Alessandro Tasora

An iterative approach for cone complementarity problems for nonsmooth dynamics

Aiming at a fast and robust simulation of large multibody systems with contacts and friction, this work presents a novel method for solving large cone complementarity problems by means of a fixed-point iteration. The method is an extension of the Gauss-Seidel and Gauss-Jacobi method with overrelaxation for symmetric convex linear complementarity problems. The method is proved to be convergent under fairly standard assumptions and is shown by our tests to scale well up to 500,000 contact points and more than two millions of unknowns.

Large-scale parallel multi-body dynamics with frictional contact on the graphical processing unit:

In the context of simulating the frictional contact dynamics of large systems of rigid bodies, this paper reviews a novel method for solving large cone complementarity problems by means of a fixed-point iteration algorithm. The method is an extension of the Gauss—Seidel and Gauss—Jacobi methods with over-relaxation for symmetric convex linear complementarity problems. Convergent under fairly standard assumptions, the method is implemented in a parallel framework by using a single instruction multiple data computation paradigm promoted by the Compute Unified Device Architecture library for graphical processing unit programming. The framework supports the simulation of problems with more than one million bodies in contact. Simulation thus becomes a viable tool for investigating the dynamics of complex systems such as ground vehicles running on sand, powder composites, and granular material flow.

A convex complementarity approach for simulating large granular flows.

Aiming at the simulation of dense granular flows, we propose and test a numerical method based on successive convex complementarity problems. This approach originates from a multibody description of the granular flow: all the particles are simulated as rigid bodies with arbitrary shapes and frictional contacts. Unlike the discrete element method (DEM), the proposed approach does not require small integration time steps typical of stiff particle interaction; this fact, together with the development of optimized algorithms that can run also on parallel computing architectures, allows an efficient application of the proposed methodology to granular fiows with a large number of particles. We present an application to the analysis of the refueling flow in pebble-bed nuclear reactors. Extensive validation of our method against both DEM and physical experiments results indicates that essential collective characteristics of dense granular flow are accurately predicted.

Using Nesterov's Method to Accelerate Multibody Dynamics with Friction and Contact

We present a solution method that, compared to the traditional Gauss-Seidel approach, reduces the time required to simulate the dynamics of large systems of rigid bodies interacting through frictional contact by one to two orders of magnitude. Unlike Gauss-Seidel, it can be easily parallelized, which allows for the physics-based simulation of systems with millions of bodies. The proposed accelerated projected gradient descent (APGD) method relies on an approach by Nesterov in which a quadratic optimization problem with conic constraints is solved at each simulation time step to recover the normal and friction forces present in the system. The APGD method is validated against experimental data, compared in terms of speed of convergence and solution time with the Gauss-Seidel and Jacobi methods, and demonstrated in conjunction with snow modeling, bulldozer dynamics, and several benchmark tests that highlight the interplay between the friction and cohesion forces.

GPU-based parallel computing for the simulation of complex multibody systems with unilateral and bilateral constraints: an overview

This work reports on advances in large-scale multibody dynamics simulation facilitated by the use of the Graphics Processing Unit (GPU). A description of the GPU execution model along with its memory spaces is provided to illustrate its potential parallel scientific computing. The equations of motion associated with the dynamics of large system of rigid bodies are introduced and a solution method is presented. The solution method is designed to map well on the parallel hardware, which is demonstrated by an order of magnitude reductions in simulation time for large systems that concern the dynamics of granular material. One of the salient attributes of the solution method is its linear scaling with the dimension of the problem. This is due to efficient algorithms that handle in linear time both the collision detection and the solution of the nonlinear complementarity problem associated with the proposed approach. The current implementation supports the simulation of systems with more than one million bodies on commodity desktops. Efforts are under way to extend this number to hundreds of millions of bodies on small affordable clusters.

Chrono: An Open Source Multi-physics Dynamics Engine

We provide an overview of a multi-physics dynamics engine called Chrono. Its forte is the handling of complex and large dynamic systems containing millions of rigid bodies that interact through frictional contact. Chrono has been recently augmented to support the modeling of fluid-solid interaction (FSI) problems and linear and nonlinear finite element analysis (FEA). We discuss Chrono’s software layout/design and outline some of the modeling and numerical solution techniques at the cornerstone of this dynamics engine. We briefly report on some validation studies that gauge the predictive attribute of the software solution. Chrono is released as open source under a permissive BSD3 license and available for download on GitHub.

Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum

This study deals with the dynamical evolutions exhibited by a simple mechanical model of building, comprising a parallelepiped standing on a horizontal plane. The main goal is the introduction of a pendulum in order to reduce oscillations. The theoretical part of the work consists of a Lagrange formulation and Galerkin approximation method, and dry friction has also been considered. From the analytical/numerical simulations, we derive some important conclusions, providing us with the tools suitable for the design of absorbers in practical cases.

A Fast NCP Solver for Large Rigid-Body Problems with Contacts, Friction, and Joints

Summary. The simulation of multibody systems with rigid contacts entails the solution of nonsmooth equations of motion. The dynamics is nonsmooth because of the discontinuous nature of noninterpenetration, collision, and adhesion constraints. We propose a solver that is able to handle the simulation of multibody systems of vast complexity, with more than 100,000 colliding rigid bodies. The huge number of nonsmooth constraints arising from unilateral contacts with friction gives rise to a nonlinear complementarity problem (NCP), which we solve by means of a highperformance iterative method. The method has been implemented as a high-performance software library, written in C++. Complex simulation scenarios involving thousands of moving parts have been extensively tested, showing a remarkable performance of the numerical scheme compared to other algorithms.

Solving Large Multibody Dynamics Problems on the GPU

Publisher Summary This chapter describes an approach for the dynamic simulation of large collections of rigid bodies interacting through millions of frictional contacts and bilateral mechanical constraints. The ability to efficiently and accurately simulate the dynamics of rigid multibody systems is relevant in computer-aided engineering design, virtual reality, video games, and computer graphics. Devices composed of rigid bodies interacting through frictional contacts and mechanical joints pose numerical solution challenges because of the discontinuous nature of the motion. Reports indicate that the most popular rigid body software for engineering simulation, which uses an approach based on the so-called “discrete element method,” runs into significant difficulties when handling problems involving thousands of contact events. Another example of commercially available rigid body dynamics software is NVIDIAs PhysX. This software is commonly used in real-time applications where performance is the primary goal. The formulation of the equations of motion, that is, the equations that govern the time evolution of a multibody system, is based on the absolute, or Cartesian, representation of the attitude of each rigid body in the system. The GPU dynamics solver data structures are implemented as large arrays (buffers) to match the execution model associated with NVIDIAs CUDA. Four main buffers used are—the contacts buffer, the constraints buffer, the reduction buffer, and the bodies buffer. The data structure for the contacts has been mapped into columns of four floats.

Posing Multibody Dynamics With Friction and Contact as a Differential Complementarity Problem

We use a complementarity approach to pose the Coulomb friction model, combine it with a non-penetration condition, and append to a differential algebraic problem to characterize the dynamics of multibody systems with friction and contact. The resulting problem is relaxed to a Cone Complementarity Problem, whose solution is shown to represent the first order optimality condition of a quadratic program with conic constraints.