On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate

Serguei A. Nazarov

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1996)

  • Volume: 30, Issue: 2, page 185-213
  • ISSN: 0764-583X

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Nazarov, Serguei A.. "On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 30.2 (1996): 185-213. <http://eudml.org/doc/193802>.

@article{Nazarov1996,
author = {Nazarov, Serguei A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {initial asymptotic terms; boundary layers; loading},
language = {eng},
number = {2},
pages = {185-213},
publisher = {Dunod},
title = {On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate},
url = {http://eudml.org/doc/193802},
volume = {30},
year = {1996},
}

TY - JOUR
AU - Nazarov, Serguei A.
TI - On the accuracy of asymptotic approximations for longitudinal deformation of a thin plate
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1996
PB - Dunod
VL - 30
IS - 2
SP - 185
EP - 213
LA - eng
KW - initial asymptotic terms; boundary layers; loading
UR - http://eudml.org/doc/193802
ER -

References

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  1. [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. [2] P. G. CIARLET, 1990, Plates and junctions in elastic multi-structures, Paris, New York, Masson. Zbl0706.73046MR1071376
  3. [3] V. L. BERDICHEVSKII, 1983, Variational principles in continuum mechanics, Moscow, Nauka (Russian). Zbl0526.73027MR734171
  4. [4] S. A. NAZAROV, 1983, Introduction to asymptotic methods of the theory of elasticity, Leningrad University, Leningrad (Russian). 
  5. [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. Zbl0701.73080MR1088549
  6. [6] K. O. FRIEDRICHS, R. F. DRESSLER, 1961, A boundary-layer theory for elastic plates, Comm. Pure Appl. Math. 14, pp. 1-33. Zbl0096.40001MR122117
  7. [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. [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). Zbl0509.35008MR664066
  9. [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. Zbl0536.73047MR739117
  10. [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). Zbl0118.41603MR170523
  11. [11] P. G. CIARLET, P. DESTUYNDER, 1979, A justification of the two-dimensional plate model, J. Mécanique, 18, pp. 315-344. Zbl0415.73072MR533827
  12. [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). Zbl0626.65129MR851753
  13. [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). Zbl0363.73049
  14. [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). Zbl0727.73023MR1037014
  15. [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. Zbl0937.35502MR1053284
  16. [16] S. A. NAZAROV, 1992, Korn's inequalities, asymptotically precise for thin domains, Vestnik St.-Petersburg Univ., no. 8, pp. 19-24 (Russian). Zbl0773.73018MR1280920
  17. [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). Zbl0722.73037MR1022416
  18. [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. [19] G. DUVAUT, J.-L. LIONS, 1972, Les inéquations en mécanique et en physique, Paris, Dunod. Zbl0298.73001MR464857
  20. [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. [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). Zbl0162.16301MR226187
  22. [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). Zbl0359.35024MR601608
  23. [23] S. A. NAZAROV, B. A. PLAMENEVSKY, 1994, Elliptic problems in domains with piecewise smooth boundaries, Berlin, New York, Walter de Gruyter. Zbl0806.35001MR1283387
  24. [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). Zbl0787.73059MR1134619
  25. [25] S. A. NAZAROV, 1992, Three-dimensional effects at plate crack tips, C.R. Acad. Sci. Paris. Ser. 2, 314, pp. 995-1000. Zbl0748.73009

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