Abstract
The theory of elasticity is concerned with the mechanics of deformable bodies which recover their original shape upon the removal of the forces causing the deformation. The first discussions of elastic phenomena occur in the writings of Hooke(1676) but the first real attempts to construct a theory of elasticity using the continuum approach, in which speculations on the molecular structure of the body are avoided and macroscopic phenomena are described in terms of field variables, date from the first half of the eighteen century1. Since that time a tremendous amount of scientific effort has been devoted to the study of the mathematical theory of elasticity and its applications to physics and engineering. The sheer volume of the published work in the subject makes it quite impossible for an author to cover the entire subject at all adequately within the compass of a single book. The present article has a much more modest aim than that: It tries to give a brief survey of certain parts of the basic theory of elasticity with sufficient discussion of special problems to give some indication of the mathematical techniques available for the solution of such problems. Even within that limited framework there are notable omissions; for example, nothing is said about such an important technological topic as the theory of elastic stability or about such a basic topic as the calculation of the elastic constants of a crystal by the theory of crystal lattices.
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Bibliography
Auerbach, F., and W. Hort, eds.: Handbuch der Physikalischen und Technischen Mechanik. Leipzig Bd. 3, 1927; Bd. 4, 1931.
Bartels, J. ed.: Handbuch der Physik, Bd. XLVII, Geophysik I. Berlin 1956.
Biezano, C. B., and R. Grammel: Technische Dynamik.
Brillouin, L.: Les Tenseurs en Mécanique et en Élasticité. Paris 1938.
Bullen, K. E.: An Introduction to the Theory of Seismology. Cambridge 1947.
Bullen, K. E.: Seismology. London 1954.
Butty, E.: Tratado de elasticidad teoricotecnica (Elastotecnia), Vol. 1. Buenos Aires 1946.
Cagniard, L.: Réflexion et Réfraction des Ondes Séismiques. Paris 1939.
Dinnik, A. N.: Torsion: Theory and Application. Moscow 1938.
Dinnik, A. N.: Torsion: Theory and Application. Moscow 1938.
Goldenveiser, A. L.: Theory of Thin Elastic Shells. Moscow 1953.
Green, A. E., and W. Zerna: Theoretical Elasticity. Oxford 1954.
Jaeger, J. C.: Elasticity, Fracture and Flow. London 1956.
Jeffreys, H.: Cartesian Tensors. Cambridge 1931.
Jeffreys, H.: The Earth, 3rd ed. Cambridge 1952.
Kantorovich, L. V.: Functional Analysis and Applied Mathematics. Nat. Bur. Stand. ( Translation.) Washington 1952.
Klitchieff, J.: Poglavja iz Teorije Elastiénosti sa Primenama. Belgrade 1950.
Kolossov, G. V.: Application of the Complex Variable to the Theory of Elasticity. Moscow 1935.
Kolsky, H.: Stress Waves in Solids. Oxford 1953.
Lecornu, L.: Théorie Mathématique de l’Élasticité. Paris 1938.
Leibenson, L. S.: Variational Methods of Solution of Problems in the Theory of Elasticity. Moscow 1943.
Lorenz, H.: Technische Elastizitätslehre. Berlin 1913.
Love, A. E. H.: Some Problems of Geodynamics. Cambridge 1911.
Love, A. E. H.: The Mathematical Theory of Elasticity, 4th ed. Cambridge 1927.
Macelwane, J. B.: An Introduction to Theoretical Seismology, Part I, Geodynamics. New York 1936.
Murnaghan, F. D.: Finite Deformations of an Elastic Solid. New York 1951.
Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity, 4th ed. Leningrad 1954.
NovozrlLov, V. V.: Foundations of Non-Linear Theory of Elasticity. Moscow 1953.
Pippard, A. J. S.: Strain Energy Methods of Stress Analysis. London 1928.
Prescott, J.: Applied Elasticity. London 1924.
Searle, G. F. C.: Experimental Elasticity, 2nd ed. Cambridge 1933.
Sokolnikoff, I. S.: Mathematical Theory of Elasticity, 2nd ed. New York 1956.
Southwell, R. V.: An Introduction to the Theory of Elasticity for Engineers and Physicists. Oxford 1936.
Synge, J. L.: The Hypercircie in Mathematical Physics. Cambridge 1957.
Timoshenko, S. P.: Theory of Elastic Stability. New York 1934.
Timoshenko, S. P.: Theory of Plates and Shells. New York 1940.
Timoshenko, S. P., and J. N. Goodier: Theory of Elasticity, 2nd ed. New York 1951.
Treloar, L. R. G.: The Physics of Rubber Elasticity. Oxford 1949.
Westergaard, H. M.: Theory of Elasticity and Plasticity. Harvard 1952.
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Sneddon, I.N., Berry, D.S. (1958). The Classical Theory of Elasticity. In: Flügge, S. (eds) Elasticity and Plasticity / Elastizität und Plastizität. Handbuch der Physik / Encyclopedia of Physics, vol 3 / 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45887-3_1
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