Generalized Coordinate Partitioning Methods for Numerical Integration of Differential-Algebraic Equations of Dynamics

1990 ◽  
pp. 97-114 ◽  
Author(s):  
Edward J. Haug ◽  
Jeng Yen
Keyword(s):  
Numerical Integration ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Partitioning Methods ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A Hybrid Numerical Integration Method for Machine Dynamic Simulation

1986 ◽  
Vol 108 (2) ◽  
pp. 211-216 ◽  
Author(s):  
T. W. Park ◽  
E. J. Haug
Keyword(s):  
Mechanical System ◽  
Dynamic Simulation ◽  
Error Control ◽  
Integration Method ◽  
Differential Algebraic Equations ◽  
Numerical Integration Method ◽  
Algebraic Equations ◽  
Stable Method ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

An efficient and stable method for solving mixed-differential algebraic equations of constrained mechanical system dynamics is presented. The algorithm combines constraint stabilization and generalized coordinate partitioning methods, taking advantage of their attractive speed and error control characteristics, respectively. Three examples are studied to demonstrate efficiency and stability of the method.

On the Numerical Scheme to Solve a Realistic Chemical Vapor Infiltration Reactor Model

2007 ◽  
Author(s):  
John K. Kamel ◽  
Samuel Paolucci
Keyword(s):  
Mathematical Model ◽  
Numerical Integration ◽  
Chemical Vapor ◽  
Differential Algebraic Equations ◽  
Chemical Vapor Infiltration ◽  
Integration Scheme ◽  
Algebraic Equations ◽  
Splitting Algorithm ◽  
Reactor Model ◽  
Vapor Infiltration

We describe the general mathematical model as well as the numerical integration procedure arising in modeling a realistic chemical vapor infiltration process. The numerical solution of the model ultimately leads to the solution of a large system of stiff differential algebraic equations. An operator splitting algorithm is employed to overcome the stiffness associated with chemical reactions, whereas a projection method is employed to overcome the difficulty arising from having to solve a large coupled system for the velocity and pressure fields. The resulting mathematical model and the numerical integration scheme are used to explore temperature, velocity, and concentration fields inside a chemical vapor infiltration reactor used in the manufacturing of aircraft brakes.

Design Sensitivity Analysis of Large-Scale Constrained Dynamic Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 156-162 ◽  
Author(s):  
E. J. Haug ◽  
R. A. Wehage ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Adjoint Equations ◽  
Design Sensitivity Analysis ◽  
Integration Algorithm ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A method for computer-aided design sensitivity analysis of large-scale constrained dynamic systems is presented. A generalized coordinate partitioning method is used for assembling and solving sets of mixed differential-algebraic equations of motion and adjoint equations required for calculation of derivatives of dynamic response measures with respect to design variables. The reduction in dimension of the equations of motion and associated adjoint equations obtained through use of generalized coordinate partitioning significantly reduces the computational burden, as compared to methods previously employed. Use of predictor-corrector numerical integration algorithms, rather than an implicit integration algorithm used in the past is shown to greatly simplify the equations that must be formulated and solved. Two examples are presented to illustrate accuracy of the design sensitivity analysis method developed.

A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems

2011 ◽  
Vol 6 (4) ◽  
Author(s):  
Shih-Tin Lin ◽  
Ming-Wen Chen
Keyword(s):  
Numerical Integration ◽  
Pid Controller ◽  
Controller Design ◽  
Equations Of Motion ◽  
Constraint Equation ◽  
Correct Choice ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Stabilization Method ◽  
Constraint Stabilization

The dynamic equations of motion of the constrained multibody mechanical system are mixed differential-algebraic equations (DAEs). The numerical solution of the DAE systems solved using ordinary-differential equation (ODE) solvers may suffer from constraint drift phenomenon. To solve this problem, Baumgarte proposed a constraint stabilization method in which a position and velocity terms were added in the second derivative of the constraint equation. Baumgarte’s method is a proportional-derivative (PD) type controller design. In this paper, an Iintegrator controller is included to form a proportional-integral-derivative (PID) controller so that the steady state error of the numerical integration can be reduced. Stability analysis methods in the digital control theory are used to find out the correct choice of the coefficients for the PID controller.

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