本文目的在於運用彈塑性增量理論結合有限元素方法，模擬分析金屬板材之U型彎曲加工製程中所產生之翹曲現象。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 法則處理金屬板材在成形時，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，可以獲得彎曲製程之全部變形履歷、沖頭負荷與位移關係、料片厚度分佈、應力與應變分佈等，並設計一組U型彎曲成形模具進行實驗，以驗證程式之可信度。本文模擬在U型彎曲成形過程翹曲現象的產生並研究如何從改變不同模具及製程參數所獲得之改善方式。此外，本文亦提供一項最佳的沖頭圓弧半徑及模具圓弧半徑去尋求翹曲改善，並進行實驗驗證，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U型彎曲加工製程之可行性，且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 thesis is to apply an elasto-plastic incremental finite element computer code to simulate the warping behavior of the U-bending process of a sheet metal. 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, 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. A set of U-shaped tools was designed for experiments to verify the reliability of the program. The thesis simulated the production of warping phenomenon in the U-bending process and investigated how to obtain improvement from the change of process parameters. Furthermore, the thesis provided suggestion of a better punch radius and die radius to acquire the improvement of warpage then carried out the experiment to prove it. The experimental results of U-bending 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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