Optimal exponentials of thickness in Korn’s inequalities for parabolic and elliptic shells

被引：0
作者：
Peng-Fei Yao
机构：
[1] Chinese Academy of Sciences,Key Laboratory of Systems and Control Institute of Systems Science, Academy of Mathematics and Systems Science
[2] University of Chinese Academy of Sciences,School of Mathematical Sciences
来源：
Annali di Matematica Pura ed Applicata (1923 -) | 2021年 / 200卷
关键词：
Korn’s inequality; Shell; Nonlinear elasticity; Riemannian geometry; 74K20 (primary); 74B20 (secondary);
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the scaling of the optimal constant in Korn’s first inequality for elliptic and parabolic shells which was first given by Grabovsky and Harutyunyan with hints coming from the test functions constructed by Tovstik and Smirnov on the level of formal asymptotic expansions. Here, we employ the Bochner technique in Remannian geometry to remove the assumption that the middle surface of the shell is given by one single principal coordinate, in particularly, including closed elliptic shells.
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页码：379 / 401
页数：22
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共 47 条
[11]  
Neff P(1989)On Korns inequalities for frame type structures and junctions C. R. Acad. Sci. Paris Ser. I Math. 309 591-596
[12]  
Pauly D(2016)On the optimal constants in korns and geometric rigidity estimates, in bounded and unbounded domains, under neumann boundary conditions Indiana Univ. Math. J. 65 377-397
[13]  
Starke G(2004)Weighted anisotropic Korns inequality for a junction of a plate and a rod Sbornik: Math. 195 553-583
[14]  
Conti S(2008)Korn inequalities for elastic junctions of massive bodies, thin plates, and rods Russ. Math. Surv. 63 35-752
[15]  
Dolzmann G(2012)Asymptotically exact Korns constant for thin cylindrical domains Comptes Rendus Mathematique 350 749-333
[16]  
Mller S(2014)On Korns constant for thin cylindrical domains Math. Mech. Solids 19 318-282
[17]  
Neff P(2018)Korn inequalities for shells with zero Gaussian curvature Ann. Inst. H. Poincar Anal. Non Linaire 35 267-3295
[18]  
Pauly D(2014)Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells SIAM J. Math. Anal. 46 3277-766
[19]  
Witsch K-J(2017)Gaussian curvature as an identifier of shell rigidity Arch. Ration. Mech. Anal. 226 743-17
[20]  
Friesecke G(1966)On the nonlinear theory of thin elastic shells I Proc. Kon. Ned. Akad. Wetensch. B 69 1-109
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