Eddy Current Calculations in Thin Conducting Plates Using a Finite Element-Stream Function Code. A Boundary Integral Method for Eddy Current Flow Around Cracks in Thin Plates

Abstract

A stream function or vector potential for the current density vector is used to develop a finite element code for calculating induced currents in thin conducting plates. While two-dimensional, the code includes self field effects for harmonic fields for skin depths on the order of the plate thickness and larger. The solution of the resulting integro-differential equation, using a Galerkin method, leads to a complex, nonsymmetric, fully populated global matrix. In addition to the current density, the code also calculates induced temperatures due to Joule heating and the magnetic forces on the plate. The results are compared to infrared measurements of induced currents in rectangular plates. Extension of the code to transient problems using both fast Fourier transform and direct integration methods is in progress. A boundary element method which employs a Green's function for a crack has been developed to calculate the induced eddy current flow around cracks in thin conducting plates. The theoretical equations employ a stream function for the current density vector and is equivalent to the electric field vector potential methods. A low frequency or large skin depth approximation leads to a Poisson equation for steady harmonic inductor fields. Induced currents around a crack in a square plate due to a uniform inductor field for various crack positions and sites have been calculated in this paper. The effect of the relative position and length of the crack, with respect to the plate width, on the eddy current density near the tips of the crack is given special attention. These results may be useful to simulate eddy current flow detection phenomena.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1981
Accession Number
ADA111013

Entities

People

  • F. C. Moon
  • J. F. Abel
  • K. Y. Yuan
  • M. A. Morjaria
  • S. Mukherjee

Organizations

  • Cornell University College of Engineering

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Applied Mechanics
  • Boundaries
  • Boundary Element Methods
  • Current Density
  • Differential Equations
  • Eddy Currents
  • Electric Fields
  • Electromagnetic Fields
  • Equations
  • Finite Element Analysis
  • Integral Equations
  • Magnetic Fields
  • Magnetic Forces
  • Mathematical Analysis
  • Poisson Equation
  • Structural Engineering
  • Two Dimensional

Readers

  • Computational Fluid Dynamics (CFD)
  • Plasma Physics / Magnetohydrodynamics
  • Structural Dynamics.