and Computational Methods

doi: 10.18698/2309-3684-2014-4-1836

The suggested thermocreep theory for thin multilayer plates is based on analysis of general three dimensional nonlinear theory of thermalcreep by constructing asymptotic expansions in terms of a small parameter being the ratio of a plate thickness and a characteristic length. Here we do not introduce any hypotheses on a distribution character for displacements and stresses through the thickness. Local problems were formulated for finding stresses in all structural elements of a plate. It was shown that the global (averaged by the certain rules) equations of the plate theory were similar to equations of the Kirchhoff–Love plate theory, but they differed by a presence of the three-order derivatives of longitudinal displacements. The method developed allows to calculate all six components of the stress tensor including transverse normal stresses and stresses of interlayer shear. For this purposes one needs to solve global equations of thermal creep theory for plates, and the rest calculations are reduced to analytical formulae use.

[1] Gureeva N.A. Proceedings of Higher Educational Institutions. Маchine Building, 2007, no. 5,

pp. 23–28.

[2] Popov B.G. Calculation of multilayer structures by variational-matrix methods. Moscow, BMSTU Publ., 1993, 294 p.

[3] Sheshenin S.V. Proc. of the Russ. Acad. Sci. Mech. Rigid Body, 2006, no. 6, pp. 71–79.

[4] Sheshenin S.V., Khodos O.A. Vychislitel'naya mekhanika sploshnoi sredy, Computational Continuum Mechanics, 2011, vol. 4, no. 2, pp. 128–139.

[5] Kohn R.V., Vogelyus M. Int. J. Solids and Struct., 1984, vol. 20, no. 4, pp. 333–350.

[6] Panasenko G.P., Reztsov M.V. Reports of Acad. Sci. USSR, 1987, vol. 294, no. 5, pp. 1061–1065.

[7] Levinski T., Telega J.J. Plates, laminates and shells. Asymptotic analysis and homogenization. Singapore, London, World Sci. Publ., 2000, 739 p.

[8] Kolpakov A.G. Homogenized models for thin-walled nonhomogeneous structures with initial stresses. Springer Verlag, Berlin, Heidelberg, 2004, 228 p.

[9] Dimitrienko Yu.I. Herald of the Bauman Moscow State Technical University. Series: Natural Science,

2012, no. 3, pp. 86–100.

[10] Dimitrienko Yu.I., Yakovlev D.O. Engineering Journal: Science and Innovation, 2013, iss. 12. Available at: http://engjournal.ru/catalog/mathmodel/technic/899.html

[11] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V. mmcm. Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 36–57.

[12] Dimitrienko Yu.I., Gubareva E.A., Yakovlev D.O. Science and Education. Electronic Scientific and Technical Joural, 2014, no. 10. doi: 10.7463/1014.0730105.

[13] Dimitrienko Yu.I., Yakovlev N.O., Erasov V.S., Fedonyuk N.N., Sborschikov S.V., Gubareva E.A., Krylov V.D., Grigoriev M.M., Prozorovskiy А.А. Kompozity i nanostruktury, Composites and Nanostructures, 2014, no. 1, vol. 6, pp. 32–48.

[14] Dimitrienko Yu.I. Continuum mechanics. In 4 vols. Vol. 4. Fundamentals of solid mechanics. Moscow, BMSTU Publ., 2013, 624 p.

[15] Dimitrienko Yu.I. Continuum mechanics. In 4 vols. Vol. 1. Tensor analysis. Moscow, BMSTU Publ., 367 p.

Dimitrienko Y., Gubareva E., Yurin Y. Asymptotic theory of thermocreep for multilayer thin plates. Маthematical Modeling and Coтputational Methods, 2014, №4 (4), pp. 18-36

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