本文探討圓斷面桿件在扭力作用下端點效應的影響，並探討在不同的邊界條件、材料異向性、功能性材料，與多層材料問題聖維南原理的適用性，以及端點效應是否可以忽略。材料力學的解只包含聖維南解的部分，僅解析徑向無束制之邊界條件問題。依據彈性力學理論，利用狀態空間法，首先對均質材料問題與材料力學的解做比較，再針對功能性材料以及雙層之複合材料圓桿的扭轉問題，探討端點效應的影響範圍。

End effects in circular bar and tube under torsion, compare with different boundary conditions, anisotropic, functionally graded material and multilayersproblem, the usability of Saint-Venant’s principle, in what situation, the end effect can be neglected. The shear stress formula in “Material Machenics” only including the non-decay term, and lateral boundary condition is traction free. According to elasticity theory, in using state space method, compare with homogeneous material problem and the shear stress formula in “Material Machenics”, then consider the functionally graded material and multilayers under torsion, the region of the end effect.

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