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Effects of couple-stresses in linear elasticity. (English) Zbl 0112.38906

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[1] Voigt, W.: Theoretische Studien über die Elasticitätsverhältnisse der Krystalle. Abh. Ges. Wiss. Göttingen 34 (1887); Über Medien ohne innere Kräfte und eine durch sie gelieferte mechanische Deutung der Maxwell-Hertzschen Gleichungen. Gött. Abh. 72-79 (1894). · JFM 25.1557.02
[2] Cosserat, E., et Cosserat, F.: Théorie des Corps Déformables. Paris: A. Hermann et Fils 1909. · JFM 40.0862.02
[3] Truesdell, C., & R. A. Toupin: The Classical Field Theories. Encyclopedia of Physics, Vol. III/1, Secs. 200, 203, 205. Berlin-Göttingen-Heidelberg: Springer 1960.
[4] Toupin, R. A.: Elastic materials with couple-stresses. Arch. Rational Mech. Anal., 11, 385-414 (1962). · Zbl 0112.16805
[5] Aero, E. L., & E. V. Kuvshinskii: Fundamental equations of the theory of elastic media with rotationally interacting particles. Fizika Tverdogo Tela 2, 1399-1409 (1960); Trans.: Soviet Physics Solid State 2, 1272-1281 (1961).
[6] Grioli, G.: Elasticità asimmetrica. Ann. di Mat. pura ed appl., Ser. IV, 50, 389-417 (1960). · Zbl 0123.40504
[7] Weatherburn, C. E.: Advanced Vector Analysis. London: G. Bell and Sons 1928.
[8] Wilson, E. B.: Vector Analysis. New Haven: Yale Univ. Press 1948.
[9] Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity, Fourth Ed. Cambridge: Cambridge Univ. Press 1927. · JFM 53.0752.01
[10] Toupin, R. A.: The elastic dielectric. J. Rational Mech. and Anal. 5, 849-914 (1956). · Zbl 0072.23803
[11] Sternberg, E.: On the integration of the equations of motion in the classical theory of elasticity. Arch. Rational Mech. Anal. 6, 34-50 (1960). · Zbl 0093.40103
[12] Atanasoff, J. V., & P. J. Hart: Dynamical determination of the elastic constants and their temperature coefficients for quartz. Phys. Rev. 59, 85-96 (1941).
[13] Mindlin, R. D.: Thickness-shear and flexural vibrations of crystal plates. J. Appl. Phys. 22, 316-323 (1951). · Zbl 0042.18603
[14] Onoe, M.: Tables of Modified Quotients of Bessel Functions of the First Kind for Real and Imaginary Arguments. New York: Columbia Univ. Press 1958. · Zbl 0085.12301
[15] Papkovitch, P. F.: The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions. Izv. Akad. Nauk SSSR, Phys.-Math. Ser. 10, 1425 (1932).
[16] Mindlin, R. D.: Note on the Galerkin and Papkovitch stress functions. Bull. Amer. Math. Soc. 42, 373-376 (1936). · JFM 62.0939.02
[17] Mindlin, R. D.: Force at a point in the interior of a semi-infinite solid. Proc. First Midwestern Conference on Solid Mechanics, Urbana, Illinois, 56-59 (1953).
[18] Galerkin, B.: Contribution à la solution générale du problème de la théorie de l’élasticité dans le cas de trois dimensions. Comptes Rendus Acad. Sci., Paris 190, 1047 (1930). · JFM 56.0700.07
[19] Timoshenko, S. P., & J. N. Goodier: Theory of Elasticity. New York: McGraw-Hill 1951. · Zbl 0045.26402
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