6,506 research outputs found
Proximal bundle method for contact shape optimization problem
From the mathematical point of view, the contact shape optimization is a problem of nonlinear optimization with a specific structure, which can be exploited in its solution. In this paper, we show how to overcome the difficulties related to the nonsmooth cost function by using the proximal bundle methods. We describe all steps of the solution, including linearization, construction of a descent direction, line search, stopping criterion, etc. To illustrate the performance of the presented algorithm, we solve a shape optimization problem associated with the discretized two-dimensional contact problem with Coulomb's friction
Cavity method for force transmission in jammed disordered packings of hard particles
The force distribution of jammed disordered packings has always been
considered a central object in the physics of granular materials. However, many
of its features are poorly understood. In particular, analytic relations to
other key macroscopic properties of jammed matter, such as the contact network
and its coordination number, are still lacking. Here we develop a mean-field
theory for this problem, based on the consideration of the contact network as a
random graph where the force transmission becomes a constraint optimization
problem. We can thus use the cavity method developed in the last decades within
the statistical physics of spin glasses and hard computer science problems.
This method allows us to compute the force distribution for random
packings of hard particles of any shape, with or without friction. We find a
new signature of jamming in the small force behavior , whose exponent has attracted recent active interest: we find a
finite value for , along with . Furthermore, we relate
the force distribution to a lower bound of the average coordination number of jammed packings of frictional spheres with
coefficient . This bridges the gap between the two known isostatic limits
(in dimension ) and by extending the naive Maxwell's counting argument to
frictional spheres. The theoretical framework describes different types of
systems, such as non-spherical objects in arbitrary dimensions, providing a
common mean-field scenario to investigate force transmission, contact networks
and coordination numbers of jammed disordered packings
Differential-Algebraic Equations and Beyond: From Smooth to Nonsmooth Constrained Dynamical Systems
The present article presents a summarizing view at differential-algebraic
equations (DAEs) and analyzes how new application fields and corresponding
mathematical models lead to innovations both in theory and in numerical
analysis for this problem class. Recent numerical methods for nonsmooth
dynamical systems subject to unilateral contact and friction illustrate the
topicality of this development.Comment: Preprint of Book Chapte
Fast Simulation of Vehicles with Non-deformable Tracks
This paper presents a novel technique that allows for both computationally
fast and sufficiently plausible simulation of vehicles with non-deformable
tracks. The method is based on an effect we have called Contact Surface Motion.
A comparison with several other methods for simulation of tracked vehicle
dynamics is presented with the aim to evaluate methods that are available
off-the-shelf or with minimum effort in general-purpose robotics simulators.
The proposed method is implemented as a plugin for the open-source
physics-based simulator Gazebo using the Open Dynamics Engine.Comment: Submitted to IROS 201
Analysis of friction coupling and the Painlevé paradox in multibody systems
Multibody models are useful to describe the macroscopic motion of the elements of physical systems. Modeling contact in such systems can be challenging, especially if friction at the contact interface is taken into account. Furthermore, the dynamics equations of multibody systems with contacts and Coulomb friction may become ill-posed due to friction coupling, as in the Painlevé paradox, where a solution for system dynamics may not be found. Here, the dynamics problem is considered following a general approach so that friction phenomena, such as dynamic jamming, can be analyzed. The effect of the contact forces on the velocity field of the system is the cornerstone of the proposed formulation, which is used to analyze friction coupling in multibody systems with a single contact. In addition, we introduce a new representation of the so-called generalized friction cone, a quadratic form defined in the contact velocity space. The geometry of this cone can be used to determine the critical cases where the solvability of the system dynamic equations can be compromised. Moreover, it allows for assessing friction coupling at the contact interface, and obtaining the values of the friction coefficient that can make the dynamics formulation inconsistent. Finally, the classical Painlevé example of a single rod and the multibody model of an articulated arm are used to illustrate how the proposed cone can detect the cases where the dynamic equations have no solution, or multiple solutions.Postprint (author's final draft
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