Combining vibrational linear-by-part dynamics and kinetic-based decoupling of the dynamics for multiple smooth impacts with redundancy

Combining vibrational linear-by-part dynamics and kinetic-based decoupling of the dynamics for multiple elastoplastic smooth impacts

“…In a previous work, we developed a version of this approach, restricted to elastic impacts, able to cope with redundancy [1]. The main idea consisted of assuming a finite linear normal stiffness (high enough to assume constant configuration throughout the process) at each impact point and solving a vibrational problem.…”

“…The result has been a piecewise linear elastoplastic compliant model compatible with the vibrational algorithm presented in [1]. The model is able to cope with redundancy and with a variable number of system's DOF associated to the creation and/or disappearance of unilateral constraints.…”

“…In order to keep the linear-by-part essence of the lossless approach presented in [1], the dissipative characteristics of the colliding surfaces have been modeled through a combination of linear springs and dry-friction dampers. As mentioned in the previous section, viscous damping yields energy losses but does not allow permanent indentation at the collision points.…”

“…The immediate consequence is that the stiffness matrix is not any more diagonal [1]. As the choice of independent colliding points may be changed along the problem, a contact point reaching the end of a compression phase, say 1 …”

Load assessment and analysis of impacts in multibody systems

“…The treatment of multi-point impacts has been discussed in the literature and several ways to deal with the problem have been proposed, e.g. [13], [17], [2], [3]. However, single-point impact scenarios are especially suitable to highlight the validity of the effective pre-impact kinetic energy as indicator of the maximum force during a collision.…”