Mesh Refinement in Finite Element Analysis by Minimization of the Stiffness Matrix Trace

Abstract

The finite element method, in general, is an approximate method to solve differential equations. Using variational calculus the differential equation under consideration is posed as a functional. The resulting functional depends upon the unknowns and their derivatives with respect to the spatial coordinates x, y and z and possibly the time, t. In structural problems the functional represents a meaningful quantity, namely, the potential energy. However, in general, the functional may not have any physical interpretation. Minimizing the functional with respect to the unknowns is equivalent to solving the differential equation. The functional is minimized by setting its first variation to zero. In structural problems this corresponds to the well known concept of minimization of the potential energy. Keywords: Differential mathematical equations; Problem solving.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1989
Accession Number
ADA219303

Entities

People

  • Madan G. Kittur
  • Ronald L. Huston

Organizations

  • University of Cincinnati

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Aircrafts
  • Algorithms
  • Aspect Ratio
  • Boundaries
  • Coefficients
  • Computational Fluid Dynamics
  • Differential Equations
  • Equations
  • Finite Element Analysis
  • Geometry
  • Heat Transfer
  • Mechanics
  • Modulus Of Elasticity
  • Potential Energy
  • Shape
  • Temperature Gradients

Readers

  • Calculus or Mathematical Analysis
  • Operations Research