Investigation of GPU Use in Conjunction With DCA-Based Articulated Multibody Systems Simulation

2015 ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Michael Hans
Keyword(s):  
Multibody Systems ◽  
Graphics Processing Units ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Time ◽  
Test Case ◽  
Time Step ◽  
Dynamic Simulations ◽  
Computational Performance ◽  
Compute Time

Since computational performance is critically important for simulations to be used as an effective tool to study and design dynamic systems, the computing performance gains offered by Graphics Processing Units (GPUs) cannot be ignored. Since the GPU is designed to execute a very large number of simultaneous tasks (nominally Single Instruction Multi-Data (SIMD)), recursive algorithms in general, such as the DCA, are not well suited to be executed on GPU-type architecture. This is because each level of recursion is dependent on the previous level. However, there are some ways that the GPU can be leveraged to increase computational performance when using the DCA to form and solve the equations of motion for articulated multibody systems with a very large number of degrees-of-freedom. Computational performance of dynamic simulations is highly dependent on the nature of the underlying formulation and the number of generalized coordinates used to characterize the system. Therefore, algorithms that scale in a more desirable (lower order) fashion with the number of degrees-of-freedom are generally preferred when dealing with large (N > 10) systems. However, the utility of using simulations as a scientific tool is directly related to actual compute time. The DCA, and other top performing methods, have demonstrated the desirable property of the required compute time scaling linearly with (O(n)) with the number of degrees-of-freedom (n) and sublinearly (O(logn) performance when implemented in parallel. However for the DCA, total compute time could be further reduced by exploiting the large number of independent operations involved in the first few levels of recursion. A simple chain-type pendulum example is used to explore the feasibility of using the GPU to execute the assembly and disassembly operations for the levels of recursion that contain enough bodies for this process to be computationally advantageous. A multi-core CPU is used to perform the operations in parallel using Open MP for the remaining levels. The number of levels of recursion that utilizes the GPU is varied from zero to all levels. The data corresponding to zero utilization of the GPU provides the reference compute-time in which the assembly and disassembly operations necessary at each level are performed in parallel using Open MP. The computational time required to simulate the system for one time-step where the GPU is utilized for various levels of recursion is compared to the reference compute time also varying the number of bodies in the system. A decrease in the compute-time when using the GPU is demonstrated relative to the reference compute-time even for systems of moderate size n < 1000 for arrangements using the GPU. This is a lower number of bodies than was expected for this test case and confirms that the GPU can bring significant increases in computational efficiency for large systems, while preserving the attractive sub-linear scalability (w.r.t. compute time) of the DCA.

Vibration analysis of multiple degrees of freedom mechanical system with dry friction

2012 ◽  
Vol 227 (7) ◽  
pp. 1505-1514 ◽  
Author(s):  
SD Yu ◽  
BC Wen
Keyword(s):  
Mechanical System ◽  
Dry Friction ◽  
Degrees Of Freedom ◽  
Simple Procedure ◽  
Mathematical Problem ◽  
Equations Of Motion ◽  
Inequality Constraints ◽  
Integration Scheme ◽  
Time Step ◽  
Multiple Degrees Of Freedom

This article presents a simple procedure for predicting time-domain vibrational behaviors of a multiple degrees of freedom mechanical system with dry friction. The system equations of motion are discretized by means of the implicit Bozzak–Newmark integration scheme. At each time step, the discontinuous frictional force problem involving both the equality and inequality constraints is successfully reduced to a quadratic mathematical problem or the linear complementary problem with the introduction of non-negative and complementary variable pairs (supremum velocities and slack forces). The so-obtained complementary equations in the complementary pairs can be solved efficiently using the Lemke algorithm. Results for several single degree of freedom and multiple degrees of freedom problems with one-dimensional frictional constraints and the classical Coulomb frictional model are obtained using the proposed procedure and compared with those obtained using other approaches. The proposed procedure is found to be accurate, efficient, and robust in solving non-smooth vibration problems of multiple degrees of freedom systems with dry friction. The proposed procedure can also be applied to systems with two-dimensional frictional constraints and more sophisticated frictional models.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

scholarly journals Smoothed Particle Hydrodynamics Simulation of a Mariculture Platform under Waves

Water ◽  
2021 ◽  
Vol 13 (20) ◽  
pp. 2847
Author(s):  
Feng Zhang ◽  
Li Zhang ◽  
Yanshuang Xie ◽  
Zhiyuan Wang ◽  
Shaoping Shang
Keyword(s):  
Smoothed Particle Hydrodynamics ◽  
Graphics Processing Units ◽  
Degrees Of Freedom ◽  
High Tide ◽  
Theoretical Data ◽  
Emergency Evacuation ◽  
Water Levels ◽  
Computational Time ◽  
Particle Hydrodynamics ◽  
Smoothed Particle

This work investigates the dynamic behaviors of floating structures with moorings using open−source software for smoothed particle hydrodynamics. DualSPHysics permits us to use graphics processing units to recreate designs that include complex calculations at high resolution with reasonable computational time. A free damped oscillation was simulated, and its results were compared with theoretical data to validate the numerical model developed. The simulated three degrees of freedom (3−DoF) (surge, heave, and pitch) of a rectangular floating box have excellent consistency with experimental data. MoorDyn was coupled with DualSPHysics to include a mooring simulation. Finally, we modelled and simulated a real mariculture platform on the coast of China. We simulated the 3−DoF of this mariculture platform under a typical annual wave and a Typhoon Dujuan wave. The motion was light and gentle under the typical annual wave but vigorous under the Typhoon Dujuan wave. Experiments at different tidal water levels revealed an earlier motion response and smaller motion range during the high tide. The results reveal that DualSPHysics combined with MoorDyn is an adaptive scheme to simulate a coupled fluid–solid–mooring system. This work provides support to disaster warning, emergency evacuation, and proper engineering design.

scholarly journals Learning data-driven reduced elastic and inelastic models of spot-welded patches

2021 ◽  
Vol 22 ◽  
pp. 32
Author(s):  
Agathe Reille ◽  
Victor Champaney ◽  
Fatima Daim ◽  
Yves Tourbier ◽  
Nicolas Hascoet ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Structural Response ◽  
Data Driven ◽  
Fine Scale ◽  
Time Step ◽  
Large Structures ◽  
Computational Performance ◽  
Local Patch ◽  
The Rich ◽  
Learning Data

Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.

Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

2013 ◽  
Author(s):  
Gilbert Gede ◽  
Dale L. Peterson ◽  
Angadh S. Nanjangud ◽  
Jason K. Moore ◽  
Mont Hubbard
Keyword(s):  
Open Source ◽  
Undergraduate Students ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Academic Research ◽  
General Purpose ◽  
Engineering Software ◽  
Symbolic Equations Of Motion ◽  
High Level

Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries — allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code.

On the Efficiency of Some Recently Developed Integration Algorithms for Offshore Problems

1983 ◽  
Vol 105 (1) ◽  
pp. 73-77 ◽  
Author(s):  
T. K. Datta ◽  
A. M. Sood
Keyword(s):  
Degrees Of Freedom ◽  
Large Time ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Response Analysis ◽  
Time Step ◽  
Beam Elements ◽  
Integration Schemes ◽  
Large Time Step ◽  
Integration Algorithms

The efficiency of some recently developed integration schemes, namely, Hilber’s ∝-method, collocation schemes and large time step integration schemes developed by Argyris, is evaluated by applying them to the response analysis of an idealized offshore tower. The tower is fixed at the base, having an additional mass at the top. For the analysis the tower has been modeled as an assemblage of 2-D beam elements. The dynamic degrees of freedom at each node are taken as those corresponding to the rotational and sway degrees of freedom. Using the normal mode theory the equations of motion have been decoupled except for the generalized loading vector which appear nonlinearly coupled, thus requiring iterative solution at every time step. The results of the study show that the large time step integration schemes developed by Argyris are more efficient than other integration methods considered here.

Dynamic Response Analysis of Large Latticed Space Structures

1989 ◽  
Vol 4 (1) ◽  
pp. 25-42 ◽  
Author(s):  
A.R. Kukreti ◽  
N.D. Uchil
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Time ◽  
Space Structures ◽  
Response Analysis ◽  
Actual System ◽  
Large Space ◽  
Element Analysis ◽  
Dynamic Response Analysis

In this paper an alternative method for dynamic response analysis of large space structures is presented, for which conventional finite element analysis would require excessive computer storage and computational time. Latticed structures in which the height is very small in comparison to its overall length and width are considered. The method is based on the assumption that the structure can be embedded in its continuum, in which any fiber can translate and rotate without deforming. An appropriate kinematically admissable series function is constructed to descrbe the deformation of the middle plane of this continuum. The unknown coefficients in this function are called the degree-of-freedom of the continuum, which is given the name “super element.” Transformation matrices are developed to express the equations of motion of the actual systems in terms of the degrees-of-freedom of the super element. Thus, by changing the number of terms in the assumed function, the degrees-of-freedom of the super element can be increased or decreased. The super element response results are transformed back to obtain the desired response results of the actual system. The method is demonstrated for a structure woven in the shape of an Archimedian spiral.

Dynamics of Serial Multibody Systems Using the Decoupled Natural Orthogonal Complement Matrices

1999 ◽  
Vol 66 (4) ◽  
pp. 986-996 ◽  
Author(s):  
S. K. Saha
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Rigid Bodies ◽  
Dynamic Equations ◽  
Orthogonal Complement ◽  
Forward Dynamics ◽  
Velocity Constraints

Constrained dynamic equations of motion of serial multibody systems consisting of rigid bodies in a serial kinematic chain are derived in this paper. First, the Newton-Euler equations of motion of the decoupled rigid bodies of the system at hand are written. Then, with the aid of the decoupled natural orthogonal complement (DeNOC) matrices associated with the velocity constraints of the connecting bodies, the Euler-Lagrange independent equations of motion are derived. The De NOC is essentially the decoupled form of the natural orthogonal complement (NOC) matrix, introduced elsewhere. Whereas the use of the latter provides recursive order n—n being the degrees-of-freedom of the system at hand—inverse dynamics and order n3 forward dynamics algorithms, respectively, the former leads to recursive order n algorithms for both the cases. The order n algorithms are desirable not only for their computational efficiency but also for their numerical stability, particularly, in forward dynamics and simulation, where the system’s accelerations are solved from the dynamic equations of motion and subsequently integrated numerically. The algorithms are illustrated with a three-link three-degrees-of-freedom planar manipulator and a six-degrees-of-freedom Stanford arm.

Multigranular Molecular Dynamics Simulations of Polymer Melts Using Multibody Algorithms

2005 ◽  
Author(s):  
Rudranarayan M. Mukherjee ◽  
Kurt S. Anderson ◽  
John Ziegler
Keyword(s):  
Molecular Dynamics ◽  
Polymer Melts ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Polymer Melt ◽  
Rigid Bodies ◽  
Computational Time ◽  
Integration Time ◽  
Test Case

In a multigranular approach for modeling molecular dynamics of polymer melts, different sections of the simulation box are modeled at different levels of detail viz. as particles, flexible bodies or rigid bodies. This approach eliminates high frequency localized motion while maintaining low frequency global conformational motion. This allows for longer integration time steps thus decreasing computational time. In this paper, we discuss our efforts to develop a consortium of dynamics algorithms capable of efficiently generating and solving the equations of motion at all three levels of modeling on a common software platform. A bead spring model of the polymer melt moving under the influence of truncated Lennard-Jones potential under periodic boundary conditions is pursued. Implementation issues and results from a test case consisting of 32 polymer chains of 16 beads each are presented. The paper also discusses the parallel implementation of this problem using MPI.

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