Abstract:
Full asymptotic solutions are constructed for the system of equations of elasticity theory for a rod (a thin cylinder whose cross-section diameter is a small parameter), a rod structure (a connected aggregate of several rods), and frame domains. The limiting equations and matching conditions are obtained.
Citation:
G. P. Panasenko, “Asymptotic solutions of the system of elasticity theory for rod and frame structures”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 85–110
\Bibitem{Pan92}
\by G.~P.~Panasenko
\paper Asymptotic solutions of the system of elasticity theory for rod and frame structures
\jour Russian Acad. Sci. Sb. Math.
\yr 1993
\vol 75
\issue 1
\pages 85--110
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\crossref{https://doi.org/10.1070/SM1993v075n01ABEH003373}
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https://www.mathnet.ru/eng/sm1450
https://doi.org/10.1070/SM1993v075n01ABEH003373
https://www.mathnet.ru/eng/sm/v183/i1/p89
This publication is cited in the following 23 articles:
Griso G., Khilkova L., Orlik J., Sivak O., “Asymptotic Behavior of Stable Structures Made of Beams”, J. Elast., 143:2 (2021), 239–299
Orlik J., Andra H., Argatov I., Staub S., “Does the Weaving and Knitting Pattern of a Fabric Determine Its Relaxation Time?”, Q. J. Mech. Appl. Math., 70:4 (2017), 337–361
Orlik J., Panasenko G., Shiryaev V., “Optimization of Textile-Like Materials via Homogenization and Beam Approximations”, Multiscale Model. Simul., 14:2 (2016), 637–667
Panasenko G., Viallon M.-C., “Error Estimate in a Finite Volume Approximation of the Partial Asymptotic Domain Decomposition”, Math. Meth. Appl. Sci., 36:14 (2013), 1892–1917
Peter I. Kogut, Günter Leugering, “Homogenization of constrained optimal control problems for
one-dimensional elliptic equations on periodic graphs”, ESAIM COCV, 15:2 (2009), 471
Pastukhova S.E., “Asymptotic Analysis in Elasticity Problems on Thin Periodic Structures”, Netw. Heterog. Media, 4:3 (2009), 577–604
Capacity and Transport in Contrast Composite Structures, 2009, 289
S. A. Nazarov, “Korn inequalities for elastic junctions of massive bodies, thin plates, and rods”, Russian Math. Surveys, 63:1 (2008), 35–107
Panasenko G., Viallon M.-C., “The Finite Volume Implementation of the Partial Asymptotic Domain Decomposition”, Appl. Anal., 87:12 (2008), 1397–1424
Panasenko G., “The Partial Homogenization: Continuous and Semi-Discretized Versions”, Math. Models Meth. Appl. Sci., 17:8 (2007), 1183–1209
Berlyand L., Cardone G., Gorb Yu., Panasenko G., “Asymptotic Analysis of an Array of Closely Spaced Absolutely Conductive Inclusions”, Netw. Heterog. Media, 1:3 (2006), 353–377
Pastukhova, SE, “Correctors in the homogenization of elasticity problems on thin structures”, Doklady Mathematics, 71:2 (2005), 177
S. A. Nazarov, “Weighted anisotropic Korn's inequality for a junction of a plate and a rod”, Sb. Math., 195:4 (2004), 553–583
Pastukhova, SE, “Homogenization of elasticity problems on periodic rod frames of critical thickness”, Doklady Mathematics, 69:1 (2004), 20
S. A. Nazarov, A. S. Slutskij, “Arbitrary Plane Systems of Anisotropic Beams”, Proc. Steklov Inst. Math., 236 (2002), 222–249
Nazarov S., Slutskii A., “Asymptotics of Eigenfrequencies of a Pi-Shaped Elastic Frame”, Dokl. Math., 64:2 (2001), 266–269
Grigori P. Panasenko, “Asymptotic partial decomposition of variational problems”, Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy, 327:11 (1999), 1185
N. S. Bakhvalov, G. P. Panasenko, A. L. Shtaras, Encyclopaedia of Mathematical Sciences, 34, Partial Differential Equations V, 1999, 211
G PANASENKO, “Asymptotic expansion of the solution of Navier–Stokes equation in a tube structure”, Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy, 326:12 (1998), 867
G PANASENKO, “Partial asymptotic decomposition of domain: Navier–Stokes equation in tube structure”, Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy, 326:12 (1998), 893
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