均匀磁场中内压功能梯度厚壁管弹性解的再探讨
Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field
摘要：
研究了功能梯度材料厚壁圆筒在均匀磁场和内压载荷作用下的力学响应。与以往研究中直接将材料常数假设成某种函数形式不同，本文首先给出了功能梯度材料圆柱体各组分的体积分数，然后确定了材料常数的表达式。利用Voigt方法，导出了径向位移、应变和应力分量以及扰动磁场矢量的相应解析解。在数值计算部分，研究了体积分数对位移、应变和应力分量以及磁场扰动矢量的影响，结果表明泊松比对功能梯度圆柱体的力学行为有显著影响。此外，通过适当选择材料常数，可以发现本文的结果可以退化为文献中给出的一些特殊情况。
英文摘要：
In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subjected to uniform magnetic field and inner-pressurized loads are studied. Rather than directly assuming the material constants into some certain function forms as displayed in previous researches, we firstly give the volume fractions of different constituents of the FGM cylinder and then determine the expressions of material constants. By the use of the Voigt method the corresponding analytical solutions of displacements in radical direction, the strain and stress components and the perturbation magnetic field vector are derived by the following. In numerical part, the influences of volume fraction on displacement, stain and stress components and the magnetic perturbation filed vector are investigated; indicated by the results, we can conclude that the Poisson's ratio has a significant effect on the FGM cylinder's mechanical behaviors. Moreover, by some appropriate choices of the material constants it can be found that the obtained results in this paper can reduce to some special cases given in previous literatures.
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