On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 2, pp. 185-213. 
@article{M2AN_1996__30_2_185_0,
     author = {Nazarov, Serguei A.},
     title = {On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {185--213},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {30},
     number = {2},
     year = {1996},
     mrnumber = {1382110},
     zbl = {0840.73032},
     language = {en},
     url = {http://archive.numdam.org/item/M2AN_1996__30_2_185_0/}
}
TY  - JOUR
AU  - Nazarov, Serguei A.
TI  - On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1996
SP  - 185
EP  - 213
VL  - 30
IS  - 2
PB  - AFCET - Gauthier-Villars
PP  - Paris
UR  - http://archive.numdam.org/item/M2AN_1996__30_2_185_0/
LA  - en
ID  - M2AN_1996__30_2_185_0
ER  - 
%0 Journal Article
%A Nazarov, Serguei A.
%T On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1996
%P 185-213
%V 30
%N 2
%I AFCET - Gauthier-Villars
%C Paris
%U http://archive.numdam.org/item/M2AN_1996__30_2_185_0/
%G en
%F M2AN_1996__30_2_185_0
Nazarov, Serguei A. On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate. ESAIM: Modélisation mathématique et analyse numérique, Tome 30 (1996) no. 2, pp. 185-213. http://archive.numdam.org/item/M2AN_1996__30_2_185_0/

[1] A. L. Gol'Denveizer, 1976, Theory of thin elastic shells, 2nd rev. ed., Moscow : Nauka (Russian : English transl. (1961) of 1st ed., Pergamon Press, Oxford).

[2] P. G. Ciarlet, 1990, Plates and junctions in elastic multi-structures, Paris, New York, Masson. | MR | Zbl

[3] V. L. Berdichevskii, 1983, Variational principles in continuum mechanics, Moscow, Nauka (Russian). | MR | Zbl

[4] S. A. Nazarov, 1983, Introduction to asymptotic methods of the theory of elasticity, Leningrad University, Leningrad (Russian).

[5] E. Sanchez-Palencia, 1990, Passage à la limite de l'élasticité tridimensionnelle à la théorie asymptotique des coques minces, C.R. Acad. Paris, Ser. 2, 311, pp. 909-916. | MR | Zbl

[6] K. O. Friedrichs, R. F. Dressler, 1961, A boundary-layer theory for elastic plates, Comm. Pure Appl. Math. 14, pp. 1-33. | MR | Zbl

[7] A. L. Gol'Denveizer, A. V. Kolos, 1965, On the construction of two-dimensional equations of the theory of thin elastic plates, Prikl. Mat. Mech. 29, pp. 141-155 (Russian).

[8] S. A. Nazarov, 1982, The structure of solutions of elliptic boundary value problems in thin domains, Vestnik Leningrad, Univ., no. 7, 65-68 (Russian : English transl. (1983) in Vesthik Leningrad Univ. Math., 15). | MR | Zbl

[9] R. D. Gregory, F. V. M. Wan, 1984, Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory, J. Elast., 14, pp. 27-64. | MR | Zbl

[10] A. L. Gol'Denveizer, 1962, Derivation of an approximate theory of bending of a plate by the method of asymptotic integration of the equations of the theory of elasticity, Prikl. Mat. Mech., 26, pp. 668-686 (Russian, English transl. (1964) in J. Appl. Mat. Mech., 26). | MR | Zbl

[11] P. G. Ciarlet, P. Destuynder, 1979, A justification of the two-dimensional plate model, J. Mécanique, 18, pp. 315-344. | MR | Zbl

[12] S. N. Leora, S. A. Nazarov, A. V. Proskura, 1986, Computer derivation of the limit equations for elliptic problems in thin domains, Zh. Vychisl. Mat. i Mat. Fiz., 26, pp. 1032-1048 (Russian : English transl. (1986) in USSR Comput. Math. and Math. Phys., 26). | MR | Zbl

[13] B. A. Shoihet, 1976, An energetic identity in the physically non-linear theory of elasticity and an estimate of the error of the plate equations, Prikl. Mat. Mech., 40, pp. 317-326 (Russian). | Zbl

[14] V. A. Kondrat'Ev, O. A. Oleinik, 1989, On the dependence of constants in Korn's inequalities on parameters, characterizing the geometry of a domain, Uspehi matem. nauk, 44, pp. 157-158 (Russian). | MR | Zbl

[15] D. Cioranescu, O. A. Oleinik, G. Tronel, 1989, On Korn's inequalities for frame type structures and junctions, C.R. Acad. Sci. Paris, Ser. 1, 309, pp. 591-596. | MR | Zbl

[16] S. A. Nazarov, 1992, Korn's inequalities, asymptotically precise for thin domains, Vestnik St.-Petersburg Univ., no. 8, pp. 19-24 (Russian). | MR | Zbl

[17] S. A. Nazarov, A. S. Zorin, 1989, The edge effect of bending of a thin three-dimensional plate, Prikl. Mat. Mech., 53, pp. 642-650 (Russian). | MR | Zbl

[18] S. A. Nazarov, A. S. Zorin, 1991, Two-term asymptotics of solutions of the problem on longitudinal deformation of a plate with clamped edge, Computer mechanics of solids, 2, pp. 10-21 (Russian).

[19] G. Duvaut, J.-L. Lions, 1972, Les inéquations en mécanique et en physique, Paris, Dunod. | MR | Zbl

[20] W. G. Mazja, S. A. Nazarov, D. A. Plamenewski, 1991, Asymptotische Theorie elliptischer Randwertaufgaben in singular gestörten Gebieten, Bd. 2. Berlin, Akademie-Verlag.

[21] V. A. Kondrat'Ev, 1967, Boundary value problems for elliptic equations in domains with conical or angular points, Trudy Moskov, Mat. Obshch, 16, pp. 209-292 (Russian, English transl. (1967) in Trans. Moscow Math. Soc., 16). | MR | Zbl

[22] V. G. Maz'Ya, B. A. Plamenevskii, 1977, On the coefficients in the asymptotics of solutions of elliptic boundary value problems in domains with conical points, Math. Nachr., 76, pp. 29-60 (Russian : English transl. (1984) in Amer. Math. Soc. Transl., 2, 123). | MR | Zbl

[23] S. A. Nazarov, B. A. Plamenevsky, 1994, Elliptic problems in domains with piecewise smooth boundaries, Berlin, New York, Walter de Gruyter. | MR | Zbl

[24] S. A. Nazarov, 1991, On the three-dimensional effect in the vicinity of the tip of a crack in a thin plate, Prikl. Mat. Mech., 55, pp. 500-510 (Russian). | MR | Zbl

[25] S. A. Nazarov, 1992, Three-dimensional effects at plate crack tips, C.R. Acad. Sci. Paris. Ser. 2, 314, pp. 995-1000. | Zbl