| Title:
|
Solution of Signorini's contact problem in the deformation theory of plasticity by secant modules method (English) |
| Author:
|
Nečas, Jindřich |
| Author:
|
Hlaváček, Ivan |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
1983 |
| Pages:
|
199-214 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level. (English) |
| Keyword:
|
Kachanov’s iterative method |
| Keyword:
|
elastostatics |
| Keyword:
|
deformation |
| Keyword:
|
unilateral contact |
| Keyword:
|
elastoplastic body |
| Keyword:
|
rigid foundation |
| Keyword:
|
neglecting friction |
| Keyword:
|
governed by Hencky-von Mises stress strain relations |
| Keyword:
|
weak solution |
| Keyword:
|
minimum of potential energy |
| Keyword:
|
corresponding variational inequality |
| Keyword:
|
secant modules |
| Keyword:
|
classical Signorini’s problem |
| Keyword:
|
convergence |
| Keyword:
|
no numerical applications |
| MSC:
|
49A29 |
| MSC:
|
49J40 |
| MSC:
|
58E35 |
| MSC:
|
73E99 |
| MSC:
|
73T05 |
| MSC:
|
74A55 |
| MSC:
|
74C99 |
| MSC:
|
74G30 |
| MSC:
|
74H25 |
| MSC:
|
74M15 |
| idZBL:
|
Zbl 0512.73097 |
| idMR:
|
MR0701739 |
| DOI:
|
10.21136/AM.1983.104027 |
| . |
| Date available:
|
2008-05-20T18:22:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104027 |
| . |
| Reference:
|
[1] J. Nečas I. Hlaváček: Mathematical Theory of Elastic and Elasto-Plastic Bodies.Elsevier, Amsterdam 1981. |
| Reference:
|
[2] J. Haslinger I. Hlaváček: Contact between elastic bodies.Apl. mat. 25 (1980), 324-348, 26 (1981), 263-290, 321-344. |
| Reference:
|
[3] I. Hlaváček J. Nečas: On inequalities of Korn's type.Arch. Ratl. Mech. Anal., 36 (1970), 305-334. MR 0252844, 10.1007/BF00249518 |
| Reference:
|
[4] 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:
|
[5] L. M. Kačanov: Mechanika plastičeskich sred.Moskva 1948. |
| Reference:
|
[6] G. Fichera: Boundary value problems of elasticity with unilateral constraints.In: S. Flüge (ed): Encycl. of Physics, vol. VIa/2, Springer-Verlag, Berlin, 1972. |
| Reference:
|
[7] I. Hlaváček J. Lovíšek: A finite element analysis for the Signorini problem in plane elastostatics.Apl. mat. 22, (1977) 215-228, 25 (1980), 273-285. MR 0446014 |
| . |
