| Title:
|
Contact between elastic bodies. I. Continuous problems (English) |
| Author:
|
Haslinger, Jaroslav |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
25 |
| Issue:
|
5 |
| Year:
|
1980 |
| Pages:
|
324-347 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
zero friction |
| Keyword:
|
small deformations |
| Keyword:
|
basic relations |
| Keyword:
|
minimum principles for potential energy |
| Keyword:
|
conditions which guarantee existence and uniqueness of weak solutions |
| Keyword:
|
one-dimensional spaces of rigid virtual displacements |
| MSC:
|
35P99 |
| MSC:
|
49J40 |
| MSC:
|
73T05 |
| MSC:
|
74A55 |
| MSC:
|
74M15 |
| idZBL:
|
Zbl 0449.73117 |
| idMR:
|
MR0590487 |
| DOI:
|
10.21136/AM.1980.103868 |
| . |
| Date available:
|
2008-05-20T18:14:58Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103868 |
| . |
| Reference:
|
[1] H. Hertz: Miscellaneous Papers.Mc Millan, London 1896. |
| Reference:
|
[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. Zbl 0226.73052, 10.1016/0020-7403(71)90032-4 |
| Reference:
|
[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. 10.1115/1.3408787 |
| Reference:
|
[4] A. Francavilla, O. C. Zienkiewicz: A note on numerical computation of elastic contact problems.Intern. J. Numer. Meth. Eng. 9 (1975), 913 - 924. 10.1002/nme.1620090410 |
| Reference:
|
[5] B. Fredriksson: Finite element solution of surface nonlinearities in structural mechanics.Соmр. & Struct. 6 (1976), 281 - 290. Zbl 0349.73036, 10.1016/0045-7949(76)90003-1 |
| Reference:
|
[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. Zbl 0332.73018, MR 0426584, 10.1007/BF00534623 |
| Reference:
|
[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. Zbl 0359.73017, MR 0669228 |
| Reference:
|
[8] G. Duvaut, J. L. Lions: Les inéquations en mécanique et en physique.Paris, Dunod 1972. Zbl 0298.73001, MR 0464857 |
| Reference:
|
[9] A. Signorini: Questioni di elasticità non linearizzata o serni-linearizzata.Rend. di Matem. e delle sue appl. 18 (1959). MR 0118021 |
| Reference:
|
[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. |
| Reference:
|
[11] I. Hlaváček, J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal., 36 (1970), 305-334. Zbl 0193.39002, MR 0252844, 10.1007/BF00249518 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| . |
