in self-consistent constitutive equations of the composite structure, as well as the equations of motion and the associated matching and boundary conditions for the composite structure. A loading parameter is identified, and closed form analytical solutions to the non-linear problem are obtained, yielding exact results within the context of the formulation. A stability criterion is established based on the second variation of the total potential energy of the system in order to identify regions of stable and unstable equilibrium configurations, and a critical temperature and a critical membrane force are determined. Simulation results based on the analytical solutions are generated and a critical and characteristic behavior is assessed for both clamped-fixed supports and hinged-fixed supports conditions. The phenomenon of “sling-shot buckling” is observed. Results of parameter studies are also presented, which demonstrate the influence that material and geometric parameters of the system have on critical behavior. In particular, thermal expansion coefficient ratio, modulus ratio and thickness ratio all play a non-trivial role in the temperature carrying capacity of the structure for relatively large patches. Because the loading parameters and geometric parameters appear explicitly in the analytical solution and simulations, the model and results will be useful towards the design of micro-electromechanical systems, smart structures and related configurations.

解析研究了均匀温度场作用下阶梯状圆形双层压板的热机械屈曲。控制方程是通过平稳势能原理导出的，从而得出了复合结构的自洽本构方程，以及运动方程以及复合结构的相关匹配和边界条件。确定加载参数，并获得非线性问题的闭式解析解，从而在配方范围内得出准确的结果。基于系统总势能的第二变化建立稳定性标准，以识别稳定和不稳定的平衡构型区域，并确定临界温度和临界膜力。生成基于分析解决方案的仿真结果，并评估了夹紧固定支架和铰链固定支架条件的关键特性行为。观察到“弹弓弯曲”现象。还介绍了参数研究的结果，这些结果证明了系统的材料和几何参数对临界行为的影响。特别地，热膨胀系数比，模量比和厚度比在相对较大的贴剂的结构的温度承载能力中均起着不小的作用。由于载荷参数和几何参数明确地出现在解析解决方案和模拟中，因此该模型和结果将对微机电系统，智能结构和相关配置的设计有用。