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Contents

• List of Figures
• List of Tables
• Introduction
• Finite element theory
  • General aspects and node labelling scheme
  • Electrical conductivity
  • Elastic moduli
  • Thermal strains (eigenstrains)
• Finite difference theory
  • General description, comparison to finite element method
  • Derivation of finite difference form of Laplace's equation
  • Boundary conditions
• Explanation of key subroutines and program usage
  • Subroutine ENERGY
  • Subroutine DEMBX
  • Subroutine CURRENT/STRESS
  • 3-D : 2-D relations for programs
  • Actual program operation
    • Electric and elastic finite element programs
    • Eigenstrain programs
    • Finite difference programs
• Exact solutions for testing programs
  • Definition of effective properties
  • Series and parallel
  • Small contrast of properties
  • Keller and Mendelsen 2-D result for conductivity
  • Field fluctuation result
  • Equal shear modulus
  • Intrinsic properties for spheres, circles, and cubes
  • Vegard's law and Goodier result for thermal strains
  • Hashin and Rosen thermal strain result
  • Mackenzie result for pressurized pore space
  • CLM Theorem
• Other possible uses of programs
  • Fixed voltages and displacements
  • Removing periodic boundary conditions
  • Fixed currents and forces
  • Surface energies
• Making and analyzing images and histograms
  • General features
  • Finite element electrical problems
  • Finite difference electrical problems
  • Finite element elastic problems
  • General features of histograms
  • Examples of histograms
  • Phase percolation in images
• References
• Listing of programs and computer requirements
  • Computer details, access information
  • Memory requirements
  • Listing of key programs
    • ELECFEM3D.F
    • ELAS3D.F
    • THERMAL3D.F
    • DC3D.F
    • AC3D.F
    • GAUSS.F
    • BURN3D.F

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  Next: List of Figures Up: Main Previous: Main