Micropolar medium, nonlocal models, thin body, composite materials, orthogonal polynomial method, mathematical theory of thin bodies, scale effects, gradient mechanics, nanomechanics, eigenvalue problem of tensor-block matrix, tensor column, eigentensor, the anisotropy symbol of tensor-block matrix , the anisotropy symbol of the material, the tensor operator of the equations, the tensor-operator of stress, the tensor-operator of stress and couple stress, the tensor-block matrix operator, the canonical presentation of a tensor.
Subject:
Classical and nonclassical theories of elasticity, viscoelasticity, mechanics of composites and nanocomposites; classical and non-classical theories of thin bodies of various rheology; classical and non-classical theories of thin bodies of various rheology using systems of orthogonal polynomials; eigenvalue problems for the tensor and tensor-block matrix of any even rank and their application in mechanics; gradient mechanics of continuous media; nanomechanics of gradient continuous media; gradient mechanics of thin bodies; nanomechanics of gradient thin bodies; mechanics of composites of thin bodies, etc.
Main publications:
M. U. Nikabadze,
A variant of the theory of multilayer structures
// Mech. Solids. 2001. No. 1. 143–158.
M. U. Nikabadze, Mathematical modeling of multilayer thin body deformation//Journal of
mathematical sciences. V. 187, No 3, 2012. P. 300-336.
M. U. Nikabadze Development of the method of orthogonal polynomials in
the classical and micropolar mechanics of elastic thin bodies // M., Publishing House of the Board
of Trustees mech.-math. facul. of MSU. 2014. 515 p (in Russian).
http://istina.msu.ru/media/publications/book/707/ea1/6738800/Monographiya.pdf
M. U. Nikabadze,
Some issues concerning a version of the theory of thin solids
based on expansions in a system of Chebyshev polynomials of the second kind
// Mech. Solids. 2007. 42. No. 3. 391-421.
M. U. Nikabadze, Topics on tensor calculus with applications to mechanics//
J. Math. Sci. 2017. Vol. 225, No. 1. 194 p. DOI: 10.1007/s10958-017-3467-4
H. A. Matevossian, M. U. Nikabadze, G. Nordo, A. R. Ulukhanyan, “Biharmonic Navier and Neumann problems and their application in mechanical engineering”, Lobachevskii J. Math., 42:8 (2021), 1876–1885
M. U. Nikabadze, “Splitting of initial boundary value problems in anisotropic linear elasticity theory”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 5, 23–30; Moscow University Mechanics Bulletin, 74:5 (2019), 103–110
M. U. Nikabadze, “Eigenvalue Problems for Tensor-Block Matrices and Their Applications to Mechanics”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 150 (2018), 40–77; J. Math. Sci. (N. Y.), 250:6 (2020), 895–931
M. U. Nikabadze, “Eigenvalue problem for some tensors used in mechanics and a number of essential compatibility conditions for the Saint-Venant deformation”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 3, 54–58; Moscow University Mechanics Bulletin, 72:3 (2017), 66–69
M. U. Nikabadze, “Eigenvalue problem for tensors of even rank and its applications in mechanics”, Contemporary Mathematics and Its Applications, 98 (2015), 22–52; Journal of Mathematical Sciences, 221:2 (2017), 174–204
M. U. Nikabadze, “Topics on tensor calculus with applications to mechanics”, CMFD, 55 (2015), 3–194; Journal of Mathematical Sciences, 225:1 (2017), 1–194
M. U. Nikabadze, “Construction of eigentensor columns in the linear micropolar theory of elasticity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2014, no. 1, 30–39; Moscow University Mechanics Bulletin, 69:1 (2014), 1–9
M. U. Nikabadze, “Compatibility conditions and equations of motion in the linear micropolar theory of elasticity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2012, no. 1, 63–66; Moscow University Mechanics Bulletin, 67:1 (2012), 18–22
M. U. Nikabadze, “Relation between the stress and couple-stress tensors in the microcontinuum theory of elasticity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 6, 59–62
M. U. Nikabadze, “Formulas for the general complex representation in the plane micropolar theory of elasticity”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 4, 65–68
2010
11.
M. U. Nikabadze, “Compatibility conditions in the linear micropolar theory”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 5, 48–51
M. U. Nikabadze, “Application of Chebyshev polynomials to the theory of thin bodies”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, no. 5, 56–63
13.
M. U. Nikabadze, “Shell theory equations consistent with boundary conditions at face surfaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, no. 2, 72–76
2006
14.
M. U. Nikabadze, “A version of a system of equations in the theory of thin bodies”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2006, no. 1, 30–35
2005
15.
M. U. Nikabadze, A. R. Ulukhanyan, “Formulation of the problem for thin deformable 3D body”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, no. 5, 43–49
2002
16.
M. U. Nikabadze, “Equations of motion and boundary conditions in the theory of multilayer plane curvilinear rods”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, no. 6, 41–46
2001
17.
M. U. Nikabadze, “Equations of motion and boundary conditions in rod theory with several base lines”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2001, no. 3, 35–39
2000
18.
M. U. Nikabadze, “The unit tensors of second and fourth ranks under a new parametrization of a shell space”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 6, 25–28
19.
M. U. Nikabadze, “Christoffel symbols and the second surface tensor with new parametrization of the shell space”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2000, no. 3, 41–45
M. U. Nikabadze, “A new kinematic hypothesis and new equations of motions and equilibrium of the theory of shells and plane curvilinear rods”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1991, no. 6, 54–61
2007
21.
D. V. Georgievskii, V. I. Gorbachev, I. A. Kiiko, A. S. Kravchuk, E. V. Lomakin, L. V. Muravleva, M. U. Nikabadze, N. N. Smirnov, G. G. Chernii, V. N. Chubarikov, E. I. Shemyakin, S. V. Sheshenin, “К семидесятилетию Бориса Eфимовича Победри”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2007, no. 5, 3–5
К теориям тонких тел M. U. Nikabadze Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov February 22, 2008 18:30
13.
К варианту теории многослойных конструкций M. U. Nikabadze Scientic seminar «Actual problems of geometry and mechanics » named after Prof. V.V. Trofimov September 28, 2001 18:30
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