本論文之研究目的，乃是運用本實驗室所發展的增量型彈塑性大變形三維有限元素計算程式，模擬金屬板材在軸對稱條件下，引伸及再引伸的成形製程。本文遵循Prandtl-Reuss塑流法則與von Mises之降伏條件，結合有限變形理論及updated Lagrangian formulation (ULF)之觀念建立一增量型彈塑性大變形三維有限元素分析程式。並利用以四邊形四節點之退化殼元素(degenerated shell element)所推導之形狀函數耦合入剛性矩陣，組成三維有限元素之分析模式，並且使用廣義rmin法則處理金屬板材在引伸及再引伸時，包含元素之降伏判斷、最大容許應變增量、最大容許旋轉增量、料片與模具間節點之接觸與分離判斷等問題。
藉由數值模擬，可以獲得引伸及再引伸過程中之全部變形歷程資料、沖頭負荷與位移關係、料片厚度分佈、應力與應變分佈等，並設計圓形及錐形兩組模具進行實驗，以驗證程式之可信度。本文模擬在圓柱沖頭的引伸及圓錐沖頭再引伸成形製程。最後並設計一系列的操作實驗，經由實驗數據與模擬分析之數據比較顯示其結果相當符合，此舉更加證明以本研究所發展之有限元素分析程式模擬錐形引伸加工製程之可行性，其分析之結果亦可提供製程分析者或模具設計者之參考。

The aim of this study is to apply an elasto-plastic incremental three-dimensional finite element computed code to simulate drawing and redrawing forming processes under axisymmetric condition. A methodology for formulating an elasto-plastic three-dimensional finite element model to simulate sheet metal forming process is developed using Prandtl-Reuss flow rule and von Mises yield criterion respectively in association with an updated Lagrangian formulation. The shape function derived from a four-node quadrilateral degenerated shell element was combined into the stiffness matrix to constitute the finite element model. An extended algorithm was proposed to formulate the boundary condition to solution drawing and redrawing forming process, such as nodal penetration and separation, strain increment and rotation increment, and altered elasto-plastic state of material.
Simulation results include the whole deformation history , the relationship between punch load and punch stroke , the distribution of thickness , stress and strain during the bending process were obtained. Two set of Circle-shaped tools and Cone-shaped tools was designed for experiments to verify the reliability of the program. The experimental results of Cone-shaped drawing process were compared with the simulation results. Both results after compensation were accurate and can be referred to process analyzers or tool designers.

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