【正文】 中起著關(guān)鍵的作用。 關(guān)鍵詞：無(wú)摩擦性接觸，大的變形，有限元 有限元方法廣泛應(yīng)用在解決接觸性問(wèn)題上。從完全的計(jì)算角度來(lái)看， 接觸性的檢測(cè)和隨后的強(qiáng)制性約束 的實(shí)現(xiàn)是有待解決一般算法結(jié)構(gòu)的發(fā)展的兩個(gè)重要問(wèn)題。 節(jié)點(diǎn)正交的使用包括一個(gè)（二個(gè)）點(diǎn)或一個(gè)（兩個(gè)）基座或點(diǎn)和面的接觸。在第 5 節(jié)中，給出了結(jié)束的評(píng)論。這意味著這兩機(jī)構(gòu)問(wèn)題一直有 ????? 21 tt （ 1） 在任何給定的時(shí)間上，所說(shuō)的這兩個(gè)機(jī)構(gòu)都與它們的邊界子集 C 有聯(lián)系，當(dāng)且僅當(dāng) ???????? Ctt :21 (2) 根據(jù)上面的定義，每個(gè)物體的定義可以被唯一的分為三個(gè)相互排斥的區(qū)域 ，根據(jù)下面的式子 Cqut ??????? ??? 當(dāng)?shù)依锟巳R和諾艾曼邊界條件 分別地 被強(qiáng)加在 ?u? 上 ?q? 。()。而且由于 0)( ??pg on ?t?? (8) 不等式 (5b)是從 (4d)的形式中得到的，而且假定 q 是非負(fù)的。約束條件 (4d)是無(wú)約束的（因此允許受約束的滲透來(lái)替代）替代區(qū)域是確定的，則有 ???? ? ??????????? ? ??? ? Cnxxx dynwwgdtwdvbwpdvtdi v w q xtt 0)(}:{ 221)(2 1 ????? ???? ? (11) 在約束條件下 ，原始的無(wú)約束問(wèn)題等同與一個(gè)凸面的最小化問(wèn)題 ，序列的解決方案 ??u 當(dāng) ??? 時(shí)表明收斂是約束問(wèn)題的解決方案 (5).12 實(shí)踐中，罰數(shù)方法成功的用在平衡狀態(tài)下與最小總勢(shì)能不相關(guān)的情況下 。 撇開推行細(xì)節(jié)，接觸面 )1(C 是被一系列正常的從1t?? 到 2t?? 的投影（不定靠近點(diǎn)）所離散，如圖表 2 中所示。這種收斂性分析，目前盡管并不適用于這里的兩體接觸問(wèn)題的動(dòng)非線性這方面，但是它為可允許區(qū)域的選擇提供了一個(gè)準(zhǔn)則 。 finite elements 1. INTRODUCTION Finite element methods are used extensively in the solution of contact problems. From a purely putational standpoint, detection of contact and subsequent satisfaction of the imperability constraint are the two key issues to be addressed in the development of a general algorithmic framework. Numerous methodologies have been proposed in the literature of pulational contact mechanics since the early works of Conry and Seircg,1 and Chan and Tuba. 2 A fairly prehensive survey on the topic is found in The present work is concerned with the development of finite element methods suitable for the solution of twobody contact problems in the presence of large motions and deformations. This class of problems is of particular significance in numerous practical applications, such as metal forming processes and vehicular crash analyses. Various mercial and research puter codes employ algorithms for the solution of such problems. Lagrange multiplier method, 4 and their regularizations (penalty and augmented Lagrangian methods ) are typically used in enforcing imperability. The choice of integration method for the worklike term associated with the contact tractions in the weak form of linear momentumbalance plays a pivotal role in the 8 construction of contact elements. Use of nodal quadrature involving the contacting nodes of one of (resp. both) surfaces yields the standard onepass (resp. twopass) nodeonsurface algorithms. 7 Other integration rules are also applicable, provided there exists a continuous discretization of the contact interface. The main contribution of the present paper is in the identification of a genneral procedure according to which the twobody problem is approached as a sequence of two simultaneous subproblems. As in the traditional twopass algorithms, the surfaces of both interacting bodies are used in the analysis without need for introduction of an (often arbitrarily chosen) intermediate contact surface. The main advantage of the proposed approach over the twopass nodeonsurface algorithms if that it allows for a straightforward interpretation of the integration rules used on the contacting surfaces and, for appropriate choices of admissible fields, permits the exact transmission of constant pressure from one body to another. In the spirit of the patch test originating in the work of Irons, 10 and its subsequent generalizations, capability for exact representation of constant pressure (in both magnitude and direction) is viewed as a necessary condition for robustness and convergence of the overall contact algorithm. A brief exposition to contact mechanics is presented in Section 2, with particular emphasis on formulations to be used in the ensuing algorithmic developments. A twodimensional contact element is proposed and analysed in Section 3,while the results of selected numerical simulations using this element are presented and discussed in Section remarks are given in Section 5. 2. THE TWOBODY CONTACT PROBLEM Consider bodies ,2,1, ?? ?? identified with open and connected sets ?? in linear space 3? , equipped with canonical basi