Formulation and Analysis of Stable Time-Stepping Algorithms for Contact Problems

Abstract

The formulation of stable time-stepping algorithms for dynamic contact problems, both frictionless and frictional, is presented. Special attention is given to the properties of the underlying continuum problem to serve as guidelines for the development of the algorithms. The proposed method conserves linear and angular momenta, and, in the frictionless case, conserves the energy by means of a restoration potential. Coulomb's friction law is used to model the friction phenomenon; the scheme presented herein is unconditionally dissipative, just as the physical system is. The scheme has been enhanced by the enforcement of a constraint on the velocities, in addition to the unilateral (impenetrability) constraint imposed on the displacements; this enhancement does not disturb the conservation/restoration properties. Numerical dissipation may also be added to stabilize the scheme for problems with high frequency energy modes. A multibody implementation is presented to show the versatility of the algorithm. In this implementation, the contract detection scheme includes an efficient sorting procedure which makes large scale simulations possible. Lastly, various numerical examples show the stability and robustness of the scheme.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1998
Accession Number
ADA336872

Entities

People

  • Eva G. Petocz

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Angular Momentum
  • Computational Fluid Dynamics
  • Detection
  • Differential Equations
  • Frequency
  • Linear Momentum
  • Mechanical Properties
  • Mechanics
  • Modulus Of Elasticity
  • Molecular Dynamics
  • Physical Properties
  • Regression Analysis
  • Simulations
  • Total Angular Momentum
  • Trees (Data Structures)
  • Two Dimensional

Readers

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