Non-smooth mechanics
Encyclopedia
Non-smooth mechanics is a modeling approach in mechanics
which does not require the time evolutions of the positions and of the velocities to be smooth function
s anymore. Due to possible impacts, the velocities of the mechanical system are even allowed to undergo jumps at certain time instants in order to fulfill the kinematical restrictions. Consider for example a rigid model of a ball which falls on the ground. Just before the impact between ball and ground, the ball has non-vanishing pre-impact velocity. At the impact time instant, the velocity must jump to a post-impact velocity which is at least zero, as else penetration would occur. Non-smooth mechanical models are often used in contact dynamics
.
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
which does not require the time evolutions of the positions and of the velocities to be smooth function
Smooth function
In mathematical analysis, a differentiability class is a classification of functions according to the properties of their derivatives. Higher order differentiability classes correspond to the existence of more derivatives. Functions that have derivatives of all orders are called smooth.Most of...
s anymore. Due to possible impacts, the velocities of the mechanical system are even allowed to undergo jumps at certain time instants in order to fulfill the kinematical restrictions. Consider for example a rigid model of a ball which falls on the ground. Just before the impact between ball and ground, the ball has non-vanishing pre-impact velocity. At the impact time instant, the velocity must jump to a post-impact velocity which is at least zero, as else penetration would occur. Non-smooth mechanical models are often used in contact dynamics
Contact dynamics
Contact dynamics deals with the motion of multibody systems subjected to unilateral contacts and friction. Such systems are omnipresent in many multibody dynamics applications...
.
Further reading
- Acary V., Brogliato, B. Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics. Springer Verlag, LNACM 35, Heidelberg, 2008.
- Brogliato B. Nonsmooth Mechanics. Communications and Control Engineering Series, Springer-Verlag, London, 1999 (2nd Ed.)
- Glocker, Ch. Dynamik von Starrkoerpersystemen mit Reibung und Stoessen, volume 18/182 of VDI Fortschrittsberichte Mechanik/Bruchmechanik. VDI Verlag, Düsseldorf, 1995
- Glocker Ch. and Studer C. Formulation and preparation for Numerical Evaluation of Linear Complementarity Systems. Multibody System Dynamics 13(4):447-463, 2005
- Jean M. The non-smooth contact dynamics method. Computer Methods in Applied mechanics and Engineering 177(3-4):235-257, 1999
- Moreau J.J. Unilateral Contact and Dry Friction in Finite Freedom Dynamics, volume 302 of Non-smooth Mechanics and Applications, CISM Courses and Lectures. Springer, Wien, 1988
- Pfeiffer F., Foerg M. and Ulbrich H. Numerical aspects of non-smooth multibody dynamics. Comput. Methods Appl. Mech. Engrg 195(50-51):6891-6908, 2006
- Potra F.A., Anitescu M., Gavrea B. and Trinkle J. A linearly implicit trapezoidal method for integrating stiff multibody dynamics with contacts, joints and friction. Int. J. Numer. Meth. Engng 66(7):1079-1124, 2006
- Stewart D.E. and Trinkle J.C. An Implicit Time-Stepping Scheme for Rigid Body Dynamics with Inelastic Collisions and Coulomb Friction. Int. J. Numer. Methods Engineering 39(15):2673-2691, 1996
- Studer C. Augmented time-stepping integration of non-smooth dynamical systems, PhD Thesis ETH Zurich, ETH E-Collection, to appear 2008
- Studer C. Numerics of Unilateral Contacts and Friction -- Modeling and Numerical Time Integration in Non-Smooth Dynamics, Lecture Notes in Applied and Computational Mechanics, Volume 47, Springer, Berlin, Heidelberg, 2009