References
Zienkiewicz, O. C., The finite element method in engineering science. London: McGraw-Hill Book Co. 1971.
Oden, J.T., Finite elements of non-linear continua. New York: McGraw-Hill Book Co. 1972.
Oden, J. T., Generalized conjugate functions for mixed finite element approximations of boundary value problems. In: The mathematical foundations of the finite element method with applications to partial differential equations (A. K. Aziz, ed.). New York and London: Academic Press, 629–669 (1972).
Gurtin, M. E., Variational principles for linear initial value problems. Quart. Appl. Math. 22, 252–256 (1964).
Gurtin, M. E., Variational principles for linear elastodynamics. Arch. Rational Mech. Anal. 16, 34–50 (1964).
Leitman, M. J., Variational principles in the linear dynamic theory of viscoelasticity. Quart. Appl. Math. 24, 37–46 (1966).
Nickell, R. E., & J. L. Sackman, Variational principles for linear coupled thermoelasticity. Quart. Appl. Math. 26, 11–26 (1968).
Emery, A., & W. Carson, An evaluation of the use of the FEM in the computation of temperature. J. Heat Transfer 93, 136–145 (1971).
Wilson, E. L., & R. E. Nickell, Application of the finite element method to heat conduction analysis. Nuc. Eng. Des. 4, 276–286 (1969).
Neuman, S. P., & P. A. Witherspoon, Theory of flow in a two aquifer system. Water Res. Research 5, 803–816 (1969).
Javandel, I., & P. A. Witherspoon, A method of analyzing transient fluid flow in multilayered aquifers. Water Res. Research 5, 857–869 (1969).
Prodhan, J. K., & S. V. K. Sarma, Application of variational principle for the solution of the gravity drainage problem. J. Hydraulic Research 9, 565–590 (1971)
Brebbia, C. A., Some applications of finite elements for flow problems. International Conference on Variational methods in Engineering, Southampton University, England, 5.1–5.26 (1972).
Ghaboussi, J., & E. L. Wilson, Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Eng. Mech. Div. ASCE. 98, 947–963 (1972).
Sandhu, R. S., & K. S. Pister, Variational methods in continuum mechanics. International Conference on Variational Methods in Engineering, Southampton University, England, 1.13–1.25 (1972).
Tonti, E., A systematic approach to the search for variational principles. International Conference on Variational methods in engineering, Southampton University, England, 1.1–1.12 (1972).
Vainberg, M. M., Variational methods for the study of non-linear operators. San Francisco: Holden-Day 1964.
Mikhlin, S. G., Variational methods in mathematical physics. Oxford: Pergamon Press 1964.
Yosida, K., Functional analysis. Berlin: Springer-Verlag 1965.
Felippa, C. A., & R. W. Clough, The finite element method in solid mechanics. Symposium on numerical solution of field problems in continuum mechanics, Durham, North Carolina, 1968.
Gelfand, I. M., & G. E. Shilov, Generalized functions, Vol. I. New York: Academic Press 1964.
Herrera, I., & J. Bielak, Discussion of Proc. Paper 9152: Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Eng. Mech. Div. ASCE (in press).
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Communicated by M. E. Gurtin
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Herrera, I., Bielak, J. A simplified version of Gurtin's variational principles. Arch. Rational Mech. Anal. 53, 131–149 (1974). https://doi.org/10.1007/BF00276580
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DOI: https://doi.org/10.1007/BF00276580