• 沒有找到結果。

經過了幾種不同方法的分析後,有關蜂窩結構之巨觀柏松比,可得如 下的結論。

1. 以尤拉梁理論所推導之解析解,係在厚長比 0.1 以下之薄壁、剛性 節點、線彈性的材料、極其微小且均勻的變形、無限延伸的區域 與外力等等完美的假設條件下。其所得與有限試體的試驗結果有 明顯的差異。

2. 重複單元體也同樣在相似的完美假設下進行分析,但壁厚、剛性 節點與線彈性的材料這三項假設則可捨去而不受限制。因而在超 薄壁的條件下,與理論解析解有良好的近似。

3. 當細胞壁厚度增加時,結構柏松比所占總體柏松比的比例逐漸以 非線性的方式降低,取而代之的是逐漸升高的材料柏松比。這使 得總體巨觀柏松比也隨之降低。這個趨勢無論在理論解析解、實 驗結果,以及幾種有限元素模型數值解中皆可觀察到。

4. 蜂窩試體非常精緻而輕巧,實驗時既需有可變形的空間,又需有 穩定的架設,實為兩難。其材料雖為多孔隙,卻與實心塊體類似,

只要0.002 的巨觀應變量即可進入塑性,加上薄壁多孔隙的複雜幾 何,使變形的量測變得困難。即使以1600 萬畫素拍照,在位移範

外改善實驗上的困難可採用磁環測微計,可解決摩擦力與彈簧形 同約束等問題。

5. 各種有限元素法所採用的數值模型,因元素性質的不同,例如網 格尺寸極限、邊界條件的給定方法、厚度的考量方式等等,各方 法所得結果不盡相同。若考慮微小變形下、完美線性彈性材料、

均勻無限平面的情況,則以重複單元所做的數值分析搭配尤拉梁 理論推導的解析解結果最為理想。但與真實的彈塑性材料性質、

有限大變形邊界、大變形的試體結果會有明顯差異。

6. 本研究得到不同厚長比對此兩種柏松效應的消長狀況,結果顯示,

厚長比在0.4~1.0 之間為結構柏松比與材料柏松比轉換的臨界區域。

以試體2 之厚長比 0.11 為例,完美無限蜂窩材料解析解所得之柏 松比為0.98,此情況為均勻變形,側向位移要一致,而其他方法 所得,若不考慮塑性變形,則結果落在0.7~0.9 之間。因此有限元 素重複單元體之薄壁情況較接近理論解,而完整蜂窩試體數值有 限元素分析,就算假設上下邊界光滑無摩擦,都不會有均勻側向 變形,其所得較接近實驗結果。

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在文檔中 蜂窩結構巨觀柏松比研究 (頁 79-84)

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