【正文】 所提出的接觸單元是建立在從發(fā)源到標(biāo)準(zhǔn) Q9 元素（等參的九個(gè)節(jié)點(diǎn)）的移置區(qū)域和引用的辛普森標(biāo)準(zhǔn) 上的。 3. 三維接觸的兩個(gè)應(yīng)用 這篇文章的其余部分專門討論在明確表達(dá)罰數(shù)的基礎(chǔ)上的離散二維接觸問題和兩表面上的缺失函數(shù)的鑒定，像在第二節(jié)中所述。位移區(qū)域 ?u 屬于空間 ?? 即 ?????? ??????? ???uxxx onuuHu |)(1 質(zhì)量函數(shù) ?w 也屬于空間 x? ，定義為 }0|)}({ 1 ??? uxx onwHw ?????? 允許函數(shù) p ≥ 0 是分段連續(xù)的。向量 ?，在線性結(jié)構(gòu)（以 t 變化）中它的范圍是用 ?t? 和 ?t?? 來確定的，因此，則有 ),(: tt ??? ? ??? 和 ),(: tt ??? ? ????? 。 各種商業(yè)和科研計(jì)算機(jī)編碼采用的算法，以解決這種 問題。一個(gè)相當(dāng)廣泛的在題目中的調(diào)查在參考書目中發(fā)現(xiàn)。至少有一個(gè)物體是假定可變的。 在不存在慣性效應(yīng)時(shí)，方程式的局部形式控制著如下給出的每個(gè)物體的運(yùn)動(dòng)， div 0?? ??? ? bt in ?t? (4a) ?? ??uu on ?u? （ 4b） ??? ?ntnt ? on ?q? (4c) 0)( ??g on ?t? (4d) 當(dāng) ?t 是克西的應(yīng)力張量， ?? 是質(zhì)量密度， ?b 是每單位質(zhì)量的質(zhì)量力， ?u 是法定的界壁位移， ??nt是在 ?q? 上的法定牽引向量。在提出的明確表達(dá)中關(guān)鍵的一步是 (10a) 和 (10b),易于接受的規(guī)則化的罰數(shù)的引入，例如 ???? )()( ?? ? gp 由 (12)，等式 (10a)可以寫為 5 }:{ )(2 1 ???? ???? ? dtwdvbwpdvtdi v w q xtt nxxx ??? ? ? ??? ? ???? 0)2()1( 22)2(11)1( ??????????? ?? CC dnwgdnwg ???? (13) 上面的 (13)中的任意兩個(gè)積分在形式上是相同的， 即積分邊界來源于一個(gè)新問題的規(guī)則化罰數(shù)。不考慮離散化使用空間的元素（例如三角形的三個(gè)定點(diǎn)和四邊形的四個(gè)點(diǎn)）的線性規(guī)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 sel