Variable bending of a three-layer rod with a compressed filler in the neutron flux

E. I. Starovoitov ; D. V. Leonenko

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 17 (2017) no. 2, pp. 196-208.

Résumé

The present paper considers variable bending of a three-layer elastoplastic bar with a compressible filler in the neutron flux. To describe kinematic properties of an asymmetric through thickness pack we have accepted the hypotheses of a broken line as follows: Bernoulli’s hypothesis is true in the thin bearing layers; Timoshenko’s hypothesis is true in the compressible through thickness filler with a linear approximation of displacements through the layer thickness. The filler's work is taken into account in the tangential direction. The physical stress-strain relations correspond to the theory of small elastoplastic deformations. By the variational method a system of differential equilibrium equations has been derived. The kinematic conditions of simply supported faces of the bar on the immovable in space rigid bases are presumed on the boundary. The solution of the boundary problem is reduced to the search for four functions, namely: deflections and longitudinal displacements of the medial surfaces of the bearing layers. An analytical solution has been derived by the method of elastic solutions by using the Moskvitin’s theorem about variable loadings. Its numerical analysis has been performed for the case of the uniform distribution of the continuous and local loads.

Bibliographie

[1] Bolotin V. V., Novichkov Yu. N., Mechanics of Multilayer Structures, Mashinostroenie, M., 1980, 375 pp. (in Russian)

[2] Gorshkov A. G., Starovoitov E. I., Tarlakovskii D. V., Foundations of the Theory of Elasticity and Plasticity, Fizmatlit, M., 2011, 416 pp. (in Russian)

[3] Kuznetsova E. L., Leonenko D. V., Starovoitov E. I., “Natural Vibrations of Three-layer Circular Cylindrical Shells in an Elastic Medium”, Mech. Solids, 50:3 (2015), 359–366 | DOI

[4] Leonenko D. V., Starovoitov E. I., “Impulsive action on the three-layered circular cylindrical shells in elastic media”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 15:1 (2015), 202–209 (in Russian) | DOI

[5] Mochalin A. A., “Parametric Oscillations of a Non-uniform Circular Cylindrical Shell of Variable Density under Different Boundary Conditions”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 15:2 (2015), 210–214 (in Russian) | DOI

[6] Tarlakovskii D. V., Fedotenkov G. V., “Nonstationary 3D Motion of an Elastic Spherical Shell”, Mech. Solids, 50:2 (2015), 118–128 | DOI

[7] Tarlakovskii D. V., Fedotenkov G. V., “Two-Dimensional Nonstationary Contact of Elastic Cylindrical or Spherical Shells”, J. Machinery Manufacture and Reliability, 43:2 (2014), 145–152 | DOI | MR

[8] Kuznetsova E. L., Tarlakovskii D. V., Fedotenkov G. V., “Propagation of Unsteady Waves in an Elastic Layer”, Mech. Solids, 46:5 (2011), 779–787 | DOI

[9] Fedotenkov G. V., Tarlakovskiy D. V., “Analytic Investigation of Features of Stresses in Plane Nonstationary Contact Problems With Moving Boundaries”, J. Math. Sci., 162:2 (2009), 246–253 | DOI | MR

[10] Belostochny G. N., Rusina E. A., “Obolochki and Geometrically Irregular Plates with a Temperature-Sensitive Thickness”, Dokl. Ross. Akad. estestvennykh nauk. Povolzhskoe mezhregional'noe otdelenie, 1999, no. 1, 28–37 (in Russian)

[11] Rabboh S., Bondok N., Mahmoud T., El Kholy H., “The Effect of Functionally Graded Materials into the Sandwich Beam Dynamic Performance”, Materials Sciences and Applications, 4 (2013), 751–760 | DOI

[12] Havaldar S., Sharma R., “Experimental Investigation of Dynamic Characteristics of Multilayer PU Foam Sandwich Panels”, J. Minerals and Materials Characterization and Engineering, 1:5 (2013), 201–206 | DOI

[13] Yang L., Harrysson O., West H., Cormier D. A., “Comparison of Bending Properties for Cellular Core Sandwich Panels”, Materials Sciences and Applications, 4:8 (2013), 471–477 | DOI

[14] Moskvitin V. V., Cyclic Loading of Elements of Designs, Nauka, M., 1981, 344 pp. (in Russian)

[15] Moskvitin V. V., Starovoitov E. I., “To the Study of the Stress-Strain State of Two-Layer Metal-Polymer Plates under Cyclic Loading”, Izv. AN SSSR. Mekhanika tverdogo tela, 1986, no. 1, 116–121 (in Russian)

[16] Il'iushin A. A., Ogibalov P. M., Elastic-Plastic Deformations of Hollow Cylinders, Moscow Univ. Press, M., 1960, 224 pp. (in Russian)

[17] Il'iushin A. A., Plastic, v. 1, Elastic-Plastic Deformation, Gostekhizdat, M., 1948, 376 pp. (in Russian)