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Original Articles

Twisting a thin periodically perforated elastic rod

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Pages 1563-1577 | Received 26 Feb 2009, Accepted 04 Apr 2009, Published online: 17 Nov 2009

References

  • Kozlova , MV and Panasenko , GP . 1992 . Averaging a three-dimensional problem of elasticity theory in a nonhomogeneous rod . Comput. Math. Math. Phys. , 31 : 128 – 131 .
  • Panasenko , G . 1994 . Asymptotic analysis of bar systems (I) . Russian J. Math. Phys. , 2 : 325 – 352 .
  • Panasenko , G . 1996 . Asymptotic analysis of bar systems II . Russian J. Math. Phys. , 4 : 87 – 116 .
  • Nazarov , SA . 2002 . Asymptotic Analysis of Thin Plates and Rods, Dimension Reduction and Integral Estimates , Vol. 1 , Novosibirsk : Nauchnaia kniga, IDMI .
  • Zhikov , VV . 2002 . Averaging of problems in the theory of elasticity on singular structures . Izv. Math. , 66 : 299 – 365 .
  • Griso , G . 2004 . Asymptotic behaviour of curved rods by the unfolding method . Math. Methods Appl. Sci. , 27 : 2081 – 2110 .
  • Lewinski , T and Telega , J . 2000 . Plates, Laminates and Shells. Asymptotic Analysis and Homogenization. Series on Advances in Mathematics for Applied Sciences , Vol. 52 , River Edge, NJ : World Scientific Publishing Co., Inc. .
  • Bensoussan , A , Lions , J-L and Papanicolaou , G . 1978 . Asymptotic Analysis of Periodic Structures , Amsterdam : North Holland Publishing Company .
  • Jikov , VV , Kozlov , SM and Oleinik , OA . 1994 . Homogenization of Differential Operators and Integral Functionals , New York : Springer-Verlag .
  • Oleinik , OA and Yosifian , GA . 1982 . On the asymptotic behaviour at infinity of solutions in linear elasticity . Arch. Rational Mech. Anal. , 78 : 29 – 53 .
  • Zhikov , VV and Pastukhova , SE . 2004 . On Korn inequalities on thin periodic frames . J. Math. Sci. (NY) , 123 : 4499 – 4521 .
  • Lukkassen , D , Meidell , A , Shamaev , AS and Piatnitski , A . 2006 . “ Symmetry-relations for elastically deformed periodic rod-structures ” . In Research Report , Narvik University College .

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