Abstract:
We study elasticity problems in the plane (space) reinforced with periodic thin network (box structure). This highly contrasting medium depends on two small related parameters ε and h connected with each other which controlling size of periodicity cell and thickness of reinforcement. For combined structures we prove classical homogenization principle the same for any interrelation between parameters ε and h that is quite contrary to the case of thin structures. We use method of 2-scale convergence with respect to variable measure natural to combined structures.
Citation:
S. E. Pastukhova, “About homogenization of elasticity problems on combined structures”, Boundary-value problems of mathematical physics and related problems of function theory. Part 35, Zap. Nauchn. Sem. POMI, 310, POMI, St. Petersburg, 2004, 114–144; J. Math. Sci. (N. Y.), 132:3 (2006), 313–330
\Bibitem{Pas04}
\by S.~E.~Pastukhova
\paper About homogenization of elasticity problems on combined structures
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~35
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 310
\pages 114--144
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl809}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2120188}
\zmath{https://zbmath.org/?q=an:1085.35027}
\elib{https://elibrary.ru/item.asp?id=9128690}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 132
\issue 3
\pages 313--330
\crossref{https://doi.org/10.1007/s10958-005-0500-9}
\elib{https://elibrary.ru/item.asp?id=13520982}
Linking options:
https://www.mathnet.ru/eng/znsl809
https://www.mathnet.ru/eng/znsl/v310/p114
This publication is cited in the following 2 articles:
Erik Kropat, Silja Meyer-Nieberg, Gerhard-Wilhelm Weber, “Computational networks and systems – homogenization of variational problems on micro-architectured networks and devices”, Optimization Methods and Software, 34:3 (2019), 586
Erik Kropat, Silja Meyer-Nieberg, Gerhard-Wilhelm Weber, “Computational networks and systems-homogenization of self-adjoint differential operators in variational form on periodic networks and micro-architectured systems”, Numerical Algebra, Control & Optimization, 7:2 (2017), 139