On the adaptation of local impact laws for multiple impact problems
- PDF / 1,492,047 Bytes
- 20 Pages / 547.087 x 737.008 pts Page_size
- 21 Downloads / 254 Views
ORIGINAL PAPER
On the adaptation of local impact laws for multiple impact problems Alejandro Cosimo · Federico J. Cavalieri · Alberto Cardona · Olivier Brüls
Received: 29 January 2020 / Accepted: 31 July 2020 © Springer Nature B.V. 2020
Abstract The classical local impact laws of Newton and Poisson are able to capture the behaviour observed in single-impact collisions in many situations. However, in the case of collisions with multiple impacts, the simultaneous enforcement of local impact laws does not reproduce essential features of the physical process, such as propagation effects. The aim of this work is to broaden the applicability of the classical Newton impact law to problems involving multiple impacts by assuming instantaneous local impact times and a rigid behaviour of the bodies in contact. The proposed method is implemented as an extension of the nonsmooth generalized-α method. In order to model events involving multiple impacts, a sequence of impact prob-
lems is defined on a vanishing time interval and the active set of each velocity-level sub-problem is redefined in such a way that closed contacts with zero preimpact velocity are considered inactive. This simple redefinition allows us to deal successfully with many situations involving multiple impacts, by generating a sequence of impact problems which is amenable to be modelled by the simultaneous enforcement of classical impact laws. Additionally, the methodology fits well under the algorithmic structure of the nonsmooth generalized-α scheme or any scheme dealing with linear complementary problems at velocity level. Several examples are analyzed in order to assess the performance of the method and to discuss its main features.
A. Cosimo · O. Brüls (B) Department of Aerospace and Mechanical Engineering, University of Liège, Allée de la Découverte 9, 4000 Liège, Belgium e-mail: [email protected]
Keywords Nonsmooth contact dynamics · Nonsmooth generalized-α · Multiple impacts · Newton’s cradle · Billiard break
A. Cosimo e-mail: [email protected]
1 Introduction
A. Cosimo · F. J. Cavalieri · A. Cardona Centro de Investigación de Métodos Computacionales (CIMEC), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) / Universidad Nacional del Litoral (UNL), Colectora Ruta Nac Nro 168, Km 0, Paraje El Pozo, 3000 Santa Fe, Argentina F. J. Cavalieri e-mail: [email protected] A. Cardona e-mail: [email protected]
In nonsmooth contact dynamics, single-impact collisions are accurately modelled by classical local impact laws such as the Newton’s impact law. Adopting local impact laws for the modelling of collisions with multiple impacts is a natural and convenient choice for its simplicity. Whenever a collision with multiple impacts takes place, the local impact laws corresponding to the many closed contacts can be enforced simultaneously. The simultaneous enforcement of local impact
123
A. Cosimo et al.
laws results in a solution which preserves symmetries already present in the system, such as in the case of the Bern
Data Loading...
