本文研究之目的在於運用彈塑性增量理論並結合有限元素法，模擬分析金屬板材S彎帽型成形之製程。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。並應用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中，組成三維有限元素之分析模式，並使用廣義 法則處理金屬板材在成形時，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S彎帽型成形製程之全部變形履歷，例如沖頭負荷與位移關係、料片厚度分佈、應力與應變分佈及製品之最終外形等資料。本文引用1996年NUMISHEET會議中所提供之S彎帽型成形之材料數據、模具幾何形狀等參數來進行模擬，並與此會議參加者之實驗數據以及模擬數據做比對，以驗證本有限元素分析程式在模擬S彎帽型成形加工製程之可行性及可靠性。最後並運用此程式模擬S彎帽型成形工件，在受到成形方向之平板壓力並限制凸緣邊界條件下之成形性分析。

The aims of this thesis is to create an elasto-plastic incremental finite element computer code to simulate the S-rail hat drawing process of a sheet metal. 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.
According to numerical simulation, it can get the information of whole deformation history, such as the distribution of thickness, the distribution of stress, the distribution of strain, and the shape after the drawing process. This thesis cited the parameters of cap-shape forming from NUMISHEET’96, including material data and mold shape and experimental data. Then compare the simulation result with experimental data from reference to verify the feasibility and reliability in simulation process using this FEM analysis program.

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