本研究提出一方法，藉由移位函數的方法發展出具非線性邊界條件之
Timoshenko 曲樑確切靜態解。一般曲樑研究可以區分為平面內與平面
外，而這類的研究多數是耦合。然而在考慮曲樑平面為主平面且橫截面
為對稱下，則平面內與平面外會解耦。根據漢米爾頓原理求得六個耦合
的微分方程式。在一些簡易的算術運算下，曲樑系統可以分解成一個完
整的六階微分特徵方程和關聯的邊界條件。利用移位函數法處理非線性
邊界問題。最後以懸臂曲樑例子及極限問題來說明與驗證本方法的正確
性。

This thesis presents a method, the shifting function method, for finding the exact static solution of curved Timoshenko beams with nonlinear boundary conditions. Most general problems of in-plane and out-of-plane curved beams are coupled. However, if the cross section of the curved beam is doubly symmetric and the plane is a principal plane of the cross section, then the in-plane and out-of-plane problems are uncoupled. Six coupled governing differential equations are derived via the Hamilton’s principle. After some simple algebraic operations, the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. Nonlinear boundary problems are solved by the shifting function method. Finally, an example of cantilever curved beam is given to illustrate the analysis, limiting studies and verification and show that the proposed method performs very well for problems with nonlinearity.

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