Contact of elastic bodies with nonlinear surface Winkler layers. (Ukrainian, English) Zbl 1313.74104
Mat. Metody Fiz.-Mekh. Polya 56, No. 3, 43-56 (2013); translation in J. Math. Sci., New York 205, No. 4, 535-553 (2015).
The authors present variational formulations of the problem on unilateral contact between elastic bodies with nonlinear surface Winkler layers in the form of nonquadratic variational inequality, and a nonlinear variational equation. Existence and uniqueness of solutions for these variational problems are investigated. To solve the nonlinear variational equation corresponding to the original contact problem, a class of parallel iterative methods of domain decomposition is proposed. Each step of these methods comprises a parallel solution of linear variational equations in separate bodies, which are equivalent, in a weak sense, to linear elasticity problems with boundary Robin conditions on possible contact zones. The proposed methods are investigated numerically by finite element approximations.
Reviewer: V. I. Guljaev (Kyïv)
MSC:
74M15 | Contact in solid mechanics |
74M10 | Friction in solid mechanics |
74S05 | Finite element methods applied to problems in solid mechanics |