Methodology for Determining the Compliance Matrix and Analyzing the Skew Anisotropic Plate with an Arbitrarily Shaped Hole
Methodology for Determining the Compliance Matrix and Analyzing the Skew Anisotropic Plate with an Arbitrarily Shaped Hole
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确定柔度矩阵并分析具有任意形状孔的斜交各向异性板的方法
DOI：
10.1155/2022/5949398
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发表时间：
2022-04
影响因子：
--
通讯作者：
Lei Wang
中科院分区：
文献类型：
--
作者：
Xiaoli Zhang;Aizhong Lu;Kezhi Song;Guangming Wu;Lei Wang
以往的分析方法主要集中于正交各向异性、横观各向同性甚至各向同性材料的分析，对非正交和极端各向异性材料特性的分析较少。在本研究中，考虑具有任意形状孔的无限倾斜各向异性板。首先沿板内斜方向建立两个局部笛卡尔坐标系，根据坐标轴旋转下的变换公式建立材料的弹性常数方程。在此基础上，结合工程常数（杨氏模量、泊松比、剪切模量）可以得到斜交各向异性材料的弹性柔量矩阵。随后，利用复变量方法推导沿孔边界的应力的解析解。分别以斜交各向异性板开制的椭圆孔、六边形孔和方孔为例，分析了不同外载荷作用下沿孔边界的应力分布。最后通过ANSYS软件有限元分析对本文提出的理论方法进行了验证。
The previous analytical methods mainly focused on the analysis of orthotropic, transversely isotropic, or even isotropic materials, and little analyses have been conducted on nonorthogonal and extreme anisotropic material properties. In this study, the infinite skew anisotropic plate with an arbitrary-shaped hole are considered. Initially, two local Cartesian coordinate systems are established along the skew orientations in the plate, and the equations for the elastic constants of the material are established according to the transformation formulae under rotation of the coordinate axes. On this basis, the elastic compliance matrix for the skew anisotropic material can be obtained in combination with the engineering constants (Young’s modulus, Poisson’s ratio, and shear modulus). Subsequently, the complex variable method is utilized to derive the analytical solutions for stress along the hole boundary. The elliptical, hexagonal, and square holes perforated in skew anisotropic plates are used as examples, respectively, and the stress distributions along the hole boundary are analyzed for different external loadings. Finally, the theoretical method presented in this paper is verified by means of the Finite Element Analysis of ANSYS software.
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影响因子：
8.7
作者：
B. P. Mishra;M. Barik
通讯作者：
B. P. Mishra;M. Barik
DOI：
10.1002/(sici)1096-9853(199902)23:2
发表时间：
1999-02
影响因子：
4
作者：
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影响因子：
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作者：
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影响因子：
2.4
作者：
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通讯作者：
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影响因子：
1.3
作者：
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