於非線性彈簧邊界之均勻曲樑的靜態分析中，首先利用漢米爾頓原理求得兩個耦合的微分方程式，再藉由兩個具有物理意義的參數簡化原來兩個耦合的微分方程式以便於分析。經由消去扭轉角後，兩個耦合的微分方程式非耦合化，而成為一個以位移為因變數的六階微分方程式。在使用Shifting function method將非線性邊界線性化，進而求得系統的實際解。最後再以一些極端的例子來說明推導的正確性，並討論邊界條件和曲率參數對曲樑位移、力矩和剪力的影響。

In Static Analysis of uniform beam with nonlinear boundary conditions, the two coupled governing equations are derived via the Hamilton’s principle. And they can be easily decoupled into a six orders differential equation after assuming two physical parameters and eliminating the rotation variable by Gaussian elimination. With help of the shifting function method, the nonlinear boundary conditions can be linearized. Combining the six orders decoupled governing equation with linearized boundary conditions, the exact solution is completed. To make sure the consequences are correct, some limiting cases are provided and discussed with different curvature and boundary conditions.

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