Vyasarayani, C P and Samukham, Surya and Khaderi, Syed Nizamuddin
(2019)
Nonsmooth modeling of distributed impacts in spatially
discretized continuous structures using the Ivanov
transformation.
arXiv.org.
Abstract
This work deals with the modeling of nonsmooth impacting motions of a structure against a rigid distributed obstacle. Finite element methods can be used to discretize the structure, and this results in a system of ordinary differential equations (ODEs). When these ODEs are subjected to unilateral constraints and velocity jump conditions, one has to use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a nontrivial and computationally demanding task. Ivanov (Ivanov, A., 1993. Analytical methods in the theory of vibro-impact systems. Journal of Applied Mathematics and Mechanics, 57(2), pp. 221-236.) proposed a nonsmooth transformation for a vibro-impacting multidegree-of-freedom (MDOF) system subjected to only a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions, but did not explore its application to simulating distributed collisions in discretized continuous structures. We adopt the Ivanov transformation to deal with multiple unilateral constraints in discretized continuous structures. The developed method is demonstrated by modeling the distributed collision of a string and a beam against a rigid surface. For validation, we compare our results with the penalty approach
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