# Conference & Tech Papers

# Modeling and numerical considerations for the real- time simulation of mechanical systems in Cartesian coordinates

Conference & Tech Papers ID |
PA421 | |

Status: |
Published | |

Published date: |
07/26/2017 | |

Updated: |
07/26/2017 | |

Reported In: | Adams |

### Author(s)

### Abstract

International Conference on Scientific Computing and Differential Equations in Vancouver, Canada, August 2001

Below are brief considerations about some conference talks that I thought might be of interest to people in our organization.

Paul Hovland: Automatic Differentiation,Tool and Techiniques

The speaker talked about how Automatic Differentiation can be used to help users of large programs generate derivative information given a routine thatis consider to define a set of outputs as functions of a set of inputs. This holds great promise for the C++ solver, as it can be used in the context of SYSARRAY, SYSFUNC, SYSPAR constructs.

JackDongara: The Impact of Computer Architecture On Linear Algebra Algorithms.

The speaker talked about the importance of having fast BLAS (Basic Linear Algebra Subroutines) available on your machine. BLAS routines are the primary building blocks for more complex numerical methods (SVD, Linear Systems, QR, eigenvalues/eigenvectors, etc.). In histalk he mentioned his latest project-ATALS, which supposedly should produce optimized libraries on almost any platform possessing an ANSI/ISO C compiler, and some Unix-like command-line tools (eg., make, cp, etc). ATLAS runs on pretty much all Unix variants (including embedded systems), as well as Windows (Windows users must install the free cygnus tools). AIX, SunOS, HP, IRIX, Linux, and W2K optimized libraries are available.

Lawrence Shampine: Variable Order Adams Codes

He talked about the impact that step-size changes has on the accuracy of the results. He claimed that the theory of fixed order codes is classical, but when the order is varied, there is no theory explaining fundamental issues; in this situation he proved convergence, and some error estimators werejustifed.

Martin Arnold: Overlapping dynamic iteration for differential-algebraic systems

I was interested in this presentation particularly because of the work that this engineer from DLR German Aerospace Center did with the SIMPACK team. Actually the results he showed were obtained using SIMPACK. The basic idea of the talk was that of running cosimulations: in each step of iteration the large coupled system is decoupled in a set of smaller subsystems that may be solved independently from each other. As an example he had a train engine, which had some flexible components (the parts that touched the electrical wire), and some rigid parts. He was integrating the motion at different rates, propagating the simulation in steps (overlapping windows).

Razvan Fetecau: Nonsmooth Lagrangian Mechanics

He used variational techniques to approach the problem of rigid-body dynamics with impact. Below is his abstract, the presentation was very theoretical. It seemed that his approach worked for adobule pendulum like problem, he said he wasn't interested at that stage in real-life applications.

"The smooth Lagrangian mechanics is extended to the nonsmooth context andsymplecticity, conservation of the extended Lagrange 1-form and a version of the Noether's theorem are derived.

Based on the Veselov theory of discrete mechanics, we develop a symplectic-momentum preserving variational integrator which exactly captures the impact and which is perfectly consistent with the continuous theory. We test the algorithm on two selected examples and

recover the excellent long-time stable energy behavior typical of variational methods."

Mihai Anitescu: Time-stepping Methods for Stiff Multi-Rigid-Body Dynamics with Contact and Friction

Unlike what we do in ADAMS in his approach Mihai uses a complementarity impulse based approach. His goal is to get real-time performance for models with contacts, and unlike the previousspeaker he mentioned he was interested in real-life applications. Below is his abstract.

"The lack of classical solutions for the problem of determining the dynamics of a system of rigid bodies subject to non-interpenetration and Coulomb frictional constraints has prompted the investigation of time-stepping schemes having velocities and impulses as the fundamental variables. Such schemes always produce a solution to the discretized equations of motion (they are consistent), but most of them do notaccomodate stiffness well since they reduce to the explicit Euler method in the unconstrained case.

In thiswork we develop a time-stepping scheme for stiff multi-rigid-body dynamics with contact and friction, based on the linearly implicit Euler method embedded in a linear complementarity problem. We show that the method remains consistent for the most commonly encountered types of stiff forces. We discuss the behavior of the method as the stiffness parameters are increased to infnity, and we present several examples to illustrate the stability issues."

David Stewart: Elastic impacts and a new kind of dynamic complementarity problem

His point was that simple models based on fixedcoeffcients of restitution are often physically inaccurate. To overcome this he introduced a simplifed model of elastic impacts. The presentation was heavily theoretic, but in the end his approach lead to a new kind

of dynamic complementarity problem, which brought him to a resolution of thesimplifed problem. He argued that his approach could be a computationally effcient way of producing physically accurate simulations.

Dan Negrut: Modeling and Numerical Considerations for the Real-Time Simulation of Mechanical Systems

The paper presented an iterative approach for the solution of the linear system that computes the generalized accelerations in a mechanical system. This is supposed to work when no or mild friction is present in the system. The approach was based on coordinate partitioning, and anitreative solver was also used for both the position and velocity projections. The iterative approach is very scalable in a Cartesian framework, when the bodies of the system are mapped onto the available processors (or threads). The integration formula considered was explicit. In the proposed approach, parallel computational threads start in the equation formulation and continue through the numerical solution of the equations of motion. I attached the presentation and the paper.