Korn inequality for a thin rod with rounded ends |
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| Authors: | Sergey A Nazarov Andrey S Slutskij Jari Taskinen |
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| Institution: | 1. Mathematics and Mechanics Faculty, St.Petersburg State University, , Petershoff, Universtetskii pr., 28, 198504 Saint Petersburg, Russia;2. Institute of Mechanical Engineering Problems, Academy of Science St. Petersburg, , V.O., Bolshoi pr., 61, 199178 Saint Petersburg, Russia;3. Physical Faculty, St. Petersburg State University, , Ul'yanovskaya., 3, Petrodvorets, 198504 Saint Petersburg, Russia;4. Department of Mathematics and Statistics, University of Helsinki, , P.O. Box 68, FI‐00014 Helsinki, Finland |
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| Abstract: | We consider an elastic rod with rounded ends and diameter proportional to a small parameter h > 0. The roundness of the ends is described by an exponent m ∈ (0,1). We derive for the rod an asymptotically sharp Korn inequality with a special weighted anisotropic norm. Weight factors with m‐dependent powers of h appear both in the anisotropic norm and the Korn inequality itself, and we discover three critical values m = 1 ∕ 4, m = 1 ∕ 2 and m = 3 ∕ 4 at which these exponents are crucially changed. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | Korn inequality rod thin domain weighted Sobolev space |
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