By Peter Wriggers, Udo Nackenhorst
This conscientiously edited booklet bargains a cutting-edge evaluate on formula, mathematical research and numerical answer methods of touch difficulties. The contributions accumulated during this quantity summarize the lectures awarded by means of major scientists within the region of touch mechanics, throughout the 4th touch Mechanics foreign Symposium (CMIS) held in Hannover, Germany, 2005.
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Additional info for Analysis and Simulation of Contact Problems (Lecture Notes in Applied and Computational Mechanics)
A coordinate system is considered on the boundary, either for a surface in 3D or for a curve in 2D. On the plane we deﬁne a curvilinear coordinate system associated with the curve by introducing two principal vectors as a basis: the tangent vector ∂ρ and the unit normal vector ν. Then a slave contact point S is found ρξ = ∂ξ as (1) rs (ξ, ζ) = ρ(ξ) + ζν(ξ). The normal unit vector ν in the case of arbitrary Lagrangian parameterizations with ξ can be deﬁned via a cross product in a Cartesian coordinate system as: [k × ρξ ] ∂ρ ; =⇒ ν = √ , (2) ρξ = ∂ξ ρξ · ρξ where k is the third unit vector in this Cartesian coordinate system.
R. Soc. Lond. , 2001, 359, 2405-2428. 9. Paumier & Y. Renard, Surface perturbation of an elastodynamic contact problem wih friction, European Journal of Applied Mathematics, vol. 14, 2003, 465-483. Mortar methods for contact problems S. I. de Abstract. For the numerical approximation of nonlinear contact problems, mortar methods provide a powerful and eﬃcient tool. To detect the correct contact zone and to decompose it into the sliding and sticking part for Coulomb friction, we use primal-dual active set strategies.
2 Regularization of the contact tractions For the normal traction N , the following regularized equation in the closed form is taken (5) N = N ζ, if ζ ≤ 0, where N is a penalty parameter for the normal interaction. As a reasonable equation for the regularization of the tangent traction T dT and the we choose a proportional relation between the full time derivative dt relative velocity vector expressed in covariant form on the tangent line ζ = 0: D1 T 1 ρ =− dt ˙ T ξρξ . (6) Expressing the covariant derivative in eqn.
Analysis and Simulation of Contact Problems (Lecture Notes in Applied and Computational Mechanics) by Peter Wriggers, Udo Nackenhorst