有限元素法及有限差分法為兩種既有的數值結構分析技巧。有限元素法因為能夠被有系統地編成電腦程式，已經被廣泛應用於一般的結構分析；數值積分表示微分元素法為陳長鈕老師所研究開發出來的一種結構分析的數值方法，除了能有系統地編寫成電腦程式外，也可以更有效地求得精確的解。
本篇論文應用陳長鈕教授所發明的數值積分表示微分元素法，來分析考慮剪變形的變斷面曲樑之面外變形及振動問題。考慮剪變形的樑，又稱Timoshenko樑，是不同於尤拉─柏努力樑的另一種樑，當樑的橫斷面尺寸與樑的長度比，為一不可忽略的有限值時，若樑受到橫
向力作用，其會因剪力而產生剪變形，而剪變形對樑整體的變位，為一不可忽略之值，因此統御方程式之重新建立為必要之步驟。
數值積分表示微分元素法，是一種具有高度耦合特性的數值分析法，也因為具有高度耦合的特性，在分析計算時可減少誤差，得到較佳的收斂，因而大幅降低計算機的運算量。

Finite Element Method and Finite Difference
Method are two existing numerical structure analytical techniques. Finite Element Method has been widely applied to general structural analyses due to its systematically encoded into computer formula. DQEM is a method of structural analysis developed by C. N. Chen. However, other than systematically encoding into computer
formula, it can be more effectively get the precise solution.
The dissertation is based on C. N. Chen’s DQEM to analyze the problem of transformation and vibration by considering simple shear. Considering simple shear’s beam, also called Timoshenko beam, is another kind of beam different from Euler-Bernoulli’s beam. DQEM can minimize inaccuracy in computing, result in better convergence, and substantially reduce the quantity of calculating.

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