Abstract
Random stress and strain fields are examined in relation to machine parts made of materials of the randomly reinforced fiberglass type subjected to random external loads. The conditions of existence of the principal axes of the fourth-order tensor representing the second-order central moments of a plane random stress or strain field are determined. A method of determining the principal axes and principal values is described. A numerical example is worked.
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Literature cited
Yu. M. Tarnopol'skii and A. M. Skudra, Structural Strength and Deformation Properties of Glass Reinforced Plastics [in Russian], Riga (1966).
S. D. Volkov and V. P. Stavrov, in: Applications of Plastics in Machine Building, [in Russian], Vol 1, Kiev (1966).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body [in Russian], GITTL (1950).
Additional information
V. A. Steklov Mathematical Institute, Sverdlovsk Branch, Academy of Sciences of the USSR. S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mechanika Polimerov, Vol. 4, No. 4, pp. 618–623, July–August, 1968.
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Volkov, S.D., Komissarova, M.L. On the statistical mechanics of deformable media. Polymer Mechanics 4, 476–480 (1968). https://doi.org/10.1007/BF00855757
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DOI: https://doi.org/10.1007/BF00855757