This paper presents is a solution for static torsion in a microtube made of bi-directional functionally graded materials (BDFGMs). The material properties are assumed to vary according to the arbitrary function along radius and length of microtube. As for the torque effect of the axial magnetic field, the well-known Maxwell’s relation is used. Couple stress theory is employed to study the influence of small-scale on static torsion of microtube. The Navier equation and boundary conditions of the size-dependent BDFG microtube were derived by the minimum potential energy. These equations were solved by employing the generalized differential quadrature method (GDQM). Comparison between the results of this work with the analytical method for static torsion of microtube made of one direction FG material reveals the accuracy of this study. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants on the static torsion of the bi-directional functionally graded microtube.

中文翻译：

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基于耦合应力理论的双向功能梯度微管在磁场作用下的静态扭转

本文提出了一种解决由双向功能梯度材料 (BDFGM) 制成的微管中的静态扭转问题。假设材料特性根据沿微管半径和长度的任意函数而变化。至于轴向磁场的转矩效应，使用了著名的麦克斯韦关系。采用耦合应力理论研究小尺度对微管静扭转的影响。通过最小势能推导出尺寸相关的BDFG微管的Navier方程和边界条件。这些方程采用广义微分求积法 (GDQM) 求解。将这项工作的结果与单向FG材料制成的微管的静态扭转分析方法进行比较，揭示了这项研究的准确性。最后，