Dan Negrut

SUMMARY: Many‐body dynamics problems are expected to handle millions of unknowns when, for instance, investigating the three‐dimensional flow of granular material. Unfortunately, the size of the problems tractable by existing numerical solution techniques is severely limited on convergence grounds. This is typically the case when the equations of motion embed a differential variational inequality problem that captures contact and possibly frictional interactions between rigid and/or flexible bodies. As the size of the physical system increases, the speed and/or the quality of the numerical solution decreases. This paper describes three methods – the gradient projected minimum residual method, the preconditioned spectral projected gradient with fallback method, and the modified proportioning with reduced gradient projection method – that demonstrate better scalability than the projected Jacobi and Gauss–Seidel methods commonly used to solve contact problems that draw on a differential‐variational‐inequality‐based modeling approach. Copyright © 2013 John Wiley & Sons, Ltd.

The last decade witnessed a manifest shift in the microprocessor industry towards chip designs that promote parallel computing. Until recently the privilege of a select group of large research centers, Teraflop computing is becoming a commodity owing to inexpensive GPU cards and multi to many-core x86 processors. This paradigm shift towards large scale parallel computing has been leveraged in CHRONO, a freely available C++ multi-physics simulation package. CHRONO is made up of a collection of loosely coupled components that facilitate different aspects of multi-physics modeling, simulation, and visualization. This contribution provides an overview of CHRONO::Engine, CHRONO::Flex, CHRONO::Fluid, and CHRONO::Render, which are modules that can capitalize on the processing power of hundreds of parallel processors. Problems that can be tackled in CHRONO include but are not limited to granular material dynamics, tangled large flexible structures with self contact, particulate flows, and tracked vehicle mobility. The paper presents an overview of each of these modules and illustrates through several examples the potential of this multi-physics library.

The premise of this work is that the presence of high stiffness and/or frictional contact/impact phenomena limits the effective use of high order integration formulas when numerically investigating the time evolution of real-life mechanical systems. Producing a numerical solution relies most often on low-order integration formulas of which the paper investigates three alternatives: Newmark, HHT, and order 2 BDFs. Using these methods, a first set of three algorithms is obtained as the outcome of a direct index-3 discretization approach that considers the equations of motion of a multibody system along with the position kinematic constraints. The second batch of three algorithms draws on the HHT and BDF integration formulas and considers, in addition to the equations of motion, both the position and velocity kinematic constraint equations. Numerical experiments are carried out to compare the algorithms in terms of several metrics: (a) order of convergence, (b) energy preservation, (c) velocity kinematic constraint drift, and (d) efficiency. The numerical experiments draw on a set of three mechanical systems: a rigid slider-crank, a slider-crank with a flexible body, and a seven body mechanism. The algorithms investigated show good performance in relation to the asymptotic behavior of the integration error and, with one exception, result in comparable CPU simulation times with a small premium being paid for enforcing the velocity kinematic constraints.

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 analysis of problems with a large number of rigid 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.

Given the highly nonlinear attribute of the underlying dynamics associated with the time evolution of multibody systems, an open question in mechanical system simulation is how one can reliably replace a model whose simulation is time consuming with a more expeditious one. Pushing this idea to the limit one can all together eliminate the dynamics of the problem using a set of simulations that train a predictor that is later used to provide the time evolution of the dynamic system. This paper investigates a Gaussian Random Function (GRF) based approach that attempts to address these questions. It relies on a framework recently proposed in the Statistical Analysis community that largely deals with the issues of model validation, calibration, and data integration. The approach investigated has several steps that are illustrated with a slider-crank mechanical systems whose time evolution is governed by a nonlinear set of index 3 Differential Algebraic Equations (DAEs). The paper concludes with a set of remarks on the potential of GRFs in the context of time domain analysis of mechanical systems.

The premise of this work is that real-life mechanical systems limit the use of high order integration formulas due to the presence in the associated models of friction and contact/impact elements. In such cases producing a numerical solution necessarily relies on low order integration formulas. The resulting algorithms are generally robust and expeditious; their major drawback remains that they typically require small integration step-sizes in order to meet a user prescribed accuracy. This paper looks at three low order numerical integration formulas: Newmark, HHT, and BDF of order two. These formulas are used in two contexts. A first set of three methods is obtained by considering a direct index-3 discretization approach that solves for the equations of motion and imposes the position kinematic constraints. The second batch of three additional methods draws on the HHT and BDF integration formulas and considers in addition to the equations of motion both the position and velocity kinematic constraint equations. The first objective of this paper is to review the theoretical results available in the literature regarding the stability and convergence properties of these low order methods when applied in the context of multibody dynamics simulation. When no theoretical results are available, numerical experiments are carried out to gauge order behavior. The second objective is to perform a set of numerical experiments to compare these six methods in terms of several metrics: (a) efficiency, (b) velocity constraint drift, and (c) energy preservation. A set of simple mechanical systems is used for this purpose: a double pendulum, a slider crank with rigid bodies, and a slider crank with a flexible body represented in the floating frame of reference formulation.