| Title:
|
Uniqueness of the solution of the boundary-initial value problem for a linear elastic Cosserat continuum (English) |
| Author:
|
Hlaváček, Miroslav |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
16 |
| Issue:
|
6 |
| Year:
|
1971 |
| Pages:
|
402-411 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper presents the proofs of two theorems of uniqueness of the solution of the mixed boundary-initial value problem for elastic Cosserat continuum. The first of the theorems deals with an anisotropic material and is deduced for bounded regions. Except for certain symmetry no restrictive assumptions are imposed on the anisotropy tensors. The second theorem concerns an isotropic material and is formulated for a certain class of unbounded regions. In addition to the inequalities that are necessary and sufficient for positive definitness of the strain energy density, two other restrictive inequalities must be assumed for the material constants. () |
| MSC:
|
74B99 |
| MSC:
|
74G30 |
| MSC:
|
74H25 |
| MSC:
|
74H99 |
| idZBL:
|
Zbl 0229.73015 |
| idMR:
|
MR0297188 |
| DOI:
|
10.21136/AM.1971.103375 |
| . |
| Date available:
|
2008-05-20T17:51:58Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103375 |
| . |
| Reference:
|
[1] Knops R. J., Payne L. E.: Uniqueness in classical elastodynamics.Arch. Ratl. Mech. Anal., 27 (1968), 5, 349-355. MR 0219261, 10.1007/BF00251437 |
| Reference:
|
[2] Wheeler L. T., Sternberg E.: Some theorems in classical elastodynamics.Arch. Ratl. Mech. Anal., 31 (1968), 1, 51 - 90. Zbl 0187.47003, MR 1553519, 10.1007/BF00251514 |
| Reference:
|
[3] Eringen A. C.: Linear theory of micropolar elasticity.Journ. Math. Mech., 15 (1966), 6, 909-923. Zbl 0145.21302, MR 0198744 |
| Reference:
|
[4] Аэро Э. Л., Кувшинский Е. В.: Континуальная теория асимметрической упругости.Физ. TB. тела, 6 (1964), 9, 2689-2699. Zbl 1117.65300 |
| Reference:
|
[5] Neuber H.: On the general solution of linear-elastic problems in isotropic and anisotropic Cosserat continua.Appl. Mech., Proc. 11-th intern, congress of appl. mech., Munich 1964. |
| Reference:
|
[6] Mindlin R. D., Tiersten F. F.: Effects of couple-stresses in linear elasticity.Arch. Ratl. Mech. Anal., 11 (1962), 415-448. MR 0144513, 10.1007/BF00253946 |
| Reference:
|
[7] Mindlin R. D., Eshel N. N.: On the first strain gradient theories in linear elasticity.Int. Journ. Solids and Struct., 4 (1968), 1, 75-95. 10.1016/0020-7683(68)90036-X |
| Reference:
|
[8] Edelstein W. S.: A uniqueness theorem in the linear theory of elasticity.Acta Mech., 8 (1969), 183-187. Zbl 0194.28403, MR 0272240, 10.1007/BF01182259 |
| Reference:
|
[9] Mindlin R. D.: Microstructure in linear elasticity.Arch. Ratl. Mech. Anal., 16 (1964), 51-78. MR 0160356, 10.1007/BF00248490 |
| Reference:
|
[10] Hlaváček M., Kopáčková M.: Theorems of the linear elastostatic Cosserat continuum for exterior domains.Zeit. f. angew. Math. Mech., 50 (1970), 5, 295-302. MR 0267820, 10.1002/zamm.19700500504 |
| Reference:
|
[11] Hlaváček I., Hlaváček M.: On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses.I - Cosserat continuum, II - Mindlin's elasticity with microstructure and the first strain-gradient theory, Aplikace matematiky 14 (1969), 5, 387-410, 411-426. MR 0250537 |
| Reference:
|
[12] Gurtin M. E., Sternberg E.: Theorems in linear elastostatics for exterior domains.Arch. Ratl. Mech. Anal., 8 (1961), 99-119. Zbl 0101.17001, MR 0133972, 10.1007/BF00277433 |
| Reference:
|
[13] Zaremba S.: Sopra un teorema d'unicitá relative alla equazione delle onde sferiche.Atti della Reale Accad. dei Lincei, ser. 5, 24 (1915), 904. |
| Reference:
|
[14] Kellogg O. D.: Foundations of potential theory.Berlin, Springer, 1929. MR 0222317 |
| . |
