數值積分表示微分元素法，將欲分析的結構物分割成有限個元素，然後利用數值積分表示微分之方式，定義於各個元素的微分或偏微分關係式做數值的離散化，且在整體結構物的離散點滿足所應具有的力學微分關係式之條件下，求取結構物之離散方程式系統。而數值積分表示微分元素法乃是一種具有高耦合特性的數值分析模式。因此，電腦處理時，除了運算的負荷量可降低外，精度亦能相對的提高。
本篇論文是開發陳長鈕教授之數值積分表示微分元素法，將其模式運用在具剪變形之任意複合變斷面樑結構物之靜變形問題，探討研究剪變形樑是一種不同於 Euler-Bernouli Beam的另一種樑的問題型式，此乃因為具剪變形之任意複合變斷面樑之橫斷面尺寸跟樑的長度尺寸的比值為一不可忽略的有限值，因此當樑遭受到橫向力之負荷時，其斷面受到剪力的作用產生之剪變形對樑整體的變位存在有一誤差值，而此誤差並不可忽略，也因此統御方程之重新建立乃為必要之步驟。
具剪變形之任意複合變斷面樑結構物之靜變形問題是本篇論文所積極表現之主軸，利用陳長鈕教授的數值積分表示微分元素法來求取數值，而其計算結果表現出此數值方法開發之成果驗証及精確度之提昇。

DQEM divides the structures waiting to be analyzed into limited elements, and then uses DQEM to define each element’s calculus or partial calculus relationship finding out the quantity of dispersion. Moreover, under the force-calculus-relating equation corresponding to the structure as a whole, retrieving the structure’s dispersion-equation system. DQEM is a highly accurate method of analysis. Therefore, when handling the computer, other than reducing the load of the computer itself, its accuracy also increases.
This thesis is to explore into depth the DQEM acknowledged by Dr. Chen Chung New, using its working method on the sheer force of the random compound beam’s static transformation problems, and to research on the difference of which to Euler-Bernouli Beam-another type of beam problem, due to the important limits of the ratio of the horizontal surface size and the beam’s length. So when the beam faces a horizontal force,the surface undertakes sheer force resulting in sheer-transformation, causing slight miscalculation in entire beam structure, leaving the miscalculation slight but undiscardible, therefore the reestablishment of equilibrium equations is one major step.
Random compound beams possessing static sheer-transformation is the core presentation of this thesis, by using Dr. Chen’s DQEM way of calculating no doubt gives us the proof of mathematical progress and increased accuracy.

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