Genre
Pre-printDate
2018-01-01Author
Grabovsky, YHarutyunyan, D
Permanent link to this record
http://hdl.handle.net/20.500.12613/4821
Metadata
Show full item recordDOI
10.1016/j.anihpc.2017.04.004Abstract
© 2017 Elsevier Masson SAS We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that are diffeomorphic to a circular cylindrical shell with zero principal longitudinal curvature and positive circumferential curvature, including, for example, cylindrical and conical shells with arbitrary convex cross sections. We prove that the best constant in the first Korn inequality scales like thickness to the power 3/2 for a wide range of boundary conditions at the thin edges of the shell. Our methodology is to prove, for each of the three mutually orthogonal two-dimensional cross-sections of the shell, a “first-and-a-half Korn inequality”—a hybrid between the classical first and second Korn inequalities. These three two-dimensional inequalities assemble into a three-dimensional one, which, in turn, implies the asymptotically sharp first Korn inequality for the shell. This work is a part of mathematically rigorous analysis of extreme sensitivity of the buckling load of axially compressed cylindrical shells to shape imperfections.Citation to related work
Elsevier BVHas part
Annales de l'Institut Henri Poincare (C) Analyse Non LineaireADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.eduae974a485f413a2113503eed53cd6c53
http://dx.doi.org/10.34944/dspace/4803