An approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure
An approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure
复制标题
DOI：
10.1016/j.compstruct.2015.08.104
复制
发表时间：
2016
影响因子：
6.3
通讯作者：
Libiao Xin;Shengyou Yang;Dong Zhou;Guansuo Dui
中科院分区：
文献类型：
--
作者：
Libiao Xin;Shengyou Yang;Dong Zhou;Guansuo Dui
本文基于Mori-Tanaka方法给出了功能梯度厚壁管在内压作用下的近似解析解。我们假设该管由两个各向同性的线弹性组分组成，其中一相的体积分数是沿径向变化的幂函数。基于Mori-Tanaka方法，得到了径向位移的微分方程，进而得到了与Mori-Tanaka方法数值结果吻合较好的近似解析解。此外，本文还讨论了另外两种方法的相同问题，即我们已经在Xin等人（2014）中提出的Voigt方法和Reuss方法。这三种不同的方法都避免了现有文献中对未知整体材料参数分布的假设。此外，它们适用于具有不同泊松比的材料，而不是现有文献中通常用于获得有效杨氏模量的恒定泊松比。
In this work an approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure is given. We assume that the tube consists of two isotropic linear elastic constituents and the volume fraction for one phase is a power function varied in the radial direction. Based on the Mori–Tanaka method, this paper obtains the differential equation of the radial displacement, and then an approximate analytical solution is obtained that agrees well with the numerical results of the Mori–Tanaka method. Furthermore, this paper discusses the same problem with two other methods, the Voigt method that we have already presented in Xin et al. (2014) and the Reuss method. All these three different methods can avoid the assumption of the distribution regularities of unknown overall material parameters appeared in existing papers. Further, they are valid for the materials with different Poisson’s ratios rather than constant Poisson’s ratios usually used in the existing references to obtain the effective Young’s modulus.