Computational Aspects of Adaptive Dimensional Reduction for Nonlinear Boundary Value Problems

Abstract

There has been increased interest recently in feed-back methods for reliable, robust, efficient computational methods in mechanics. We will outline the construction of such methods for a class of problems describing special (anti-plane shear) deformations of bars of rectangular or arched cross section. In particular, we will show how to reduce the dimension of the underlying problem adaptively . For brittle or linear materials, this method is adaptive (optimal in rate of convergence). We shall emphasize the computational aspects tht have practical import to the performance of this method, such as the construction of a posteriori error estimators that are simple to compute, the selection of basis functions in the dimensional reduction and the heuristic principle for extension. We will illustrate these concepts with computations.

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Document Details

Document Type
Technical Report
Publication Date
Feb 24, 1990
Accession Number
ADA219889

Entities

People

  • Soren Jensen

Organizations

  • University of Maryland, Baltimore

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algebra
  • Asymptotic Series
  • Boundaries
  • Boundary Value Problems
  • Closed Loop Systems
  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Estimators
  • Magnetic Flux Density
  • Materials
  • Mechanics
  • Partial Differential Equations
  • Polynomials
  • Universities

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Materials Science (Mechanical Engineering).
  • Theoretical Analysis.