Geodesic
Analysis of stresses of bi-material plane and half-plane at action of a point force for two models of harmonic materials
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2016), pp. 38-52
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Analytical solutions of the nonlinear problems (plane strain) are obtained for bi-material plane and half-plane exposed to the point force. Two models of harmonic materials are considered: semi-linear and John's. These models allow to use the methods of complex functions for the solution of the plane problems of elasticity. Expressions for nominal stresses and Cauchy stresses, as well as for current coordinates are founded. On the base of the general expressions the asymptotic expansions are constructed for stresses and displacements in a vicinity of a point force. A comparison between the singular members of stresses and displacements is made for the two models of a material. Refs 15.
Keywords: bi-material plane, plane strain, method of complex functions, asymptotic expansions.
Mots-clés : point force 
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V. M. Malkov; Yu. V. Malkova; T. O. Domanskaya. Analysis of stresses of bi-material plane and half-plane at action of a point force for two models of harmonic materials. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 1 (2016), pp. 38-52. http://geodesic.mathdoc.fr/item/VSPUI_2016_1_a3/

[1] John F., “Plane strain problems for a perfectly elastic material of harmonic type”, Commun. Pure and Appl. Math., 13:2 (1960), 239–296 | DOI | MR | Zbl

[2] Lurie A. I., Non-linear elasticity, Nauka Publ., M., 1980, 512 pp. (In Russian) | MR

[3] Chernykh K. F., Litvinenkova Z. N., Theory of large elastic deformations, Leningrad State University Publ., L., 1988, 256 pp. (In Russian)

[4] Varley E., Cumberbatch E., “Finite deformation of elastic materials surrounding cylindrical holes”, Journal of Elasticity, 10:4 (1980), 341–405 | DOI | Zbl

[5] Ru C. Q., “On complex-variable formulation for finite plane elastostatics of harmonic materials”, Acta Mechanica, 156:3–4 (2002), 219–234 | Zbl

[6] Ru C. Q., Schiavone P., Sudak L. J., Mioduchowski A., “Uniformity of stresses inside an elliptic inclusion in finite plane elastostatics”, Intern. Journal of Non-linear mechanics, 38:2–3 (2005), 281–287 | MR

[7] Malkov V. M., Malkova Yu. V., “Plane problem of non-linear elasticity for harmonic material”, Vestnik of Saint Petersburg State University. Series 1. Mathematics. Mechanics. Astronomy, 2008, no. 3, 114–126 (In Russian)

[8] Malkov V. M., Malkova Yu. V., Stepanova V. A., “Bi-material plane of John's material with interface crack loaded by pressure”, Vestnik of Saint Petersburg State University. Series 1. Mathematics. Mechanics. Astronomy, 2013, no. 3, 113–125 (In Russian)

[9] Malkov V. M., Malkova Yu. V., “Plane problems of elasticity for semi-linear material”, Vestnik of Saint Petersburg State University. Series 1. Mathematics. Mechanics. Astronomy, 2012, no. 3, 93–106 (In Russian)

[10] Malkov V. M., Malkova Yu. V., “Plane problems of concentrated forces for semi-linear material”, Vestnik of Saint Petersburg State University. Series 10. Applied mathematics. Computer science. Control processes, 2013, no. 3, 83–96 (In Russian)

[11] Malkov V. M., Malkova Yu. V., “Investigation of non-linear Flamant's problem”, Izv. RAS. Mechanics of solids, 2006, no. 5, 68–78 (In Russian)

[12] Malkov V. M., Malkova Yu. V., “Analysis of singularity of stresses in non-linear Flamant's problem for some material models”, Applied mathematics and mechanics, 72:3 (2008), 453–462 (In Russian) | MR

[13] Malkov V. M., Introduction in non-linear elasticity, Saint Petersburg State University Publ., Saint Petersburg, 2010, 276 pp. (In Russian)

[14] N. I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Nauka Publ., M., 1966, 708 pp.

[15] Malkova Yu. V., Some problems for bi-material plane with curvilinear cracks, Saint Petersburg State University Publ., Saint Petersburg, 2008, 160 pp. (In Russian)