Invariant Integrals for the Equilibrium Problem for a Plate with a Crack |
| |
Authors: | Rudoy E M |
| |
Abstract: | We consider the equilibrium problem for a plate with a crack. The equilibrium of a plate is described by the biharmonic equation. Stress free boundary conditions are given on the crack faces. We introduce a perturbation of the domain in order to obtain an invariant Cherepanov–Rice-type integral which gives the energy release rate upon the quasistatic growth of a crack. We obtain a formula for the derivative of the energy functional with respect to the perturbation parameter which is useful in forecasting the development of a crack (for example, in study of local stability of a crack). The derivative of the energy functional is representable as an invariant integral along a sufficiently smooth closed contour. We construct some invariant integrals for the particular perturbations of a domain: translation of the whole cut and local translation along the cut. |
| |
Keywords: | biharmonic equation crack nonsmooth domain derivative of the energy functional invariant integral |
本文献已被 SpringerLink 等数据库收录! |