Asymptotically exact joining conditions at the junction of plates with very different characteristics

Journal of Applied Mathematics and Mechanics

Volumn 62, Issue 2, 1998, Pages 253-261

  Aldoshina, I A ^a   Nazarov, S A ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032219230     PISSN: 00218928     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8928(98)00032-X     Document Type: Article

References (31)

1. 1. GOL'DENVEIZER, A. L., Theory of Thin Elastic Shells. Nauka, Moscow, 1976.
2. 2. GOL'DENVEIZER, A. L. and KOLOS, A. V., The construction of the two-dimensional equations of elastic thin plates. Prikl. Mat. Mekh., 1965, 29(1), 141-155.
3. 3. FRIEDRICHS, K. O. and DRESSLER, R. F., A boundary-layer theory for elastic plates. Communs. Pure Appl. Math., 1961, 14, 1, 1-33.
4. 4. NAZAROV, S. A., Introduction to Asymptotic Methods in the Theory of Elasticity. Izd. Leningrad. Gos. Univ., Leningrad, 1983.
5. 5. GREGORY, R. D. and WAN, F. V., Decaying states of plane strain in a semi-infinite strip and boundary conditions for plate theory. J. Elast., 1984, 14, 1, 27-64.
6. 6. KOITER, W. T., On the mathematical foundation of shell theory. Act. Congr. Int. Math. Paris, 1971, 3, 123-130.
7. 7. SHOIKHET, B. A., An energy identity in physically non-linear elasticity and an estimate of the error in the equations of plates. Prikl. Mat. Mekh., 1976, 40(2), 317-326.
8. 8. CIARLET, P. G., Plates and junctions in elastic multi-structures. Paris: Masson, 1990, 215.
9. 9. KUCHERENKO, V. V. and POPOV, V. A., Asymptotic behaviour of the solution of problems of elasticity theory in thin domains. Dokl. Akad. Nauk SSSR, 1984, 274(1), 58-61.
10. 10. ZORIN, I. S. and NAZAROV, S. A., Edge effect in the bending of a thin three-dimensional plate. Prikl. Mat. Mekh., 1989, 53(4), 642-650.
11. 11. ZORIN, I. S. and NAZAROV, S. A., Two-term asymptotic form of the solution of a problem on the longitudinal deformation of a plate, clamped along the edge. Vychisl. Mekh. Deform. Tverd. Tela, 1991, 2, 10-21.
12. 12. NAZAROV, S. A. and SEMENOV, B. N., The asymptotic form of the solution of the problem of the bending of plates with discontinuous loads. Prikl. Mekh., Izd. Leningrad Gos. Univ., Leningrad, 1981, No. 5, 135-145.
13. 13. GOLD'SHTEIN, R. V. and KOREL'SHTEIN, L. B., The method of asymptotic integration and the "method of springs" in problems of elastic plates with an elongated cut. Prikl. Mat. Mekh., 1988, 52(4), 666-674.
14. 14. NAZAROV, S. A. and PLAMENEVSKII, B. A., Elliptic Problems in Domains with a Piecewise Smooth Boundary. Nauka, Moscow, 1991.
15. 15. PÓLYA, G. and SZEGÖ, G., Isoperimetric Inequalities in Mathematical Physics. Princeton University Press, Princeton, NJ, 1951.
16. 16. ZORIN, I. S., MOVCHAN, A. B. and NAZAROV, S. A., On the application of elastic capacitance, polarization and associated deformation tensors. In Investigations in Elasticity and Plasticity. Izd. Leningrad. Gos. Univ., Leningrad, 1990, 16, 75-91.
17. 17. VISHIK, M. I. and LYUSTERNIK, L. A., Regular degeneration and the boundary layer for linear differential equations with a small parameter. Uspekhi Mat. Nauk, 1957, 12, 5, 3-122.
18. 18. NAZAROV, S. A. and ROMASHEV, Yu. A., The change in the intensity factor when a narrow ligament between two collinear cracks fractures. Izv. Akad. Nauk ArmSSR. Mekhanika, 1982, 35(4), 30-40.
19. 19. MAZ'YA, V. G., NAZAROV, S. A. and PLAMENEVSKII, B. A., Calculation of the "intensity factor" when corner or conical points approach one another. Zh. Vychisl. Mat. Mat. Fiz., 23(2), 333-346.
20. 20. SANCHEZ-PALENCIA, E., Forces appliquées á une petit région de la surface d'un corps élastique. Application aux jonctions. Cr. Acad. Sci. Paris. Ser. II., 1988, 307, 689-694.
21. 21. NAZAROV, S. A. and POLYAKOVA, O. R., The fracture of a narrow ligament between cracks lying in the same plane. Prikl. Mat. Mekh., 1991, 55(1), 157-165.
22. 22. GADYL'SHIN, R. R., The method of matched asymptotic expansions in the problem of a Helmholtz acoustic resonator. Prikl. Mat. Mekh., 1992, 56(3), 412-418.
23. 23. MAZJA, W. G., NASAROW, S. A. and PLAMENEWSKI, B. A., Asymptotische Theori elliptischer Randwertaufgaben in singulär gestörten Gebieten. Berlin: Akademie, 1991, 430.
24. 24. NAZAROV, S. A. and PLAMENEVSKII, B. A., The asymptotic form of the spectrum of the Neyman problem in singularly degenerating domains. Algebra i Analiz, 1990, 2(2), 85-111.
25. 25. LEGUILLON, D. and SANCHEZ-PALENCIA, E., Approximation of a 2-D problem of junctions. Comput. Mech., 1990, 6, 5/6, 435-455.
26. 26. MAMPASSI, B., Un type de jonction bidimensionelle d'une tige et d'un massif elastiques. Cr. Acad. Sci. Paris. Ser. II., 1992, 315, 3, 261-266.
27. 27. ARGATOV, I. I. and NAZAROV, S. A., Asymptotic analysis at the joints of domains of different limiting dimensionality. A body-pierced by a thin rod. Izv. Ross. Akad. Nauk, Ser. Mat., 1996, 60(1), 3-36.
28. 28. SANCHEZ-PALENCIZ, E., Non-homogeneous Media and Vibration Theory. Springer, New York, 1980.
29. 29. KAGAWA, V., YAMABUCHI, T., SUGIHRA, K. and SHINODU T., A finite element approach to a coupled structural-radiation system with application to loudspeaker characteristic calculation. J. Sound Vibrat., 1980, 69, 2, 229-243.
30. 30. SUZUKI, K. and NOMOTO, I., Computerized analysis and observation of the vibration modes of a loudspeaker cone. J. Audio Eng Soc., 1982, 30, 3, 98-106.
31. 31. ALDOSHINA, I. A., Etectrodynamic Loudspeakers. Radio i Svyaz', Moscow, 1989.