Existence of an extremal crack shape in the equilibrium problem for the timoshenko plate

被引：0

作者：

Lazarev N.P. ^{[1
]}

机构：

[1] Lavrent’ev Institute of Hydrodynamics SB RAS, 15 pr. Akad. Lavrent’eva, Novosibirsk

来源：

Journal of Mathematical Sciences | 2013年 / 195卷 / 6期

关键词：

Variational Inequality; Equilibrium Problem; Strong Convergence; Elastic Plate; Normal Cross Section;

D O I：

10.1007/s10958-013-1620-2

中图分类号：

学科分类号：

摘要：

We consider the variational problem of equilibrium of an elastic plate (the Timoshenko model) containing a crack. On the curve describing the crack, we impose boundary conditions in the form of inequalities. We study the dependence of the solutions on the curve shape. We prove the existence of an extremal curve shape and show that the solutions weakly converge in the Sobolev space as the parameter describing the crack shape tends to zero. The convergence is strong if the external forces satisfy the Lipschitz condition. © 2013 Springer Science+Business Media New York.

引用

页码：815 / 826

页数：11