Abstract
Consider a material system (either a system of discrete points or a rigid body) with N degrees of freedom and submitted to holonomic constraints.
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References
Smith, D. and Smith, C., When is Hamilton’s principle an extremum principle, A.I.A.A. Journal, 12, 1573, 1974.
Bailey, C.D., The method of Ritz applied to the equation of Hamilton, comp. Meth. in Appl. Mech. and Eng., 7, 135, 1976.
Bailey, C.D., Application of Hamilton’s law of varying action, Journal, 13, 1154, 1975.
Bailey, C.D., A new look at Hamilton’s principle, Found. of Phys., 5, 433, 1975.
Trefftz, E., Zur Theorie der Stabilität des elastischen Gleichgewichts, Zeit. Ang. Math. Mech., 13, 160, 1933.
Koiter, W., On the concept of stability of equilibrium for continuum bodies, Proc. Kon. Ned. Ak. Wet., B66, 173, 1963.
Koiter, W., Lecture notes on elastic stability, C.I.S.M., Udine, 1971.
Timoshenko, S. and. Gere, J., Theory of elastic stability, Mac Graw Hill, New-York, 1961.
Pearson, C.E., Theoretical elasticity, Harvard Univ. Press, Cambridge, 1959.
Reissner, E., On a variational theorem in elasticity, J. Math. Phys., 29, 90, 1950.
Washizu, K., Variational methods in elasticity and plasticity, Pergamon, New-York, 1968.
Hill, R., Mathematical plasticity, Oxford Univ. Press, Oxford, 1950.
Prager, W. and Hodge, P., Theory of perfectly plastic solids, Wiley, New-York, 1951.
Lippmann, H., Extremum and variational principles in mechanics, C.I.S.M. Lecture n°54, Springer Verlag, Berlin, 1970.
Koiter, W., On the complementary energy theorem in nonlinear elasticity theory, in: Trends in applications of pure mathematics to mechanics, 6, Fichera, Ed., Pitman Pb., London, 1976.
Nemat-Nasser, S., General principles in nonlinear and linear elasticity with applications, in: Mechanics Today, vol. 1, Nemat Nasser, Eds., Pergamon, New-York, 1972.
Stumpf, H., Generating functionals and extremum principles in nonlinear elasticity with applications to nonlinear plate and shallow shell theory, in I.U.T.A.M. — I.M.U. Symposium on applications of the methods of functional analysis to problems of mechanics, Lecture Notes in Mathematics, 503, Springer-Verlag Berlin, 1976.
Stumpf, H., Dual extremum principles and error boands in nonlinear elasticity theory, J. of Elasticity, 8, 425, 1978.
Fung, Y., Foundations of solid mechanics, Prentice Hall, New-York, 1965.
Gurtin, M., Variational principles for linear elastodynamics, Arch. Rat. Mech. Anal., 16, 34, 1964.
Hlavacek, I., Variational formulation of the Cauchy problem for equations with operator coefficients, Aplik. Mkth., 16, 46, 1971.
Bailey, C., Hamilton, Ritz and elastodynamics, J. Appl. Mech., 98, 684, 1976.
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© 1980 Springer-Verlag Wien
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Lebon, G., Perzyna, P. (1980). Variational Principles in Classical Mechanics and in Elasticity. In: Lebon, G., Perzyna, P. (eds) Recent Developments in Thermomechanics of Solids. International Centre for Mechanical Sciences, vol 262. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3351-4_14
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DOI: https://doi.org/10.1007/978-3-7091-3351-4_14
Publisher Name: Springer, Vienna
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