Bending of a sandwich beam by local loads in the temperature field

E. I. Starovoitov ; D. V. Leonenko

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 18 (2018) no. 1, pp. 69-83.

Résumé

Deformation of sandwich beam in a temperature field under the action of uniformly distributed and sinusoidal local loads is considered. An analytical view of the loads was set by using functions of Heaviside. To describe kinematic properties of an asymmetric through thickness of sandwich beam 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 kinematic conditions of simply supported faces of the beam on the immovable in space rigid bases are presumed on the boundary. The filler’s work is taken into account in the tangential direction. Temperature variations were calculated by the formula obtained from averaging thermophysical properties of the materials of the layers through the beam thickness. Stress and strain are related by relations of the deformation theory of plasticity. By the variational method a system of differential equilibrium equations has been derived. The solution of the boundary value problem of thermo-elastoplasticity is reduced to the search for four functions, namely: deflections and lengthwise displacements of the medial surfaces of the bearing layers. An analytical solution has been derived by the method of elastic solutions. In the case of repeated alternating loading solution using Moskvitin theorem received. Numerical analysis of solutions is performed for a continuous, locally distributed and repeated alternating loads. The graphs of stresses and displacements in sandwich beam under the isothermal and thermal-force loads are given.

Bibliographie

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

[4] 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

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

[6] 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

[7] Starovoitov E. I., Kubenko V. D., Tarlakovskii D. V., “Vibrations of circular sandwich plates connected with an elastic foundation”, Russian Aeronautics, 52:2 (2009), 151–157 | DOI

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

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

[10] 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 | MR

[11] Blinkov Yu. A., Mesyanzhin A. V., Mogilevich L. I., “Wave Occurrences Mathematical Modeling in Two Geometrically Nonlinear Elastic Coaxial Cylindrical Shells, Containing Viscous Incompressible Liquid”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 16:2 (2016), 184–197 (in Russian) | DOI | MR

[12] 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

[13] Belostochnyi G. N., Ul'yanova O. I., “Continuum Model for a Composition of Shells of Revolution with Thermosensitive Thickness”, Mechanics of Solids, 46:2 (2011), 184–191 | DOI

[14] Vaziri A., Xue Z., Hutchinson J. W., “Metal sandwich plates with polymer foam-filled cores”, Journal of Mechanics of Materials and Structures, 1:1 (2006), 97–127 | DOI

[15] Leonenko D. V., Starovoitov E. I., “Deformation of a three-layer elastoplastic beam on an elastic foundation”, Mechanics of Solids, 46:2 (2011), 291–298 | DOI

[16] Starovoitov E. I., Leonenko D. V., “Variable Bending of a Three-layer Rod with a Compressed Filler in the Neutron Flux”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 17:2 (2017), 196–208 (in Russian) | DOI | MR

[17] Franus D. V., “Thickness Influence of the Multylayer Corneal Shell on the Value of Intraocular Pressure”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 17:2 (2017), 183–195 (in Russian) | DOI

[18] Yankovskii A. P., “A Study of Steady Creep of Layered Metal-composite Beams of Laminated-fibrous Structures with Account of Their Weakened Resistance to the Transverse Shift”, Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki, 20:1 (2016), 85–108 (in Russian) | DOI

[19] Wilde M. V., Sergeeva N. V., “Development of Asymptotic Methods for the Analysis of Dispersion Relations for a Viscoelastic Solid Cylinder”, Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 17:2 (2017), 183–195 (in Russian) | DOI | MR

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

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