Approximation of Thermoelasticity Contact Problem With Nonmonotone Friction
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摘要: 给出了一个变形体和刚性基础之间用双边摩擦表达其接触性质的、静态热弹性问题的方程式及其近似解法.以非单调、多值性表示该摩擦定律.忽略了问题的耦合效应,则问题的传热部分与弹性部分各自独立处理.位移矢量公式化为非凸的次静态问题,用局部Lipschitz连续函数来表示变形体的总势能.用有限单元法近似求解全部问题.Abstract: The formulation and approxmiation of a static thermoelasticity problem that described bilateral frictional contact between a deformable body and a rigid foundation was presented. The friction was in the form of nonmonotone and multivalued law. The coupling effect of the problem was neglected, therefore the thermic part of the problem was considered independently of the elasticity problem. For the displacement vector, a substationary problem for non-convex, locally Lipschitz continuous functional representing the total potential energy of the body was form ulated. All problems form ulated were approxmiated by the finite element method.
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[1] Panagiotopoulos P D.Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions[M]. Boston, Basel, Stuttgart: Birkhuser, 1985. [2] Panagiotopoulos P D.Hemivariational Inequalities: Applications in Mechanics and Engineering[M]. Berlin, Heidelberg, New York: Springer, 1993. [3] Denkowski Z, Migórski S. A system of evolution hemivariational inequalities modeling thermoviscoelastic frictional contact[J].Nonlinear Analysis, 2005, 60(8): 1415-1441. doi: 10.1016/j.na.2004.11.004 [4] Goeleven D, Motreanu D, Dumont Y,et al.Variational and Hemivariational Inequalities. Theory, Methods and Applications, Volume Ⅰ: Unilateral Analysis and Unilateral Mechanics[M]. Boston, Dordrecht, London: Kluwer, 2003. [5] Goeleven D, Motreanu D.Variational and Hemivariational Inequalities. Theory, Methods and Applications, Volume Ⅱ: Unilateral Problems[M]. Dordrecht, London: Kluwer, 2003. [6] Naniewicz Z, Panagiotopoulos P D.Mathematical Theory of Hemivariational Inequalities and Applications[M]. New York, Basel, Hong Kong: Marcel Dekker, 1995. [7] Haslinger J, Miettinen M, Panagiotopoulos P D.Finite Element Method for Hemivariational Inequalities. Nonconvex Optimization and Its Applications[M].Vol 35, Dordrecht: Kluwer, 1999. [8] Baniotopoulos C C, Haslinger J, Morávková Z. Mathematical modeling of delamination and nonmonotone friction problems by hemivariational inequalities[J].Appl Math, 2005, 50(1): 1-25. doi: 10.1007/s10492-005-0001-7 [9] Miettinen M, Haslinger J. Approximation of nonmonotone multivalued differential inclusions[J].IMA J Numer Anal, 1995, 15(4): 475-503. doi: 10.1093/imanum/15.4.475 [10] Miettinen M, Mkel M M, Haslinger J. On numerical solution of hemivariational inequalities by nonsmooth optimization methods[J].J Global Optimization, 1995, 6(4): 401-425. doi: 10.1007/BF01100086 [11] Miettinen M, Haslinger J. Finite element approximation of vector-valued hemivariational problems[J].J Global Optimization, 1997, 10(1): 17-35. doi: 10.1023/A:1008234502169 [12] Lukan L, Vlcˇek J. A bundle-Newton method for nonsmooth unconstrained minimization[J].Math Prog, 1998, 83(1/3): 373-391. [13] Baniotopoulos C C, Haslinger J, Morávková Z.Contact problems with nonmonotone friction: discretization and numerical realization[J].Comput Mech, 2007, 40(1): 157-165. doi: 10.1007/s00466-006-0092-3 [14] Adams R S. Sobolev Spaces.Pure and Applied Mathematics[M].Vol 65.New York,London: Academic Press, 1975. [15] Kufner A, John O, Fucˇik S.Function Spaces[M]. Leyden: Noordhoff International Publishing and Prague: Academia, 1977. [16] Necˇas J.Les Méthodes Directes en Théorie des quations Elliptiques[M]. Paris: Masson, 1967. [17] Clarke F H.Optimization and Nonsmooth Analysis[M]. New York, Chichester, Brisbane, Toronto and Singapore: Wiley, 1983. [18] Ciarlet P G.The Finite Element Method for Elliptic Problems[M]. Amsterdam: North-Holland, 1978. [19] Glowinski R, Lions J L. Trémoliéres R.Numerical Analysis of Variational Inequalities. Series in Mathematics and Applications[M]. Vol 8. Amsterdam: North-Holland, 1981.
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