功能梯度材料圆柱壳基于变分渐近法的高保真简化模型

High-fidelity Simplified Model for Functionally Graded Cylindrical Shells Based on Variational Asymptotic Method

为有效分析涂覆型功能梯度圆柱壳顶面作用正弦荷载下的响应,基于变分渐近方法(VAM)建立高保真简化模型。根据Hamilton扩展原则建立功能梯度材料圆柱壳3维能量方程;利用壳体固有小参数将3维能量渐近扩展为系列2维近似能量方程,并将近似能量转换为工程常用的Reissner-Mindlin模型形式;提供重构关系以准确预测沿厚度方向的3维场分布。通过SiC-Al功能梯度面层-均质基层圆柱壳顶面作用正弦分布荷载的柱形弯曲算例验证,基于该理论和模型重构的位移和应力分量与3维精确解相一致;在应变很小时,可考虑任意大位移和全局旋转,并可准确捕捉翘曲几何非线性。

In order to effectively analyze the response of coating functionally graded cylindrical shell under sinusoidal pressure on the top surface,a high-fidelity simplified model was developed based on variational asymptotic method（VAM）.The 3D energy equation of functionally graded shell was established based on the expanded Hamilton principle.The 3D energy equation was asymptotic expanded into a series of 2D approximate energy equation by using the inherent small parameters,and the approximate energy was converted to a form of Reissner-Mindlin model.The recovery relationships were provided to accurately predict the 3D field distribution along the thickness direction.The cylindrical bending example of a homogeneous substrate with a thin Sic-Al functionally graded coating under sinusoidal pressure on the top surface showed that the recovered 3D displacement and stress components agree well with 3D precise solutions.The present model is valid for large displacements and global rotations and can accurately capture the warping geometric nonlinearity when the strains are small.