複合桿件在聖維南扭轉問題中，存在兩種不完美界面，一種是模擬低剪力模數的薄層界面，另一種是模擬高剪力模數的薄層界面。與完美界面相比，第一種界面的翹曲位移不連續，第二種界面的法線應力分量不連續，我們以界面剪力模數及厚度所定義的界面參數來表示不完美界面的特性。本文主要內容是藉由變分學理論，推導任意截面形狀的複合桿件其不完美界面扭轉剛度之上下限，基於合理的應力及位移場量架構下，討論界面的不完美連結對桿件扭轉剛度上下限的影響，桿件截面為圓形時定義一個參數 Rcr，當內含物半徑等於Rcr ，扭轉剛度上下限會重合，因此得到此桿件扭轉剛度的解析解。

On the Saint-Venant torsion problem of composite shafts, two kinds of imperfect interfaces are considered. One models a thin interphase of low shear modulus and the other models a thin interphase of high shear modulus. Comparing with the case of perfect bonding, the first case undergoes a jump in the warping function and the second case undergoes a jump in the axial shear traction. The imperfect interfaces are characterized by parameters given in terms of the thickness and shear modulus of the interphase. By variational principles, we derive bounds for the torsional rigiditiy of composite shafts with cross-sections of arbitrary shapes. The analysis is based on the construction of admissible fields in the inclusions and in the matrix. To understand how the imperfect bonding influences the torsional rigidity which is obtained by a shaft with circular cross-section, we define the parameter Rcr. When the inclusion radius equals Rcr, the lower and upper bounds will coincide. In this situation, the torsional rigidity is theoretically exact.

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