本文之目的在於使用彈塑性增量理論並利用有限元素法，模擬金屬板材側邊不同寬度帽型引伸成形之製程，並採用Prandtl-Reuss塑流法則和von Mises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程式，並應用四邊形四節點退化殼元素(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，以及使用廣義 法則處理板材成形時，元素降伏判斷、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等問題。
藉由數值模擬，可得到成形製程之變形過程資料，如沖頭負荷與沖頭位移關係、板材厚度分佈、應力與應變分佈等。此外，亦製作一組模具進行實驗，並將實驗結果與數值模擬結果作一比較以驗證有限元素分析程式之可信性。

The aim of this thesis is to apply an elasto-plastic incremental finite element computer code to simulate the different side width of hat drawing process. A methodology for formulating an elasto-plastic three-dimensional finite element model, which is based on Prandtl-Reuss flow rule and von Mises yield criterion respectively, associated with an updated Lagrangian formulation, is developed to simulate sheet metal forming process. The shape function derived from a four-node quadrilateral degenerated shell element is associated into the stiffness matrix to constitute the finite element model. 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.
The whole deformation history, such as the distribution of thickness, stress and strain during the forming process was obtained. The experimental results of different side width of hat drawing process were made in comparing with the simulation results. The results of both after compensation were accurate.

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