Geodesic
Method of solution composition in contact problems with friction of deformable bodies
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 659-674

Voir la notice de l'article provenant de la source Math-Net.Ru

A new iterative method for solving static contact problems of two deformable bodies is proposed. The method is based on alternately solving the unilateral contact problem for the first body and the linear elasticity problem with natural boundary conditions for the second body. Fulfillment of Coulomb's friction law involves correction of tangential nodal forces in the sliding area and setting kinematic boundary conditions in the sticking area for the contact boundary of the first body. The goal of solving the linear elasticity problem for the second body is to gradually equalize contact loads on the interacting surfaces. The advantages of the method are demonstrated by solving a number of model examples, including unilateral contact of a linear-elastic plate with a solid foundation, bilateral contact of pressing a deformable block into the foundation, the Hertz problem of contact of two deformable cylinders etc. The method can solve problems on flat and curvilinear contact boundaries.
Keywords: contact problem, finite element method
Mots-clés : Coulomb's friction law 
@article{VUU_2023_33_4_a7,
     author = {A. S. Karavaev and S. P. Kopysov},
     title = {Method of solution composition in contact problems with friction of deformable bodies},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {659--674},
     publisher = {mathdoc},
     volume = {33},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a7/}
}
TY  - JOUR
AU  - A. S. Karavaev
AU  - S. P. Kopysov
TI  - Method of solution composition in contact problems with friction of deformable bodies
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2023
SP  - 659
EP  - 674
VL  - 33
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a7/
LA  - ru
ID  - VUU_2023_33_4_a7
ER  - 
%0 Journal Article
%A A. S. Karavaev
%A S. P. Kopysov
%T Method of solution composition in contact problems with friction of deformable bodies
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2023
%P 659-674
%V 33
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a7/
%G ru
%F VUU_2023_33_4_a7
A. S. Karavaev; S. P. Kopysov. Method of solution composition in contact problems with friction of deformable bodies. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 33 (2023) no. 4, pp. 659-674. http://geodesic.mathdoc.fr/item/VUU_2023_33_4_a7/