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Keywords:
zero friction; small deformations; basic relations; minimum principles for potential energy; conditions which guarantee existence and uniqueness of weak solutions; one-dimensional spaces of rigid virtual displacements
zero friction; small deformations; basic relations; minimum principles for potential energy; conditions which guarantee existence and uniqueness of weak solutions; one-dimensional spaces of rigid virtual displacements
Summary:
Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.
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References:
[1] H. Hertz: Miscellaneous Papers. Mc Millan, London 1896.
[2] S. H. Chan, I. S. Tuba: A finite element method for contact problems of solid bodies. Intern. J. Mech. Sci, 13, (1971), 615-639. DOI 10.1016/0020-7403(71)90032-4 | Zbl 0226.73052
[3] T. F. Conry, A. Seireg: A mathematical programming method for design of elastic bodies in contact. J.A.M. ASME, 2 (1971), 387-392. DOI 10.1115/1.3408787
[4] A. Francavilla, O. C. Zienkiewicz: A note on numerical computation of elastic contact problems. Intern. J. Numer. Meth. Eng. 9 (1975), 913 - 924. DOI 10.1002/nme.1620090410
[5] B. Fredriksson: Finite element solution of surface nonlinearities in structural mechanics. Соmр. & Struct. 6 (1976), 281 - 290. DOI 10.1016/0045-7949(76)90003-1 | Zbl 0349.73036
[6] P. D. Panagiotopoulos: A nonlinear programming approach to the unilateral contact - and friction - boundary value problem in the theory of elasticity. Ing. Archiv 44 (1975), 421 to 432. DOI 10.1007/BF00534623 | MR 0426584 | Zbl 0332.73018
[7] G. Duvaut: Problèmes de contact entre corps solides deformables. Appl. Meth. Fund. Anal. to Problems in Mechanics, (317 - 327), ed. by P. Germain and B. Nayroles, Lecture Notes in Math., Springer-Verlag 1976. MR 0669228 | Zbl 0359.73017
[8] G. Duvaut, J. L. Lions: Les inéquations en mécanique et en physique. Paris, Dunod 1972. MR 0464857 | Zbl 0298.73001
[9] A. Signorini: Questioni di elasticità non linearizzata o serni-linearizzata. Rend. di Matem. e delle sue appl. 18 (1959). MR 0118021
[10] G. Fichera: Boundary value problems of elasticity with unilateral constraints. Encycl. of Physics (ed. by S. Flugge), vol. VIa/2, Springer-Verlag, Berlin 1972.
[11] I. Hlaváček, J. Nečas: On inequalities of Korn's type. Arch. Ratl. Mech. Anal., 36 (1970), 305-334. DOI 10.1007/BF00249518 | MR 0252844 | Zbl 0193.39002
[12] J. Nečas: On regularity of solutions to nonlinear variational inequalities for second-order elliptic systems. Rend. di Matematica 2, (1975), vol. 8, Ser. Vl, 481 - 498. MR 0382827
[13] J. Nečas, I. Hlaváček: Matematická teorie pružných a pružně plastických těles. SNTL Praha (to appear). English translation: Mathematical theory of elastic and elastoplastic bodies. Elsevier, Amsterdam 1980. MR 0600655
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