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Conference Paper (international conference)

On the Solution of Contact Problems with Tresca Friction by the Semismooth* Newton Method

Gfrerer H., Outrata Jiří, Valdman Jan

: Large-Scale Scientific Computing, p. 515-523 , Eds: Lirkov I., Margenov S.

: International Conference on Large-Scale Scientific Computing /13./, (Sozopol, BG, 20210607)

: GF19-29646L, GA ČR

: Contact problems, Tresca friction, Semismooth* Newton method, Finite elements, Matlab implementation

: 10.1007/978-3-030-97549-4_59

: http://library.utia.cas.cz/separaty/2022/MTR/valdman-0563211.pdf

(eng): An equilibrium of a linear elastic body subject to loading and satisfying the friction and contact conditions can be described by a variational inequality of the second kind and the respective discrete model attains the form of a generalized equation. To its numerical solution we apply the semismooth* Newton method by Gfrerer and Outrata (2019) in which, in contrast to most available Newton-type methods for inclusions, one approximates not only the single-valued but also the multi-valued part. This is performed on the basis of limiting (Morduchovich) coderivative. In our case of the Tresca friction, the multi-valued part amounts to the subdifferential of a convex function generated by the friction and contact conditions. The full 3D discrete problem is then reduced to the contact boundary. Implementation details of the semismooth* Newton method are provided and numerical tests demonstrate its superlinear convergence and mesh independence.

: BA

: 10101

2019-01-07 08:39