350 rub
Journal Science Intensive Technologies №11 for 2015 г.
Article in number:
Variational formulation and computational algorithm for solving of the problem on wear of the elastic half-plane with the non-uniform coating of the winkler type
Keywords: wear contact problem coating variational inequality integrated fundamental solutions boundary element method
Authors:
A.A. Bobylov - Ph. D. (Phys.-Math.), Associate Professor. E-mail: abobylov@gmail.com I.S. Belashova - Dr. Sc. (Eng.), Professor, MADI. E-mail: irina455@inbox.ru
Abstract:
A plane contact problem of wear of a thin non-uniform coating of an elastic half-plane by a rigid wear-free punch is considered. The coating is modelled by an elastic layer of the Winkler type. The variational formulation of the problem in the form of a system of an evolutionary variational inequality and an ordinary differential equation of the first order is obtained. The explicit differential scheme of Euler is used for discretization of the problem of time. Boundary element approach is applied at discretization of the problems in spatial coordinates. As a result, it is necessary to solve a square programming problem with restrictions in the form of equalities and inequalities on each temporary layer. The linear transformation of variables allowing to simplify a type of restrictions is offered. A modification of the conjugate gradients method considering specifics of restrictions is used for numerical solution of the problems. The carried out calculations showed that the heterogeneous coating significantly influences the nature of the interface wear process.
Pages: 8-20
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