Quasistatic normal-compliance contact problem of visco-elastic bodies with Coulomb friction implemented by QP and SGBEM

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• 作者：Roman Vodička^a ; ^{roman.vodicka@tuke.sk} ; Vladislav Mantič^b ; ^mantic@us.es ; Tomá ; &scaron ; Roubí ; ček^c ; ^d ; ^{roubicek@karlin.mff.cuni.cz}
• 关键词：35Q90 ; 49N10 ; 65K15 ; 65M38 ; 74A55 ; 74S15 ; 90C20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：315
• 期：Complete
• 页码：249-272
• 全文大小：889 K
• 卷排序：315

文摘

The quasistatic normal-compliance contact problem of isotropic homogeneous linear visco-elastic bodies with Coulomb friction at small strains in Kelvin–Voigt rheology is considered. The discretization is made by a semi-implicit formula in time and the Symmetric Galerkin Boundary Element Method (SGBEM) in space, assuming that the ratio of the viscosity and elasticity moduli is a given relaxation-time coefficient. The obtained recursive minimization problem, formulated only on the contact boundary, has a nonsmooth cost function. If the normal compliance responds linearly and the 2D problems are considered, then the cost function is piecewise-quadratic, which after a certain transformation gets the quadratic programming (QP) structure. However, it would lead to second-order cone programming in 3D problems. Finally, several computational tests are presented and analysed, with an additional discussion on numerical stability and convergence of the involved approximated Poincaré–Steklov operators.