Differential-Difference Iterative Domain Decomposition Methods for the Problems of Contact of Elastic Bodies with Nonlinear Winkler Surface Layers

被引：0

作者：

Prokopyshyn І.І. ^{[1
]}

Shakhno S.M. ^{[2
]}

机构：

[1] Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv

[2] I. Franko National University of Lviv, Lviv

来源：

Journal of Mathematical Sciences | 2022年 / 261卷 / 1期

关键词：

contact problems; differential-difference iterative methods; domain decomposition methods; finite-element method; semismooth Newton method; variational equations;

D O I：

10.1007/s10958-022-05736-9

中图分类号：

学科分类号：

摘要：

We consider the problem of contact interaction of several elastic bodies with nonlinear Winkler surface layers. To solve a nonlinear variational equation with nondifferentiable operator corresponding to this contact problem, we propose to use implicit two-point combined differential-difference parallel iterative Robin-type domain decomposition algorithms. We propose software realization of these algorithms for the case of plane contact problems based on finite-element approximations. We compare the numerical efficiency of the two-point and one-point iterative domain decomposition methods for the problem of contact of two elastic bodies containing a groove through a nonlinear Winkler layer. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：41 / 58

页数：17

共 29 条

[1]

Bartish M.Y., Shcherbyna Y.M., On one difference method for the solution of nonlinear operator equations, Dop. Akad. Nauk Ukr. RSR. Ser. А, 7, pp. 579-582, (1972)

[2]

Kravchuk A.S., Formulation of the problem of contact between several deformable bodies as a nonlinear programming problem, Prikl. Mat. Mekh, 42, 3, pp. 467-473, (1978)

[3]

Lions J.-L., Quelques Méthodes de Résolution des Problèms aux Limites Non Linéares, (1969)

[4]

Martynyak R.M., Prokopyshyn I.A., Prokopyshyn I.I., “Contact of elastic bodies with nonlinear Winkler surface layers, ,” Mat. Met. Fiz.-Mekh. Polya, 56, pp. 43-56, (2013)

[5]

Equivalent Variational Formulations of Unilateral Contact Problems for Elastic Bodies with Nonlinear Surface Layers, In: Abstracts of the Republican Sci.-Eng. Conf. “Efficient Numerical Methods for the Solution of Boundary- Value Problem of Mechanics of Deformable Solids” [In Russian], pp. 83-85, (1989)

[6]

Prokopyshyn I.I., Domain Decomposition Schemes Based on the Penalty Method for the Problems of Contact of Elastic Bodies [in Ukrainian], Candidate-Degree Thesis, (2010)

[7]

Prokopyshyn I.I., Dyyak I.I., Martynyak R.M., Numerical analysis of the problems of contact of three elastic bodies by the domain decomposition methods,” Fiz, Khim. Mekh. Mater, 49, 1, pp. 46-55, (2013)

[8]

Prokopyshyn I., Domain decomposition methods for the problems of unilateral contact between nonlinear elastic bodies, Fiz.- Mat. Model. Inform. Tekhnol., Issue, 15, pp. 75-87, (2012)

[9]

Prokopyshyn I., Parallel schemes of the domain decomposition method for the frictionless contact problems of the theory of elasticity, Visn. L’viv. Univ. Ser. Prykl. Mat. Inform., Issue, 14, pp. 123-133, (2008)

[10]

Prokopyshyn I., Shakhno S., Differential-difference iterative domain decomposition algorithms for the problems of unilateral contact of several elastic bodies, Fiz.-Mat. Model. Inform. Tekhnol., Issue, 25, pp. 125-140, (2017)

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