GENERALIZED CO-ORDINATE PARTITIONING IN STATIC EQUILIBRIUM ANALYSIS OF LARGE-SCALE MECHANICAL SYSTEMS.

Parviz E Nikravesh, Manohar Srinivasan

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This paper presents a computer-based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co-ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i. e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co-ordinates and constructs an influence coefficient matrix that relates variations in dependent and independent co-ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large-scale systems is presented.

Original languageEnglish (US)
Pages (from-to)451-464
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Volume21
Issue number3
StatePublished - Mar 1985

Fingerprint

Equilibrium Analysis
Constrained optimization
Static Analysis
Large-scale Systems
Mechanical Systems
Partitioning
Potential energy functions
Jacobian matrices
Potential energy
Conservative force
Large scale systems
Kinematics
Gaussian elimination
Pivoting
Dependent
Constrained Systems
Jacobian matrix
Unconstrained Optimization
Constrained Optimization
Constrained Optimization Problem

ASJC Scopus subject areas

  • Engineering (miscellaneous)
  • Computational Mechanics
  • Applied Mathematics

Cite this

GENERALIZED CO-ORDINATE PARTITIONING IN STATIC EQUILIBRIUM ANALYSIS OF LARGE-SCALE MECHANICAL SYSTEMS. / Nikravesh, Parviz E; Srinivasan, Manohar.

In: International Journal for Numerical Methods in Engineering, Vol. 21, No. 3, 03.1985, p. 451-464.

Research output: Contribution to journalArticle

@article{2796871f3ba04cb98abc17060a41ff22,
title = "GENERALIZED CO-ORDINATE PARTITIONING IN STATIC EQUILIBRIUM ANALYSIS OF LARGE-SCALE MECHANICAL SYSTEMS.",
abstract = "This paper presents a computer-based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co-ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i. e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co-ordinates and constructs an influence coefficient matrix that relates variations in dependent and independent co-ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large-scale systems is presented.",
author = "Nikravesh, {Parviz E} and Manohar Srinivasan",
year = "1985",
month = "3",
language = "English (US)",
volume = "21",
pages = "451--464",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "3",

}

TY - JOUR

T1 - GENERALIZED CO-ORDINATE PARTITIONING IN STATIC EQUILIBRIUM ANALYSIS OF LARGE-SCALE MECHANICAL SYSTEMS.

AU - Nikravesh, Parviz E

AU - Srinivasan, Manohar

PY - 1985/3

Y1 - 1985/3

N2 - This paper presents a computer-based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co-ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i. e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co-ordinates and constructs an influence coefficient matrix that relates variations in dependent and independent co-ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large-scale systems is presented.

AB - This paper presents a computer-based method for automatic formulation and efficient numerical solution of static equilibrium equations for nonlinear constrained mechanical systems with conservative forces. Nonlinear holonomic constraint equations and a potential energy function are written in terms of a maximal set of Cartesian generalized co-ordinates. A stable static equilibrium configuration is found by minimizing the potential energy of the system, subject to the kinematic constraint equations, i. e. constrained optimization. A Gaussian elimination algorithm with full pivoting decomposes the constraint Jacobian matrix, identifies dependent and independent co-ordinates and constructs an influence coefficient matrix that relates variations in dependent and independent co-ordinates. This information is employed to convert the constrained optimization problem to an unconstrained optimization problem. A simple example is presented to illustrate the method. An algorithm that may be used in analysis of large-scale systems is presented.

UR - http://www.scopus.com/inward/record.url?scp=0022029306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022029306&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0022029306

VL - 21

SP - 451

EP - 464

JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

SN - 0029-5981

IS - 3

ER -