Geometrically Exact Theory of Contact Interactions—Applications with Various Methods FEM and FCM

Alexander  Konyukhov

doi:10.4236/jamp.2015.38126

Alexander Konyukhov^1,2

Abstract: Geometrically exact theory of contact interactions is aiming on the development of the unified geometrical formulation of computational contact algorithms for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, curve-to-surface, point-to-surface, curve-to-curve, point-to-curve, point-to-point. The construction of the corresponding computational contact algorithms is considered in accordance with the geometry of contacting bodies in covariant and closed forms. These forms can be easily discretized within various methods such as the finite element method (FEM), the finite discrete method (FDM) independently of the order of approximation and, therefore, the result is straightforwardly applied within any further method: high order finite element methods, iso-geometric finite element methods etc. As particular new development it is shown also the possibility to easy combine with the Finite Cell Method.

Keywords: Closest Point Projection Procedure, Curvilinear Coordinate System, Covariant Derivative and Linearization, Finite Cell Method

Cite this paper: Konyukhov, A. (2015) Geometrically Exact Theory of Contact Interactions—Applications with Various Methods FEM and FCM. Journal of Applied Mathematics and Physics, 3, 1022-1031. doi: 10.4236/jamp.2015.38126.

References

[1] Laursen, T.A. (2002) Computational Contact and Impact Mechanics. Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis. Springer, Berlin, 454.

[2] Wriggers, P. (2006) Computational Contact Mechanics. 2nd Edition, Springer, Berlin, 520. http://dx.doi.org/10.1007/978-3-540-32609-0

[3] Litewka, P. (2010) Finite Element Analysis of Beam-to-Beam Contact. Springer, Berlin, 160. http://dx.doi.org/10.1007/978-3-642-12940-7

[4] Konyukhov, A. and Schweizerhof, K. (2013) Computational Contact Mechanics—Geometrically Exact Theory for Arbitrary Shaped Bodies. Springer, Heidelberg, 444.

[5] Konyukhov, A. and Izi, R. (2015) Introduction into Computational Contact Mechanics: A Geometricall Approach. Wiley, 304.

[6] De Lorenzis, L., Wriggers, P. and Hughes, T.J.R. (2014) Isogeometric Contact a Review. GAMM Mitteilungen, 37, 85-123. http://dx.doi.org/10.1002/gamm.201410005

[7] Konyukhov, A. and Schweizerhof, K. (2008) On the Solvability of Closest Point Projection Procedures in Contact Analysis: Analysis and Solution Strategy for Surfaces of Arbitrary Geometry. Comput. Method Appl. M., 197, 3045- 3056. http://dx.doi.org/10.1016/j.cma.2008.02.009

[8] Konyukhov, A. and Schweizerhof, K. (2010) Geometrically Exact Covariant Approach for Contact between Curves. Comput. Method Appl. M., 199, 2510-2531. http://dx.doi.org/10.1016/j.cma.2010.04.012

[9] Konyukhov, A. and Schweizerhof, K. (2012) Geometrically Exact Theory for Contact Interactions of 1D Manifolds. Algorithmic Implementation with Various Finite Element Models. Comput. Methods in Appl. M., 205-208, 130-138.

[10] Konyukhov, A. and Schweizerhof, K. (2015) On Some Aspects for Contact with Rigid Surfaces: Surface-to-Rigid Surface and Curves-to-Rigid Surface Algorithms. Comput. Methods in Appl. M., 283, 74-105.

[11] Konyukhov, A. (2013) Contact of Ropes and Orthotropic Rough Surfaces. ZAMM, Z. Angew. Math. Mech., 1-18.

[12] Konyukhov, A. and Schweizerhof, K. (2005) Covariant Description for Frictional Contact Problems. Comput. Mech., 35, 190-213. http://dx.doi.org/10.1007/s00466-004-0616-7

[13] Euler, L. (1769) Remarques sur l’effet du frottement dans l’equilibre. Memoires de l’Academie des Sciences de Berlin, 18, 265-278.

[14] Düster, A., Parzivian, J., Yang, Z. and Rank, E. (2008) The Finite Cell Method for Three-Dimensional Problems of Solid Mechanics. Comput. Methods in Appl. M., 197, 3768-3782.

[15] Konyukhov, A., Lorenz, Ch. and Schweizerhof, K. (2015) Various Contact Approaches for the Finite Cell Method, Computational Mechanics. http://dx.doi.org/10.1007/s00466-015-1174-x