An analytical solution is given to the problem of non-uniform torsion of an elliptical cylinder made of functionally graded anisotropic linear elastic material. The material moduli of the considered anisotropic non-homogeneous elastic bar are smooth functions of the axial coordinate. The contour of the elliptical cross section depends on the elastic constants. This dependence provides the zero warping property of the considered elliptical cross section. The obtained stress field is independent of the axial coordinate as in the case of Saint-Venant’s torsion problem, but the rate of twist depends on the axial coordinate.

中文翻译：

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椭圆截面功能梯度各向异性杆的非均匀扭转

给出了功能梯度各向异性线弹性材料椭圆圆柱非均匀扭转问题的解析解。所考虑的各向异性非均匀弹性杆的材料模量是轴向坐标的光滑函数。椭圆截面的轮廓取决于弹性常数。这种相关性提供了所考虑的椭圆横截面的零翘曲特性。获得的应力场与轴坐标无关，就像圣维南扭转问题的情况一样，但扭曲率取决于轴坐标。