Abstract
The paper gives on overview of possible formulations of spatial contact situations as they occur in dynamic systems composed of rigid bodies. We will discuss formulations of the contact problem of sliding and rolling as linear complementarity problems in standard form, where general approximations of convex sets by polytopes are also presented. For completeness, a short treatise on spatial contact kinematics and the structure of the equations of motion is given.
Highlights
Multibody systems are usually considered to be bilaterally coupled or to possess interconnections in the form of force laws
We present linear complementarity formulations (LCP) and nonlinear complementarity problem (NCP) formulations in standard form for friction pyramids and for the friction cone, respectively
We have presented different formulations of the unilateral contact problem with Coulomb friction in dynamic multibody systems
Summary
Multibody systems are usually considered to be bilaterally coupled or to possess interconnections in the form of force laws. First difficulties usually occur when this problem is accompanied by sticking contacts that might undergo a transition to sliding This situation requires a formulation of the Coulomb friction law on the level of acceleration, sometimes called the rolling contact problem. If the conic friction law is considered, nonlinearities are involved in the formulation of the complementarity conditions, and one cannot expect linear complementarity to be available In most cases this situation is treated with special algorithms such as in [1,9,8] but no formulation as a standard problem is given. Both contact laws are first stated in their original form at the level of displacements and velocities, respectively, and transferred to the acceleration level.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Computer Methods in Applied Mechanics and Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
