English

Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells

Analysis of PDEs 2013-12-16 v1

Abstract

Understanding asymptotics of gradient components in relation to the symmetrized gradient is im- portant 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 derive an ana- logue of the Kirchho? ansatz, whose most prominent feature is its singular dependence on the slenderness parameter, in marked contrast with the classical case of plates and rods.

Keywords

Cite

@article{arxiv.1312.3902,
  title  = {Exact scaling exponents in Korn and Korn-type inequalities for cylindrical shells},
  author = {Yury Grabovsky and Davit Harutyunyan},
  journal= {arXiv preprint arXiv:1312.3902},
  year   = {2013}
}