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Nonlinear thermomechanical behaviors of thin functionally graded sandwich shells with double curvature

机译：具有双曲率的功能梯度薄夹层薄壳的非线性热力学行为

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摘要

Analytical closed-form solutions for thermos-mechanical stability and explicit expressions for free- and forcedvibration of thin functionally graded sandwich shells with double curvature resting on elastic bases are investigated for the first time in this study. A core layer of ceramic and two cover layers of functionally graded materials constitute the shell structure. Governing equations are derived from the classical shell theory using Hamilton's principle admitting Volmir assumption and von Karman nonlinear displacement fields. Theoretical solutions are achieved by using the Bubnov-Galerkin procedure in solving differential equations. Parametric studies showing the effects of temperature-dependent features, material constituents, initial geometry imperfections, external thermos-mechanical loadings, elastic bases, and geometry configuration on static and dynamic behaviors of the shells are performed. Thin functionally graded sandwich spherical, cylindrical, and hyperbolic paraboloid shells are studied. Snap-through phenomena under load-control conditions are recognized in thin functionally graded sandwich cylindrical shells. The fourth-order Runge-Kutta method is employed to numerically solve dynamic problems and four analogies are drawn to validate theoretical formulations.
机译：本研究首次研究了热力学稳定性的解析式闭合解，以及具有双曲率的薄功能梯度夹层薄壳的自由振动和强迫振动的明确表达式。陶瓷的芯层和两个功能梯度材料的覆盖层构成了外壳结构。控制方程是从经典壳理论出发，使用汉密尔顿原理接受Volmir假设，并采用von Karman非线性位移场。理论解是通过使用Bubnov-Galerkin过程求解微分方程来实现的。进行了参数研究，显示了温度相关特征，材料成分，初始几何缺陷，外部热力学-机械载荷，弹性基座和几何构型对壳体静态和动态行为的影响。研究了功能梯度薄的球形，圆柱形和双曲线抛物面壳。在功能控制的薄型夹层圆柱壳中，可以识别出在负载控制条件下的卡扣现象。采用四阶Runge-Kutta方法对动力学问题进行数值求解，并绘制了四个类比来验证理论公式。

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