Abstract
For many years, a standard treatise on elasticity has been the book by Love (1927). Another standard text on linear elasticity has been prepared by Timoshenko and Goodier (1970), which first appeared in 1934. Among other books on nonlinear elasticity, we mention those by Novozhilov (1948) and Fung (1965). Both of these cover the classical nonlinear case in detail. The book by Novozhilov also deals with a simplified nonlinear case of small strains and large rotations that has found important applications to large deflections of thin structures by many authors. The treatise by Fung further deals with foundations of solid mechanics in general. His book includes a very well-prepared bibliography, covering the literature in solid mechanics before 1965.
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References
Biot, M.A. (1939) Nonlinear Theory of Elasticity and the Linearized Case for a Body under Initial Stress. Philosophical Magazine, Vol. 27, Ser. 7, pp. 468–489.
Fung, Y.C. (1965) Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey.
Hu, H.C. (1954) On Some Variational Principles in the Theory of Elasticity and the Theory of Plasticity. Acta Physica Sinica, Vol. 10, p. 259. (Also, Scientia Sinica, Vol. 4, p. 33, 1955.)
Kirchhoff, G. (1883) Vorlesungen über math. Physik, Mechanik, 3rd Ed. Leipzig.
Love, A.E.H. (1927) A Treatise on the Mathematical Theory of Elasticity, 4th Ed. Cambridge University Press. (Also, Dover Publications, first American edition, 1944.)
Marguerre, K. (1962) Handbook of Engineering Mechanics, edited by W. Flügge, Chap. 33. McGraw-Hill, New York.
Novozhilov, V.V. (1948) Foundations of the Nonlinear Theory of Elasticity. First Russian edition: Gostekhizdat; English translation: Graylock Press, Rochester, New York, 1953.
Reissner, E. (1950) On a Variational Theorem in Elasticity. Journal of Mathematics and Physics, Vol. 29, pp. 90–95.
Timoshenko, S. and J.N. Goodier. (1970) Theory of Elasticity, 3rd Ed. McGraw-Hill, New York.
Washizu, K. (1955) On the Variational Principles of Elasticity and Plasticity. M.I.T. Aeroelastic Structures Research Laboratory Technical Report 25.18, Cambridge, Massachusetts.
Washizu, K. (1968) Variational Methods in Elasticity and Plasticity. Pergamon Press, New York.
Yu, Y.Y. (1964) Generalized Hamilton’s Principle and Variational Equation of Motion in Nonlinear Elasticity Theory, with Application to Plate Theory. Journal of the Acoustical Society of America, Vol. 36, pp. 111–120.
Yu, Y.Y. (1991) On Equations for Large Deflections of Elastic Plates and Shallow Shells. Mechanics Research Communications, Vol. 18, pp. 373–384.
Yu, Y.Y. (1995a) On the Ordinary, Generalized, and Pseudo-Variational Equations of Motion in Nonlinear Elasticity, Piezoelectricity, and Classical Plate Theory. Journal of Applied Mechanics, Vol. 62, pp. 471–478.
Yu, Y.Y. (1995b) Some Recent Advances in Linear and Nonlinear Dynamical Modeling of Elastic and Piezoelectric Plates. Journal of Intelligent Material Systems and Structures, Vol. 6, pp. 237–254.
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© 1996 Springer-Verlag New York, Inc.
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Yu, YY. (1996). Nonlinear Elasticity Theory. In: Vibrations of Elastic Plates. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2338-2_1
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DOI: https://doi.org/10.1007/978-1-4612-2338-2_1
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