Numerical solution of an equilibrium problem for a membrane with a delaminated thin rigid inclusion

All-Russian conference on Nonlinear Waves: Theory and New Applications

Rudoy, Evgeny M.^1,2

Lavrentyev Institute of Hydrodynamics, Russian Academy of Sciences, Novosibirsk

630090, Russia^1

Novosibirsk State University, Novosibirsk

630090, Russia^2

关键词: Elastic membranes;    Equilibrium problem;    Initial problem;    Numerical solution;    Rigid inclusion;    Saddle point;    Thin inclusions;    Uzawa algorithms;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012033/pdf
DOI  :  10.1088/1742-6596/722/1/012033

来源: IOP

【 摘 要 】

The paper deals with the numerical solution of an equilibrium problem for an elastic membrane with a thin rigid inclusion. The thin inclusion is supposed to delaminate, therefore a crack between the inclusion and the membrane is considered. The boundary conditions for nonpenetration of the crack faces are fulfilled. We provide the relaxation of the problem and propose an iterative method for the numerical solution of the approximated problem. The method is based on a domain decomposition and the Uzawa algorithm for finding a saddle point of the Lagrangian. Examples of the numerical solution of the initial problem are presented.