钟轶峰, 余文斌. 基于变分渐近法的功能梯度板高保真简化模型[J]. 工程力学, 2012, 29(10): 211-217. DOI: 10.6052/j.issn.1000-4750.2011.02.0066
引用本文: 钟轶峰, 余文斌. 基于变分渐近法的功能梯度板高保真简化模型[J]. 工程力学, 2012, 29(10): 211-217. DOI: 10.6052/j.issn.1000-4750.2011.02.0066
ZHONG Yi-feng, YU Wen-bin. HIGH-FIDELITY SIMPLIFIED MODEL FOR FUNCTIONALLY GRADED PLATES BASED ON VARIATIONAL ASYMPTOTIC METHOD[J]. Engineering Mechanics, 2012, 29(10): 211-217. DOI: 10.6052/j.issn.1000-4750.2011.02.0066
Citation: ZHONG Yi-feng, YU Wen-bin. HIGH-FIDELITY SIMPLIFIED MODEL FOR FUNCTIONALLY GRADED PLATES BASED ON VARIATIONAL ASYMPTOTIC METHOD[J]. Engineering Mechanics, 2012, 29(10): 211-217. DOI: 10.6052/j.issn.1000-4750.2011.02.0066

基于变分渐近法的功能梯度板高保真简化模型

HIGH-FIDELITY SIMPLIFIED MODEL FOR FUNCTIONALLY GRADED PLATES BASED ON VARIATIONAL ASYMPTOTIC METHOD

  • 摘要: 为有效分析非均质功能梯度板在载荷下的力学性能, 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板的三维能量方程;利用板固有小参数将三维能量渐近扩展为系列二维近似能量方程, 从而将三维各向异性弹性问题简化为沿板厚向的一维分析和二维板分析;提供重构关系以准确预测沿厚度方向的三维场分布。通过SiC-Al功能梯度板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三维精确解相一致;在应变很小时, 可考虑任意大位移和全局旋转, 并可准确捕捉板所有的几何非线性。

     

    Abstract: In order to effectively analyze the mechanical behavior of inhomogeneous functionally graded plates, a high-fidelity simplified model is developed based on variational asymptotic method (VAM). The 3D energy equation of functionally graded plate is established based on the expanded Hamilton principle. The 3D energy equation is asymptotically expanded into a series of 2D approximate energy equations by taking advantage of the inherent small parameters. The three-dimensional, anisotropic elasticity problem is rigorously decoupled into a one-dimensional through-the-thickness analysis and a two-dimensional plate analysis. The recovery relationships are provided to accurately predict the 3D field distribution along the thickness direction. The cylindrical bending example of SiC-Al functional gradient plate shows 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 all the geometric nonlinearity when the strains are small.

     

/

返回文章
返回