×

zbMATH — the first resource for mathematics

A simplified version of Gurtin’s variational principles. (English) Zbl 0288.49018

MSC:
49L99 Hamilton-Jacobi theories
49S05 Variational principles of physics (should also be assigned at least one other classification number in Section 49-XX)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zienkiewicz, O. C., The finite element method in engineering science. London: McGraw-Hill Book Co. 1971. · Zbl 0237.73071
[2] Oden, J.T., Finite elements of non-linear continua. New York: McGraw-Hill Book Co. 1972. · Zbl 0235.73038
[3] 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).
[4] Gurtin, M. E., Variational principles for linear initial value problems. Quart. Appl. Math. 22, 252-256 (1964). · Zbl 0173.37602
[5] Gurtin, M. E., Variational principles for linear elastodynamics. Arch. Rational Mech. Anal. 16, 34-50 (1964). · Zbl 0124.40001 · doi:10.1007/BF00248489
[6] Leitman, M. J., Variational principles in the linear dynamic theory of viscoelasticity. Quart. Appl. Math. 24, 37-46 (1966). · Zbl 0151.37203
[7] Nickell, R. E., & J. L. Sackman, Variational principles for linear coupled thermoelasticity. Quart. Appl. Math. 26, 11-26 (1968). · Zbl 0165.27504
[8] Emery, A., & W. Carson, An evaluation of the use of the FEM in the computation of temperature. J. Heat Transfer 93, 136-145 (1971). · doi:10.1115/1.3449775
[9] Wilson, E. L., & R. E. Nickell, Application of the finite element method to heat conduction analysis. Nuc. Eng. Des. 4, 276-286 (1969). · doi:10.1016/0029-5493(66)90051-3
[10] Neuman, S. P., & P. A. Witherspoon, Theory of flow in a two aquifer system. Water Res. Research 5, 803-816 (1969). · doi:10.1029/WR005i004p00803
[11] Javandel, I., & P. A. Witherspoon, A method of analyzing transient fluid flow in multilayered aquifers. Water Res. Research 5, 857-869 (1969). · doi:10.1029/WR005i004p00856
[12] 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) · doi:10.1080/00221687109500373
[13] 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).
[14] Ghaboussi, J., & E. L. Wilson, Variational formulation of dynamics of fluid-saturated porous elastic solids. J. Eng. Mech. Div. ASCE. 98, 947-963 (1972).
[15] 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). · Zbl 0303.49034
[16] 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).
[17] Vainberg, M. M., Variational methods for the study of non-linear operators. San Francisco: Holden-Day 1964.
[18] Mikhlin, S. G., Variational methods in mathematical physics. Oxford: Pergamon Press 1964. · Zbl 0119.19002
[19] Yosida, K., Functional analysis. Berlin: Springer-Verlag 1965. · Zbl 0126.11504
[20] 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.
[21] Gelfand, I. M., & G. E. Shilov, Generalized functions, Vol. I. New York: Academic Press 1964.
[22] 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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.