Sharp Weighted Korn and Korn-Like Inequalities and an Application to Washers
نویسندگان
چکیده
منابع مشابه
. Korn and Korn - like inequalities for perfect cylindrical shells by Davit Harutyunyan
It is well known that Korn's inequality plays a central role in the theory of linear elasticity. In their recent work Grabovsky and Truskinovsky (2007) proved a connection between the Korn inequalities and buckling problems coming from nonlinear elasticity. It has been shown that when the general buckling theory by Grabovsky and Truskinovsky is applicable, then Korn's inequality gives a lower b...
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It is known that the classic Korn inequality is not valid for Hölder α domains. In this paper we prove a family of weaker inequalities for this kind of domains, replacing the standard L-norms by weighted norms where the weights are powers of the distance to the boundary. In order to obtain these results we prove first some weighted Poincaré inequalities and then, generalizing an argument of Kon...
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Understanding asymptotics of gradient components in relation to the symmetrized gradient is important for the analysis of buckling of slender structures. For circular cylindrical shells we obtain the exact scaling exponent of the Korn constant as a function of shell’s thickness. Equally sharp results are obtained for individual components of the gradient in cylindrical coordinates. We also deri...
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ژورنال
عنوان ژورنال: Journal of Elasticity
سال: 2016
ISSN: 0374-3535,1573-2681
DOI: 10.1007/s10659-016-9596-z