转向节外文文献翻译--一种无摩擦接触问题的有限元方法(编辑修改稿)

转向节外文文献翻译--一种无摩擦接触问题的有限元方法(编辑修改稿)内容摘要：

sts 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 basis ( 1E , 2E , 3E ) and the usual Euclidean norm. At least one of the bodies is assumed to be deformable. A typical material point of  in the reference configuration is algebraically specified by vector  of material point  in the current configuration is given by ),( t   at each time t, and the displacement 9 vector u is defined according to    ),(:),( ttu The mapping  is assumed smooth throughout its domain and invertible at least on  .Body and its boundary in the current configuration (at time t) are identified with t and t ,respectively, hence ),(: tt    and ),(: tt    .Also, the outer unit normal to t is denoted by n . The motion of any system of bodies (including a single body) is subject to the principle of imperability of matter, as stated by Truesdell and Toypin in Reference11 ().This implies for the twobody problem that at all times  21 tt （ 1） At any given time, the two bodies are said to be in contact along a subset C of their boundaries if, and only if,  Ctt :21 (2) It follows from the above defiion that the boundary of each body can be uniquely deposed into three mutually exclusive regions according to Cqut   Where Dirichlet and Neumann boundary conditions are enforced on u and q , respectively. Although not explicitly noted, it should be clear from the above that u , q and C generally depend on time. Gap functions )(g , possibly multivalued, can be defined on the boundary of each body as follows: for each 22 tx  ,  12)1( : ttg is given by 112)1( )( nxxg  （ 2a） Where )。 ( 1211 nxxx  is such that 0)( 112  nxx see Fifure of 1 renders )1(g singlevalued, although such a restrictive geometric condition will not be 10 imposed at the outset . A pletely analogous definition for  21)2( : ttg yields 221)2( )(: nxxg  (2b) Where,again, for each 11 tx  , )。 ( 2122 nxxx  satisfies 0)( 221  nxx .Defining equations (2a) and (2b) imply that gap functions )1(g and )2(g are identically equal to zero on C, namely that 0)(:)。 ()。 ( 2)2(1)1(  CgCgCg tt (3) Consequently, imperability condition (1) can be rewritten in terms of the above gap functions as 0,0 )2()1(  gg At the absence of inertial effects, the local form of the equati。