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Collective buckling of nonuniform nanobeams interacting through an elastic substrate. (English) Zbl 1268.74024
Summary: We analyze the collective buckling of a row of vertical beams with their lower ends built into an elastic substrate. The beams interact among themselves through the deformation of the substrate. The present analysis is more sophisticated than a previous one in that the beams’ height and spacing are no longer uniform. This allows us to study the buckling of beams with specific height and spacing variation profiles. The effect of irregularity when the height of a particular beam or the distance between a particular pair of neighboring beams is different from the rest is also examined.

MSC:
74G60 Bifurcation and buckling
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] Xia, Y.N.; Whitesides, G.M., Soft lithography, Ann. Rev. Mater. Sci., 28, 153-184, (1998)
[2] Chou, S.Y.; Krauss, P.R.; Renstrom, P.J., Imprint of sub-25 nm vias and trenches in polymers, Appl. Phys. Lett., 67, 3114-3116, (1995)
[3] Chou, S.Y.; Krauss, P.R.; Renstrom, P.J., Nanoimprint lithography, J. Vac. Sci. Technol. B, 14, 4129-4133, (1996)
[4] Chuang, W.C.; Ho, C.T.; Wang, W.C., Fabrication of a high-resolution periodical structure using a replication process, Opt. Express, 13, 6685-6692, (2005) · Zbl 0839.17017
[5] Delamarche, E.; Schmid, H.; Michel, B.; Biebuyck, H., Stability of molded polydimethylsiloxane microstructures, Adv. Mater., 9, 741-746, (1997)
[6] Evans, B.A.; Shields, A.R.; Carroll, R.L.; Washburn, S.; Falvo, M.R.; Superfine, R., Magnetically actuated nanorod arrays as biomimetic cilia, Nano Lett., 7, 1428-1434, (2007)
[7] Schmid, H.; Michel, B., Siloxane polymers for high-resolution, high-accuracy soft lithography, Macromolecules, 33, 3042-3049, (2000)
[8] Timoshenko S.P.: Theory of Elastic Stability. McGraw-Hill, New York (1936)
[9] Alfutov N.A.: Stability of Elastic Stability. Springer, Germany (2000) · Zbl 0970.74001
[10] Hui, C.Y.; Jagota, A.; Lin, Y.Y.; Kramer, E.J., Constraints on microcontact printing imposed by stamp deformation, Langmuir, 18, 1394-1407, (2002)
[11] Lin, H.; Yang, J.; Tan, L.; Xu, J.; Li, Z., Collective buckling of periodic soft nanostructures on surfaces and promotion for nanolithography, J. Phys. Chem. C, 111, 13348-13356, (2007)
[12] Chen, L.; Deng, X.G.; Wang, J.; Takahashi, K.; Liu, F., Defect control in nanoimprint lithography, J. Vac. Sci. Technol. B, 23, 2933-2938, (2005)
[13] Cheng, X.; Li, D.W.; Guo, L.J., A hybrid mask-mould lithography scheme and its application in nanoscale organic thin film transistors, Nanotechnology, 17, 927-932, (2006)
[14] Perret, C.; Gourgon, C.; Lazzarino, F.; Tallal, J.; Landis, S.; Pelzer, R., Characterization of 8-in wafers printed by nanoimprint lithography, Microelectron. Eng., 73-74, 172-177, (2004)
[15] Scheer, H.C.; Schulz, H., A contribution to the flow behaviour of thin polymer films during hot embossing lithography, Microelectron. Eng., 56, 311-332, (2001)
[16] Michel, B.; Bernard, A.; Bietsch, A.; Delamarche, E.; Geissler, M.; Juncker, D.; Kind, H.; Renault, J.P.; Rothuizen, H.; Schmid, H.; Schmidt-Winkel, P.; Stutz, R.; Wolf, H., Printing meets lithography: soft approaches to high-resolution printing, Ibm. J. Res. Dev., 45, 697-719, (2001)
[17] Timoshenko S.P., Goodier J.N.: Theory of Elasticity, 3rd edn. McGraw-Hill, New Jersey (1970) · Zbl 0266.73008
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