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Rock Mechanics pp 111-129 | Cite as

Introductory Lecture on Finite Element Analysis for Jointed Rocks

  • R. E. Goodman
Part of the International Centre for Mechanical Sciences book series (CISM, volume 165)

Abstract

Finite element analysis is an application of the direct stiffness method of structural analysis; the steps of the method are as follows:
  1. 1.

    Conceive of a prototype embracing the important feature of actual structure. Subdivide it into nodal points and elements.

     
  2. 2.

    Form the matrix connecting displacements and forces at each nodal point of element (element stiffness matrices).

     
  3. 3.

    Assemble the structural stiffness matrix from each element stiffness matrix.

     
  4. 4.

    Introduce applied forces and write the equations of equilibrium.

     
  5. 5.

    Introduce displacement boundary conditions.

     
  6. 6.

    Solve for displacements at nodal points.

     
  7. 7.

    From known displacement in each nodal point of an element, find element stresses.

     
  8. 8.

    Recycle for non-linear properties

     

Keywords

Finite Element Analysis Stiffness Matrix Initial Stress Nodal Point Joint Rock 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Dough, R.N., “The Finite Element Method in Plane Stress Analysis,” Proceedings 2nd ASCE Conference on Electronic Computation, 1960, pp. 345–378.Google Scholar
  2. [2]
    Ghaboussi, J., E. Wilson, and J. Isenberg, “Finite Element Analysis for Rock Joints and Interfaces,” Journal Soil Mechanics and Foundations Division, Proceedings ASCE, 1973, Vol. 99, No. SM 10, pp. 833–848.Google Scholar
  3. [3]
    Goodman, R.E., “The Mechanical Properties of Joints,” Proceedings 3rd. Congress of the International Society of Rock Mechanics, 1973, Vol. 1, Part 2, Supplementary Reports Volume (pre Congress volume).Google Scholar
  4. [4]
    Goodman, R.E.,“Methods of Geological Engineering in Discontinuous Rocks” West Publishing Company, in preparation (estimated 1975 ).Google Scholar
  5. [5]
    Goodman, R.E., and J. Dubois, “Duplication of Dilatancy in Analysis of Jointed Rocks,” Journal Soil Mechanics and Foundation Division, Proceedings ASCE, 1972, Vol. 98, No. SM 4, pp. 399–422.Google Scholar
  6. [6]
    Goodman, R.E., and St. John, “Static Finite Element Analysis of Jointed Rock,” Numerical Methods in Geotechnical Engineering, McGraw Hill, Christian and Desai, Editors, in preparation.Google Scholar
  7. [7]
    Malina, H., “The Numerical Determination of Stresses and Deformations in Rock Taking Into Account Discontinuities,” Proceedings 19th Colloquium on Geomechanics, Salzburg, 1969.Google Scholar
  8. [8]
    Zinkiewicz, O.C., The Finite Element Method in Structural and Contiuum Mechanics, McGraw Hill, 1967, p. 272.Google Scholar
  9. [9]
    Zinkiewicz, O.C., B. Best, C. Dullage, and K. Stagg, “Analysis of Non-Linear Problems in Rock Mechanics with Particular Reference to Jointed Rock Systems,” Proceedings 2nd Congress ISRM, Belgrade, 1970, Vol. 3, Paper 8–14.Google Scholar

Copyright information

© Springer-Verlag Wien 1972

Authors and Affiliations

  • R. E. Goodman
    • 1
  1. 1.Department of Civil EngineeringUniversity of CaliforniaBerkeleyUSA

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