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（DQEM)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。
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的技巧，對定義於各個元素的微分或偏微分關係式做數值的離散化，然後由考慮在整體結構物的離散點滿足所應具有的力學微分關係式的條件下，可得到結構物的離散方程式系統。
本文應用陳長鈕老師獨創之數值積分表示微分元素法(DQEM)來求解在不同邊界下受任意側向力與軸向力之樑的結構問題。數值計算的結果證明此方法的有效性。

A new numerical approach for solving the problem of a beam with random force is proposed. The approach uses the differential quadrature (DQ) to discretize the governing differential equations defined on all elements, the transition conditions defined on the interelement boundaries of two adjacent elements, and the boundary conditions of the beam. By assembling all the discrete relation equations, a global linear algebraic system can be obtained. Numerical results of the solutions of beams resting on a foundations obtained by the DQEM are presented.
The differential quadrature element method (DQEM) proposed by Dr.C.N. Chen is a numerical analysis method for analyzing continuum mechanics problems. The numerical procedure of this method can systematically implemented into a computer program. The coupling of solutions at discrete points is strong. In addition, all fundamental relations are considered in constructing the overall discrete algebraic system. Consequently, convergence can be assured by using less discrete points, and accurate results can be obtained by using less arithmetic operations which can reduce the computer CPU time required.

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