傳統有限元素法直接假設位移場求解，微分後獲得的應變場、應力場存在不連續的跳躍，而位移場也不保證平滑；因此本研究直接假設線性應變場並以積分的方式獲得以應變為未知數表達的位移函數，其中積分產生的積分常數以位移諧和條件解出，最後以最小總勢能原理求解應變未知數。

本研究先推導出二維平面應力狀態下應變有限元素法之演算流程，編寫程式實踐理論之算法，最後將運算結果視覺化輸出，並創建二維懸臂梁、軸力桿兩種典型的結構，以不同細密程度的網格劃分做收斂性分析，探討該理論的正確性；其成果在軸力桿模型有相當滿意的結果，收斂速度快且精準，懸臂梁模型則僅有在梁長度方向細分才能達到較好的結果，目前推測該方法對諧和要求較嚴苛有過度約束的疑慮。

Traditional finite element method directly assumes displacement field to solve problem, the stress field and strain field obtained after differentiation have discontinuous gap and displacement field is not ensured to be smooth; Therefore, this research assumes a linear strain field and obtains the displacement field expressed by the strain unknowns from integration, the constant of integration is solved by displacement compatibility conditions and the strain unknowns is solved by principle of minimum potential energy.

This research derives the algorithms of Strain-FEM from plane stress, program coding practices the theoretical algorithms; finally, output the visualized algorithm results. Thus, create 2D cantilever beam and 2D axial force member these two typical structures, then conduct convergence analysis based on the fineness level of mesh division in order to examine the correctness of the theory. The result gives positive feedback on model of axial force member which shows convergence rate is high and accurate; however, the model of cantilever beam only shows positive result when the length of the beam is subdivided. Currently, it is inferred that the method has more strict requirement of compatibility and has issue of over-constraint.

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[8] 陳建銘(2018)，「假設應變場的結構分析」，碩士論文，國立台灣科技大 學營建工程系，台北。

[8] 陳建銘(2018)，「假設應變場的結構分析」，碩士論文，國立台灣科技大
學營建工程系，台北。