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An improved model for unsymmetric plates

机译：未对称板材的改进模型

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For an unsymmetric plate, a pure bending (plate curvature) inevitably causes a certain amount of stretching to the geometric mid-plane due to the stretching-bending coupling. According to classical thin plate theory, the geometric mid-plane is assumed to remain unstrained under pure bending. In this study, we demonstrate that the classical thin plate theory based on Kirchhoff-Love hypothesis is not accurate enough to model the structural behavior of unsymmetric plates. To overcome this limitation, we propose an improved theoretical model for unsymmetric plates through taking advantages of neutral plane strains in defining the geometric functions instead of mid-plane strains. Subsequently, the new governing equations and energy expression for the cylindrical bending of unsymmetric plates are derived using a modified constitutive equation. An alternative derivation approach based on the general stress equations is also presented for further validation. A direct consideration of stretching-bending coupling in the constitutive equation can significantly reduce the number of unknown parameters in establishing an accurate analytical model for unsymmetric plates. The pure bending problem of unsymmetric plates with small deformation is first studied, for which the improved model proposed in this paper is shown to capture the out-of-plane deformation of unsymmetric plates, accurately. However, many previous works have to take into account the nonlinear von Karman strains even in the model of this small deformation problem. For the pure plate bending problem with large deformation, few unknown terms are needed for the improved model to give accurate results compared with the conventional mid-plane strain based method. Later, this improved model is applied to predict the stable configurations, the bifurcation/loss-of-bifurcation and the static snap-through phenomena of bistable cross-ply composite laminates. Furthermore, the application of this improved model for the accurate simulation of the nonlinear dynamics of unsymmetric plates is also demonstrated. Applying this proposed improved model, the model is reduced into an analogous one for isotropic or symmetric plates, therefore, the problem of unsymmetric plates can be solved readily and accurately.
机译：对于不对称的板，由于拉伸弯曲耦合，纯弯曲（板曲率）不可避免地导致一定量的拉伸到几何中间平面。根据经典薄板理论，假设几何中间平面在纯弯曲下保持不受限制。在这项研究中，我们证明了基于Kirchhoff-Love假设的古典薄板理论不足以模拟非对称板的结构行为。为了克服这种限制，我们通过采取中性平面菌株在定义几何函数而不是中间平面菌株中的优点来提出改进的非对称板的理论模型。随后，使用修改的本构体方程来导出非对手板圆柱形弯曲的新的控制方程和能量表达。还介绍了基于一般应力方程的替代推导方法以进行进一步的验证。在本构体方程中的拉伸弯曲耦合的直接考虑可以显着降低建立非对手板精确分析模型的未知参数的数量。首先研究了具有小变形小变形的非对称板的纯弯曲问题，本文提出的改进模型被示出为捕获非对称板的外平面变形，准确。然而，即使在这个小变形问题的模型中，许多以前的作品也必须考虑非线性von Karman菌株。对于具有大变形的纯板弯曲问题，对于改进的模型，需要几个未知的术语，以便与传统的中间平面应变的方法相比提供精确的结果。之后，应用这种改进的模型以预测稳定的配置，分叉/损失和静态的静态交叉层复合层压材料的静态捕获量。此外，还证明了这种改进模型的应用，用于精确模拟非对称板的非线性动力学。应用这一提出的改进模型，该模型被减少成用于各向同性或对称板的类似物质，因此，可以容易且准确地解决非对手板的问题。

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