Discontinuous function constraints arise during the calculation of surface contact, stiction, and friction effects in studies of the behavior of complex systems. These nonlinear effects are mathematically defined by inequality constraints of the form The unknown in the problem is the time, when the equality condition is reached. This paper presents an exact solution for which is obtained by introducing a slack variable that replaces time as the independent variable, leading to an extended state-space that is noniteratively integrated to the constraint surface. Several applications are presented to demonstrate the method.
On the Simulation of Discontinuous Functions
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 12, 2000; final revision, Apr. 16, 2001. Associate Editor: N. C. Perkins. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Turner, J. D. (April 16, 2001). "On the Simulation of Discontinuous Functions ." ASME. J. Appl. Mech. September 2001; 68(5): 751–757. https://doi.org/10.1115/1.1387022
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