By Peter Wriggers, Udo Nackenhorst
This rigorously edited e-book deals a state of the art review on formula, mathematical research and numerical answer systems of touch difficulties. The contributions gathered during this quantity summarize the lectures awarded by way of major scientists within the quarter of touch mechanics, throughout the 4th touch Mechanics overseas 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)
6) Expressing the covariant derivative in eqn. (6) the following equation is obtained ρξξ · ρξ dT h11 ˙ = − T (ρξ · ρξ )ξ˙ + ξ˙ − ζ, (7) dt (ρξ · ρξ ) a11 where T is a penalty parameter for the tangential interaction, a11 and h11 are components of the metric tensor resp. of the curvature tensor for the cylindrical surface. If a path length s = ξ is used for parameterization, then eqn. (7) is transformed as dT =− dt T s˙ ˙ − κζ, (8) where κ is a curvature of the master contact plane curve. 3 Linearization for a Newton type solution scheme The derivation of the contact matrices can be performed either according to the cylindrical geometry, or according to the geometry of the plane curves.
The primal-dual active set strategy as a semi-smooth Newton method. SIAM J. , 13(3):865-888, 2003. 6. P. Hild and P. Laborde. Quadratic ﬁnite element methods for unilateral contact problems. Appl. Numer. , 41:410-421, 2002. 7. S. H¨ ueber, A. Matei, and B. Wohlmuth. Eﬀcient algorithms for problems with friction. Technical Report 007, Universit¨ at Stuttgart SFB 404, 2005. 8. S. H¨ ueber and B. Wohlmuth. A primal-dual active set strategy for non-linear multibody contact problems. Comput. Methods Appl.
The combined ﬁnite-discrete element method is a new computational method for the simulation of fracturing and fragmenting solids or particulate media where individual particles are deformable. The method combines the power of the ﬁnite element method in capturing deformability of solid particles with the power of the discrete element method to accurately represent interaction between individual particles for systems comprising millions of particles. In addition, the method is suitable for the simulation of extensive fracture and/or fragmentation processes.
Analysis and Simulation of Contact Problems (Lecture Notes in Applied and Computational Mechanics) by Peter Wriggers, Udo Nackenhorst