Affiliation:
1. National Advanced Driving Simulator and Simulation Center, The University of Iowa, 2401 Oakdale Boulevard, Iowa City, IA 52242-5003
Abstract
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 0⩾gxt,t. The unknown in the problem is the time, t*, when the equality condition is reached. This paper presents an exact solution for t*, 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.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Reference8 articles.
1. Carver, M. B.
, 1978, “Efficient Integration Over Discontinuities in Ordinary Differential Equation Simulations,” Math. Comput. Simul., 20, No. 3, pp. 190–196.
2. Ellison, D.
, 1981, “Efficient Automatic Integration Of Odes With Discontinuities,” Math. Comput. Simul., 23, No. 1, pp. 12–20.
3. Enright, W. H., Jackson, K. R., Nørsett, S. P., and Thomson, P. G., 1986, “Effective Solution of Discontinuous Ivps Using a Runge-Kutta Formula Pair With Interpolants,” Appl. Math. Comput., 27, pp. 313–335.
4. Filippov, A. F.
, 1964, “Differential Equations With Discontinuous Right Hand Side,” ASM Trans. 42, pp. 199–231.
5. Halin, H. J., 1976, “Integration of Ordinary Differential Equations Containing Discontinuities,” Proceedings of the Summer Computer Simulation Conference 976, La Jolla, SCI Press, La Jolla, CA, pp. 46–53.
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