Contact between elastic bodies. I. Continuous problems

Jaroslav Haslinger; Ivan Hlaváček

Aplikace matematiky (1980)

  • Volume: 25, Issue: 5, page 324-347
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Haslinger, Jaroslav, and Hlaváček, Ivan. "Contact between elastic bodies. I. Continuous problems." Aplikace matematiky 25.5 (1980): 324-347. <http://eudml.org/doc/15157>.

@article{Haslinger1980,
abstract = {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.},
author = {Haslinger, Jaroslav, Hlaváček, Ivan},
journal = {Aplikace matematiky},
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},
language = {eng},
number = {5},
pages = {324-347},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Contact between elastic bodies. I. Continuous problems},
url = {http://eudml.org/doc/15157},
volume = {25},
year = {1980},
}

TY - JOUR
AU - Haslinger, Jaroslav
AU - Hlaváček, Ivan
TI - Contact between elastic bodies. I. Continuous problems
JO - Aplikace matematiky
PY - 1980
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 25
IS - 5
SP - 324
EP - 347
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/15157
ER -

References

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  1. H. Hertz, Miscellaneous Papers, Mc Millan, London 1896. 
  2. S. H. Chan, I. S. Tuba, 10.1016/0020-7403(71)90032-4, Intern. J. Mech. Sci, 13, (1971), 615-639. (1971) Zbl0226.73052DOI10.1016/0020-7403(71)90032-4
  3. T. F. Conry, A. Seireg, 10.1115/1.3408787, J.A.M. ASME, 2 (1971), 387-392. (1971) DOI10.1115/1.3408787
  4. A. Francavilla, O. C. Zienkiewicz, 10.1002/nme.1620090410, Intern. J. Numer. Meth. Eng. 9 (1975), 913 - 924. (1975) DOI10.1002/nme.1620090410
  5. B. Fredriksson, 10.1016/0045-7949(76)90003-1, Соmр. & Struct. 6 (1976), 281 - 290. (1976) Zbl0349.73036DOI10.1016/0045-7949(76)90003-1
  6. P. D. Panagiotopoulos, 10.1007/BF00534623, Ing. Archiv 44 (1975), 421 to 432. (1975) Zbl0332.73018MR0426584DOI10.1007/BF00534623
  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. (1976) Zbl0359.73017MR0669228
  8. G. Duvaut, J. L. Lions, Les inéquations en mécanique et en physique, Paris, Dunod 1972. (1972) Zbl0298.73001MR0464857
  9. A. Signorini, Questioni di elasticità non linearizzata o serni-linearizzata, Rend. di Matem. e delle sue appl. 18 (1959). (1959) MR0118021
  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. (1972) 
  11. I. Hlaváček, J. Nečas, 10.1007/BF00249518, Arch. Ratl. Mech. Anal., 36 (1970), 305-334. (1970) Zbl0193.39002MR0252844DOI10.1007/BF00249518
  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. (1975) MR0382827
  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. (1980) MR0600655

Citations in EuDML Documents

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  1. Jindřich Nečas, Ivan Hlaváček, Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method
  2. Jaroslav Haslinger, Miroslav Tvrdý, Approximation and numerical solution of contact problems with friction
  3. Jaroslav Haslinger, Ivan Hlaváček, Contact between elastic perfectly plastic bodies
  4. S. Drabla, M. Sofonea, B. Teniou, Analysis of a frictionless contact problem for elastic bodies
  5. Jaroslav Haslinger, Ivan Hlaváček, Contact between elastic bodies. II. Finite element analysis
  6. Van Bon Tran, Dual finite element analysis for contact problem of elastic bodies with an enlarging contact zone

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