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- W47985 abstract "In this dissertation we investigate the behavior of radially symmetric non-Euclidean plates of thickness t with constant negative Gaussian curvature. We present a complete study of these plates using the Foppl-von Karman and Kirchhoff reduced theories of elasticity. Motivated by experimental results, we focus on deformations with a periodic profile. For the Foppl-von Karman model, we prove rigorously that minimizers of the elastic energy converge to saddle shaped isometric immersions. In studying this convergence, we prove rigorous upper and lower bounds for the energy that scale like the thickness t squared. Furthermore, for deformation with n-waves we prove that the lower bound scales like nt while the upper bound scales like nt. We also investigate the scaling with thickness of boundary layers where the stretching energy is concentrated with decreasing thickness. For the Kichhoff model, we investigate isometric immersions of disks with constant negative curvature into R, and the minimizers for the bending energy, i.e. the L norm of the principal curvatures over the class of W 2,2 isometric immersions. We show the existence of smooth immersions of arbitrarily large geodesic balls in H 2 into R. In elucidating the connection between these immersions and the nonexistence/singularity results of Hilbert and Amsler, we obtain a lower bound for the L∞ norm of the principal curvatures for such smooth isometric immersions. We also construct piecewise smooth isometric immersions that have a periodic profile, are globally W , and numerically have lower bending energy than their smooth counterparts. The number of periods in these configurations is set by the condition that the principal curvatures of the surface remain finite and grow approximately exponentially with the radius of the disc." @default.
- W47985 created "2016-06-24" @default.
- W47985 creator A5049172187 @default.
- W47985 date "2012-01-01" @default.
- W47985 modified "2023-10-16" @default.
- W47985 title "Shape Selection in the Non-Euclidean Model of Elasticity" @default.
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- W47985 cites W1596617541 @default.
- W47985 cites W1754571422 @default.
- W47985 cites W1773762783 @default.
- W47985 cites W1949248870 @default.
- W47985 cites W1967208361 @default.
- W47985 cites W1970576706 @default.
- W47985 cites W1971481657 @default.
- W47985 cites W1974743608 @default.
- W47985 cites W1975285551 @default.
- W47985 cites W1979297974 @default.
- W47985 cites W1979623823 @default.
- W47985 cites W1988326337 @default.
- W47985 cites W1989467747 @default.
- W47985 cites W1991423628 @default.
- W47985 cites W1992476388 @default.
- W47985 cites W1993682504 @default.
- W47985 cites W1993726971 @default.
- W47985 cites W1994351320 @default.
- W47985 cites W1996160600 @default.
- W47985 cites W1998425599 @default.
- W47985 cites W1999240617 @default.
- W47985 cites W2008342328 @default.
- W47985 cites W2010296342 @default.
- W47985 cites W2011738801 @default.
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- W47985 cites W2025900039 @default.
- W47985 cites W2040885943 @default.
- W47985 cites W2041324809 @default.
- W47985 cites W2041842031 @default.
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- W47985 cites W2046266844 @default.
- W47985 cites W2048879692 @default.
- W47985 cites W2051320523 @default.
- W47985 cites W2052679444 @default.
- W47985 cites W2060565280 @default.
- W47985 cites W2061979831 @default.
- W47985 cites W2068495985 @default.
- W47985 cites W2068687945 @default.
- W47985 cites W2074096988 @default.
- W47985 cites W2075077967 @default.
- W47985 cites W2076740121 @default.
- W47985 cites W2078639636 @default.
- W47985 cites W2092067729 @default.
- W47985 cites W2094197950 @default.
- W47985 cites W2094438648 @default.
- W47985 cites W2095495421 @default.
- W47985 cites W2115644711 @default.
- W47985 cites W2121015218 @default.
- W47985 cites W2126869345 @default.
- W47985 cites W2133842540 @default.
- W47985 cites W2135789936 @default.
- W47985 cites W2144237170 @default.
- W47985 cites W2144769466 @default.
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- W47985 cites W2158503864 @default.
- W47985 cites W2159439735 @default.
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- W47985 cites W225357580 @default.
- W47985 cites W2318624729 @default.
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- W47985 cites W233239409 @default.
- W47985 cites W2333620035 @default.
- W47985 cites W2396299143 @default.
- W47985 cites W2501693933 @default.
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- W47985 cites W2583860733 @default.
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- W47985 cites W3043060850 @default.
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- W47985 cites W3105016663 @default.
- W47985 cites W3109393067 @default.
- W47985 cites W323741540 @default.
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- W47985 hasPublicationYear "2012" @default.
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