本文主要研究接觸面(contact surface)問題下，物體的黏結(tie)情形分析。
共同面的位移場使用無元素法來建立，其餘結構以有限元素來分析，首先說明共同面位移場建立所遭遇的問題，並以特殊的固體元素來解決，之後推導其形狀函數與勁度矩陣參數應用於碰撞體的碰撞面上進行程式分析。
以文獻回顧的方式說明：(1)罰數法、(2)拉格朗其法、(3)網格重新切割法；再與本文研究的獨立共同介面法作比較。另外個別探討接觸面的滑動問題，分為滑動外力、滑動束制條件、滑動位移自由度來探討，並在滑動位移自由度內加入特殊固體元素來建立滑動位移場。

This paper studies the contact problem and the tie problem.
The common displacement field is establishedby element free formulation method, the remaining structure use the finite element to analyze. First, to explain the problems in creating common displacement field, and use special solid elements to resolve the problems . After the derivation of the shape functions and stiffness matrix parameters used in the collision plane of crash bodies to conduct program analysis.
Note the methods shown in the literature review: (1) penalty number, (2) Lagrange multiplier method, (3) automesh method. Further with this paper, the common interface is an independent method for comparison. In addition to individual issues of the sliding contact surface is divided into external sliding, sliding beam system conditions, the displacement degrees of freedom to explore the sliding and sliding displacement degrees of freedom to add a special element to create a solid sliding displacement field.

【1】 Yukio Tada and Shoutatsu Nishlhara ,“Optimum shape design of contact surface with inite element method” , Advances in Engineering Software, Vol.18, pp.75-85, (1993) .

【2】 A.R. Khoei*, M. Nikbakht , “An enriched finite element algorithm for numerical computation of contact friction problems”, International Journal of Mechanical Sciences, Vol. 49, pp.183-199, (2007).

【3】 Alexander Konyukhov, Karl Schweizerhof *, “Covariant description of contact interfaces considering anisotropy for adhesion and friction.Part 2. Linearization, finite element implementation and numerical analysis of the model”, Comput. Methods Appl. Mech. Engrg, Vol.196, pp.289-309, (2006).

【4】 C. Mary, S. Fouvry*, “Numerical prediction of fretting contact durability using energy wear approach: Optimisation of finite-element model”, Wear, Vol.263, pp.444-450, (2007).

【5】 Xian Chen and Kenji Sunagaw and Toshiaki Hisada, “Development of a finite element contact analysis algorithmfor charged-hydrated soft tissues with large sliding”, Int. J. Numer. Meth. Engng, Vol.78, pp.483-504, (2009).

【6】 W.-H. Chen and J.-T. Yen, “Three-Dimensional finite element analysis of static and dynamic contact problems with friction”, Compurers & Sfructures, Vol.35, No.5, pp. 541-552, (1990).

【7】 A.R.Khoei *, S.O.R. Biabanaki, M. Anahid, “A Lagrangian-extended finite-element method in modeling large-plasticity deformations and contact problems”, International Journal of Mechanical Sciences, Vol.51, pp.384-401, (2009).
【8】 Chan-Ping Pan and Hsing-Chih Tsai, “Element free formulationfor connecting sub-domains modeled by finite elements”, Structural Engineering and Mechanics, Vol.25, No. 4, pp. 467-480, (2007).
【9】 蔡幸致，「獨立位移場間之連接」，博士論文，國立台灣科技大學營建工程系，(2004)。
【10】 徐秉業、劉信聲，「應用彈性力學」，凡異出版社，(1997)。
【11】 潘子瑜，「結構有限元素分析：理論與AMPS套裝軟體支應用」，碩士論文，國立台灣科技大學營建工程系，(2007)。
【12】 梁文明，「以有限元素法求取鋼筋混凝土桿件之勁度矩陣」，碩士論文，國立台灣科技大學營建工程系，(2008)。
【13】 林嘉員，「二為平面應力無元素法之推導及程式建構」，碩士論文，國立台灣科技大學營建工程系，(2003)。
【14】 沈國瑞，「無元素分析之積分權值調整法」，博士論文，國立中央大學土木工程系，(2002)。
【15】 錢偉長，「變分法及有限元素法」，亞東書局，(1991)。
【16】 洪維聰，「二為無元素法之網格自動佈建」，碩士論文，國立台灣科技大學營建工程系，(2005)。