臺灣博碩士論文加值系統

本文採用Prandtl-Reuss塑流法則和Hill的降伏條件，結合有限變形理論及Updated Lagrangian Formulation(ULF)的觀念建立一增量型彈塑性大變形三維有限元素分析模式，並利用廣義之 法則處理板金成形時，元素之降伏、最大容許應變增量、最大容許旋轉增量、工件與模具間邊界節點之接觸或分離等問題。此分析程式模擬等向性與異向性金屬胚料引伸成形之製程，在三維模式下，模擬金屬胚料成形時沖頭負荷與衝程關係、CPU運算時間、變形歷程、耳緣成形、厚度分佈，以及各變形歷程應力與應變分佈關係，並與圓杯引伸成形實驗之實驗數據做比較，以驗證本論文所發展的彈塑性有限元素分析程式之可信度及精確度。
本文有限元素分析是採用四節點四邊形退化殼元素(degenerated shell element)，所推導之形狀函數偶合入剛性矩陣中，組成有限元素之分析模式。經由圓杯引伸之異向性圓形胚料數值模擬與實驗之沖頭負荷與衝程關係及工件厚度分佈之比較，顯示異向性數值分析與實驗結果吻合，故本彈塑性大變形有限元素分析程式可合理的模擬圓杯引伸成形之製程。

A methodology for formulating an elasto-plastic three-dimensional finite element model, which is based on Prandl-Reuss flow rule and Hill''s yield criterion respectively, associated with an Updated Lagrangian Formulation, is developed to simulate isotropic and anisotropic sheet metal forming process. An extended algorithm is proposed to formulate the boundary condition, such as nodal penetration and separation, strain increment and rotation increment, and altered elasto-plastic state of material. Under the model of three-dimensions, the numerical simulation results include relationship between the punch load and punch displacement, CPU time, the earing contour, the variation of sheet thickness, deformation diagrams in different forming stages, the distribution of stress and strain and so on. Then, comparison between the simulation and experimental data can be used to verify the reliability and accuracy of the finite element program developed in this thesis.
The shape function derived from a four-node quadrilateral degenerated shell element is associated into the stiffness matrix to constitute the finite element model. This study examined the numerical simulation on cylindrical cup drawing of anisotropic circular blank; and the experiments on the relationship between punch load and punch displacement; and the thickness distribution of work pieces. The findings of numerical simulation and experimental data indicated consistence. Therefore, the elasto-plastic large deformation finite element program can reasonably simulate cylindrical cup drawing process.

第一章 緒論 -------------------------------------------------- 1
1.1 前言 ------------------------------------------------- 1
1.2 研究動機與目的 --------------------------------------- 1
1.3 文獻回顧 --------------------------------------------- 2
1.4 論文之構成 ------------------------------------------- 5
第二章 基本理論 ---------------------------------------------- 7
2.1 基本假設 --------------------------------------------- 7
2.2 有限元素之應變與應變率 ------------------------------- 7
2.3 有限變形之應力與應率力 ------------------------------ 10
2.4 有限變形之Total Lagrangian Formulation -------------- 14
2.5 有限變形之Update Lagrangian Formulation ------------- 17
2.6 材料之彈塑性構成關係式 ------------------------------ 18
第三章 有限元素分析 ----------------------------------------- 26
3.1 簡介 ------------------------------------------------ 26
3.2 虛速度原理的離散化 ---------------------------------- 28
3.3 退化殼元素（Degenerated Shell Element）之分析 ------- 29
3.4 不同積分法則推導退化殼元素之剛性矩陣 ---------------- 31
3.5 摩擦處理 -------------------------------------------- 33
3.6 廣義 法之增量步驟的計算 ----------------------------- 36
第四章 圓杯引伸實驗與數值模擬分析 --------------------------- 42
4.1 邊界條件 -------------------------------------------- 42
4.2 材料參數與實驗數據 ---------------------------------- 42
4.3 數值模擬分析 ---------------------------------------- 43
4.4 數值分析與實驗結果之比較 ---------------------------- 45
4.4.1 沖頭負荷之比較 -------------------------------- 45
4.4.2 CPU運算時間之比較 ----------------------------- 46
4.4.3 異向性材料之模擬分析 -------------------------- 47
4.5 圓杯引伸成形之分析 ---------------------------------- 47
4.5.1 圓杯引伸成形歷程之比較 ------------------------ 48
4.5.2 耳緣成形之分析 -------------------------------- 48
4.5.3 厚度分佈之比較 -------------------------------- 49
4.5.4 應力分佈之比較 -------------------------------- 50
4.5.5 應變分佈之比較 -------------------------------- 51
第五章 結論 ------------------------------------------------- 87
5.1 結論 ------------------------------------------------ 87
5.2 未來展望 -------------------------------------------- 88
參考文獻 ---------------------------------------------------- 90
符號索引 ---------------------------------------------------- 94

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