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Extra resources for Variational Methods in Elasticity and Plasticity , 2ed.(Monographs in Aeronautics & Astronautics)
V. SOUTHWELL, Castigliano's Principle of Minimum Strain Energy, Pmceedings of the Royal Society, VoL 154, No. 881, pp. 4-21, March 1936. 15. R. V. , Castigliano's Principle of Minimum Strain Energy and Conditions of Compatibility for Strains, S. Timoshenko 60th Aniversary Volume, pp. 211—17, 1938. 16. W. S. D0RN and A. SCHILD, A Converse to the Virtual Work Theorem for Deformable Solids, Quarterly of Applied Mathenwàtics, Vol. 14, No. 2, pp. 209—13, July 1956. 17. C. €s of the National Academy of Science, Washington, Vol.
DUNCAN, Galerkin's Method in Mechanics and Differential Equatioiu, Aeronautical Research Committee, Report and Memoranda No. 1798, 1931. Technirche Dynamik, Springer-Verlag, 1939. 8. C. BIEZBNO and R. Springer-Verlag, 9. L. ATZ, NwnerLcche &han&wtg von 1951. 10. N. J. Horv, The Analysis of Structures, John WIley, 1956. 1. H. Aaovius and S. KaLsar, Energy Theorems and Structural Analym, Butterwozlh. 1960. 12. R. COURANT and D. HILBERT, Methods of Moihematical Physics, VoL 1, Intcrecience, New York, 1953.
Of the intermediate problem, they Therefore, if we obtain exact provide lower bounds for the cigciwslues of the original problem. The Rayleigh-Ritz method fpr the free vibration problem has been illus- trated. It is obvious that the methOd also finds a field of application in other cigenvalue problems. directed to Refs. 13, 16 and 26 for further details and numerical illustrations of the Rayleigh-Ritz method applied to eigenvalue problems. 9. 9. It is obvious that the first terms of Eqs. 74) may be replaced by dU and ÔV,respectively, for t Ref's.