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 本研究主要係針對結構行為中的接觸問題進行詳盡的討論。對結構之接觸問題，本文提供了一個新的演算法則，並推導出相關的靜態與動態特性公式。 本方法主要是將接觸區域的邊界協調條件與平衡方程式直接導入有限元素公式中，並舉二維椼架結構、二維樑結構、三維椼架結構、空間板結構與實體元素結構等例子加以驗證。研究結果顯示本方法具有相當意義。對預知兩結構或多結構在接觸區域間的磨耗或結構因高速旋轉而產生的瞬間撞擊與破壞…等方面之研究將可提供重要的參考價值。
 ABSTRACT In this research, contact problems in structural behaviors are studied. A new algorithm is introduced and the corresponding formulations in both the static and the natural dynamic responses are derived. The idea of this work is initiated by directly substituting the conditions of compatibility and equilibrium into the finite element formula on the contact regions. Typical structures, such as two-dimensional truss, two-dimension beam, three-dimension frame, spatial plate and solid elements are demonstrated. Results show that the algorithm proposed here is significant and value for further studies such as the prediction of wears at contact regions on two or more structures, sudden impact of structures caused by high-speed rotation or crack-induced parts, etc.
 目 錄 誌 謝.................................................Ⅰ 中文摘要.................................................Ⅱ 英文摘要.................................................Ⅲ 目 錄.................................................Ⅳ 圖 目 錄.................................................Ⅵ 表目錄...................................................Ⅹ 符號說明.................................................XI 第一章 緒論..............................................1 1.1前言.............................................1 1.2文獻回顧.........................................2 1.3研究方法與目的...................................4 第二章 靜態接觸問題公式推導...............................6 2.1前言.............................................6 2.2兩物體靜態接觸公式推導...........................7 2.3多物體靜態接觸公式推導..........................10 2.4靜態接觸公式討論................................15 第三章 動態接觸問題公式推導..............................16 3.1前言............................................16 3.2兩物體動態接觸公式推導..........................17 3.3多物體動態接觸公式推導..........................22 3.4動態接觸公式討論................................30 第四章 實例與討論........................................31 4.1前言............................................31 4.2二維衍架結構....................................32 4.3平面樑結構......................................36 4.4空間樑結構......................................40 4.5空間板元素結構..................................43 4.6殼元素之葉片結構................................46 4.7實體元素之葉片結構..............................59 第五章 結論與展望........................................71 5.1結論............................................71 5.2展望............................................72 附錄一：有限元素特性矩陣.................................73 附錄二：高斯積分法.......................................83 參考文獻.................................................85 作者簡介.................................................90
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