Contact Problems & Complementarity

MD05.1 Complementarity & Mechanical Contact with Friction Anders Klarbring, Jong-Shi Pang --- Linkoping Univ., Dept. of Mech. Eng., S0581 83 Linkoping, , Sweden (andkl@ikp.liu.se)

The ability to analyze and simulate mechanical bodies in frictional¨ contact is of crucial importance in many mechanical engineering¨ problems. These contact problems can profitably be formulated as¨ complementarity problems. The present work reports on the benefits¨ of such formulations, presents new existence results and discusses¨ numerical examples.

MD05.2 A Velocity-Based Time-Stepping Scheme for Simulating Rigid Body Systems with Contact David E. Stewart, Jeffrey C. Trinkle --- TX A&M Univ., Dept. of Math., College Station, TX 77843-3122, (des@isc.tamu.edu)

We present a new numerical method for solving the system motion¨ equations of rigid bodies with intermittent frictional contact(s).¨ At each time step, these equations are formulated as a NCP in body¨ positions and/or velocities. This NCP can be solved as a sequence of¨ LCPs. Our velocity-based method avoids the problem of solution¨ nonexistence that plagues acceleration-based methods.

MD05.3 A Lemke-Type Method for Multi-Rigid-Body Contact Problems with Friction Pyramid Constraints Grace Lo, Jong-Shi Pang --- Johns Hopkins Univ., Dept. of Math. Sci., Baltimore, MD 21218-2689, (lo@brutus.mts.jhu.edu)

A Lemke-type method is proposed to solve multi-rigid-body contact¨ problems with friction pyramid constraints. Instead of introducing¨ new variables to transform the model to a standard LCP, our modified¨ Lemke method directly treats the friction conditions as constraints¨ of the variable upper bound type. Theoretical and numerical results¨ are presented.

MD05.4 LCPs in Fractal Geometries: Cracks in Structures with Debonding & Friction P. D. Panagiotopoulos, O. Panagouli --- Aristotle Univ., Dept. of Civil Eng., Thessaloniki, 54006 , Greece (pdpana@heron.civil.auth.gr)

The geometry of cracks in structures is of fractal nature. If a¨ crack occurs debonding and friction on the interface, the free¨ boundaries between the contact and noncontact regions and the¨ adhesive and sliding friction regions need to be determined. The¨ fractal geometry of the crack is approximated by an iterated¨ function system...