178 TIME-DEPENDENT AND NON-LINEAR PROBLEMS
actual boundary of the excavated volume is represented by imposing
fictitious forces on its boundary in order to enforce the zero applied
tractions there. The analysis is then capable of determining the
stresses and displacements in the surrounding medium after the
excavation has taken place. There is good agreement between the
numerical and analytic solutions, for the stresses and induced
displacements around thin slits in a triaxial stress field as well as for a
circular tunnel between soft horizontal seams.
REFERENCES
1.
Cruse, T. A. and Rizzo, F. J., Ά Direct Formulation and Numerical Solution of
the General Transient Elastodynamic Problem, Γ, J. Math. Anal. Applic, 22, No.
1,
244-59 (1968)
2.
Cruse, T. A., 'A Direct Formulation and Numerical Solution of the General
Transient Elastodynamic Problem. ΙΓ, J. Math. Anal. Applic., 22, No. 2, 341-55
(1968)
3.
Rizzo, F. J. and Shippy, D. J., 'An Application of the Correspondence Principle of
Linear Viscoelasticity Theory', SIAM J. Appl. Math., 21, No. 2, 321-30
4.
Shippy, D. J., 'Application of the Boundary-Integral Equation Method to
Transient Phenomena in Solids', Boundary Integral Equation Method:
Computational Applications in Applied Mechanics, AMD-Vol. II, ASME, New
York (1975)
5. Hutchinson, J. R., 'Determination of Membrane Vibrational Characteristics by
the Boundary-Integral Equation Method', Proc. 1st Int. Seminar on Recent
Advances in Boundary Element Methods, Southampton University, July 1978,
Pentech Press (1978)
6. Banerjee, P. K. and Mustoe, G. G., 'The Boundary Element Method for Two-
Dimensional Problems of Elastoplasticity', Proc. 1st Int. Seminar on Recent
Advances in Boundary Element Methods, Southampton University, July 1978,
Pentech Press (1978)
7. Jeffreys, H. and Jeffreys B. S., Methods of Mathematical Physics, Cambridge
University Press (1946)
8. Newland, D. E., An Introduction to Random Vibrations and Spectral Analysis,
Longman, London and New York (1975)
9. Smith, G., Laplace Transform Theory, Van Nostrand (1963)
10.
Carrier, F., Krook, M. and Pearson, C. E., Functions of a Complex Variable,
McGraw-Hill (1952)
11.
Schapery, R. A., 'Approximate Methods of Transform Inversion in Viscoelastic
Stress Analysis', Proc. 4th US Nil. Congr. on Applied Mechanics, 2, 1075 (1962)
12.
Doyle, J. M., 'Integration of the Laplace Transformed Equations of Classical
Elastokinetics', J. Math. Anal. Applic, 13, (1966)
13.
Watson, G. N. A Treatise
on
the Theory of
BesseI
Functions,
2nd Edn, Cambridge
University Press (1958)
14.
Bellman, R. E., Kalaba, R. E. and Lockett, J., Numerical
Inversion
of the Laplace
Transform, American Elsevier, New York (1966)
15.
Adey, R. A. and Brebbia, C. A., 'Efficient Method for Solution of Viscoelastic
Problems', Proc. ASCE J. Engng Mech. Div., Dec. (1973)
16.
McHenry,
D.,'
A New Aspect of Creep in Concrete and its Application to Design',