THE SECOND DEFORMATION OF THE THREE-LAYER ELASTOPLASTIC ROD BY LOCAL LOAD

ZHURAVKOV Mikhail A., D. Sc. in Phys.-Math. , Prof., Minister of Education of the Republic of Belarus, E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

STAROVOYTOV Eduard I., D. Sc. in Phys.-Math., Prof., Head of the Department "Structural Mechanics", Belarusian State University of Transport, Gomel, Republic of Belarus, E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

LEONENKO Denis V., D. Sc. in Phys.-Math., Assoc. Prof., Professor of the Department "Structural Мechanics", Belarusian State University of Transport, Gomel, Republic of Belarus, E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Within the framework of the theory of small elastoplastic deformations one class of simple variables local loading of sandwich bars of rectangular transverse-cross section with elastoplastic bearing layers and physically nonlinear elastic fillers, for which the possibility of constructing a solution of the boundary value problem under repeated loading is indicated, if the solution during loading from the natural state is known (hypothesis of Moskvitin). The paper shows the formulation and methodology of solving boundary value problem of the deformation of the threelayer asymmetric thickness of the rod by repeated exposure to the local rectangular load. To describe the kinematics of asymmetrical thickness rod package were adopted by the broken normal hypothesis: in thin layers bearing valid hypo-theses Bernoulli, in a hard incompressible thickness relatively thick filler normal is straight. It does not change its length, but some extra turns at an angle. The equilibrium equations are derived using the Variational method of Lagrange the work of the filler in the tangential direction is taken into account. Analytic solutions of problems of the theory of small elastic deformations during the forward and backward on-laden are obtained by the method of elastic solutions Ilyushin. The numerical analysis of the solutions is given.

second local loading, plasticity, three-layer beam

• Bolotin V.V., Novichkov Yu.N. Mekhanika mnogosloinykh konstruktsii [Mechanics of Layered Structures]. Moscow, Mashinostroenie, 1980. 375 p. (in Russian).
• Golovko K.G., Lugovoy P.Z., Meysh V.F. Dinamika neodnorodnyh obolochek pri ne-stacionarnyh nagruzkah [The Dynamics of Inhomogeneous Shells under Transient Load Condiions]. Kiev: Kievskij universitet, 2012. 541 p. (in Russian).
• Pleskatshevskiy U. M., Starovoitov E. I., Yarovaya A. V. Dinamika metallopolimernyh sistem [Dynamics of Metal-polymeric Systems]. Minsk, Belaruskaja navuka, 2004. 386 p. (in Russian).
• Zhuravkov M.A., Starovoytov E.I. Matematicheskie modeli sploshnyh sred. Teorija uprugosti i plastichnosti [Mathematical models of continuous media. The theory of Elasticity and Plasticity]. Minsk, BSU, 2011. 540 p. (in Russian).
•  Škec L., Jelenić G. Analysis of a Geometrically Exact Multi-layer Beam with a Rigid Interlayer Connection. Acta Mechanica, 2014, vol. 225, no. 2, pp. 523-541. doi: 10.1007/s00707-013-0972-5.
• Hohe J., Becker W. An Energetic Homogenisation Procedure for the Elastic Properties of Eneral Cellular Sandwich Cores. Composites Part B-Engineering, 2001, issue 3, vol. 32, pp. 185-197.
• Ivañez I., Moure M.M., Garcia-Castillo S.K., Sanchez-Saez S. The Oblique Impact Response of Сomposite Sandwich Plates. Composite Structures, 2015, no. 133, pp. 1127-1136.
• Yankovskii A.P. Analysis of Creep of Reinforced Beams-wall from Nonlinear-hereditary Materials within of the Second Variant of Tymoshenko Theory. Mekhanika kompozicionnykh materialov I konstrukcij [Mechanics of Composite Materials and Designs], 2014, vol. 20, no. 3, pp. 469-489. (in Russian)
• Gorshkov A. G., Starovoytov E. I., Yarovay A. V. Harmonic Loading Viscoelasticoplastic Layered Systems. Izvestija Rossijskoj akademii nauk. Mehanika tverdogo tela [Proceedings of the Russian Academy of Sciences. Mechanics of Solids], 2000, no. 6, pp. 91-98. (in Russian).
• Starovoytov E.I., Dorovskaya E.P. Bending of Rectangular Sandwich Plate on an Elastic Foundation. Problemy mashinostroeniya i avtomatizatsii [Engineering and Automation Problems], 2006, no. 3, pp. 45-50. (in Russian).
• Starovoytov E.I., Leonenko D.V., Suleyman M. Thermoelastic Bending of RingSandwich Plate on Elastic Foundation. Ekologicheskiy vestnik nauchnyh centrov Chernomorskogo ekonomicheskogo sotrudnichestva [Journal of Environmental science centers Black Sea Economic Cooperation], 2006, no. 4, pp. 55-62. (in Russian).
• Starovoytov E.I., Leonenko D.V. Deformation of Three-layer Beam in a Temperature Field. Mehanika mashin, mehanizmov i materialov [Mechanics of Machines, Mechanisms and Materials], 2013, no. 1 (22), pp. 31-35. (In Russian).
• Gorshkov A. G., Starovoytov E. I., Leonenko D. V. Vibrations of Sandwich Beams under the Action of Local Loads of the Different Forms . Ekologicheskiy vestnik nauchnyh centrov Chernomorskogo ekonomicheskogo sotrudnichestva [Journal of Environmental science centers Black Sea Economic Cooperation], 2004, no. 1, pp. 45-52. (in Russian).
• Grover N., Singh B.N., Maiti D.K. An Inverse Trigonometric Shear Deformation Theory for Supersonic Flutter Characteristics of Multilayered Composite Plates. Aerospace Science and Technology, 2016, vol. 52, pp. 41-51.
• Kulikov G.M., Plotnikova S.V. Advanced Formulation for Laminated Composite Shells: 3D Stress Analysis and Rigid-body Motions. Composite Structures, 2013, vol. 95, pp. 236-246.
• Starovoytov E.I., Leonenko D.V., Yarovaya A.V. Circular Sandwich Plates under Local Impulsive Loads. International Applied Mechanics, 2003, vol. 39, no. 8, pp. 945-952.
• Pleskatshevskiy Y.M., Starovoytov E. I., Leonenko D. V. Dynamics of Circular Metal-polymeric Plates on en Elastic Foundation. Part 1. Free Vibrations. Mehanika mashin, mehanizmov i materialov [Mechanics of Machines, Mechanisms and Materials], 2008, no. 4 (5), pp. 48-52. (in Russian).
• Moskvitin V.V., Starovoytov E.I. On the Study of Stress-Strain State of Multilayered Metal-Plates under Cyclic Loading. Izvestija Akademii nauk SSSR. Mehanika tverdogo tela [Proceedings of the Academy of Sciences of the USSR. Mechanics of Solids], 1986, no. 1, pp. 116-121. (in Russian).
• Ilyushin A.A. Plastichnost'. Ch. 1. Uprugoplasticheskie deformacii [Plastic. P. 1. Elastoplastic Deformations]. Moscow, Gostehizdat, 1948, 376 p. (In Russian).
• Moskvitin V. V. Ciklicheskoe nagruzhenie jelementov konstrukcij [Cyclic Loading of Structural Elements]. Moscow, Nauka, 1981, 344 p. (in Russian).