Acta Mechanica

, Volume 230, Issue 11, pp 3823–3824 | Cite as

Special issue on structural mechanics dedicated to the memory of Vladimir Yeliseyev (1947–2017)

  • Yury VetyukovEmail author
  • Alexander Belyaev

Prof. Vladimir Vasilyevich Yeliseyev (alternative spelling: Eliseev) used to live, work, and teach in St. Petersburg, Russia. Belonging to the famous school of Prof. Anatoliy Isaakovich Lurie at the Chair of Mechanics and Control of the Leningrad Polytechnic Institute, Vladimir Yeliseyev did his best at rethinking and further developing the heritage of his outstanding teacher. Strongly believing that mechanics is the most rewarding branch of physical and mathematical sciences, he generously shared his passion for mechanics with his own students. His passionate lectures, which he held at a high scientific level, clearly and rigorously presented the most challenging and modern questions of continuum and classical mechanics. Teaching, as well as applied and fundamental research of Prof. Yeliseyev, proved to be extremely efficient owing to the analytical technologies, which he developed to a high level of perfection [1, 2, 3]: mixed indexed and direct tensor notation, procedure of asymptotic splitting of equations for thin-walled and periodic structures, Lagrangian mechanics, and computational mathematics.

Among the scientific achievements of Prof. Yeliseyev, one should start with mentioning the modern versions of the linear and nonlinear theories of thin elastic rods, plates, and shells. For the first time ever, he systematically studied the asymptotic splitting of the three-dimensional equations of elasticity to a dimensionally reduced structural problem and to a problem in the cross section of a rod with a structure [4, 5, 6] or in the through-the-thickness element of a plate. He succeeded at developing geometrically nonlinear equations in a compact tensorial form based on the principle of virtual work, applied for material lines [7] and surfaces [8, 9]. Proving important fundamental theorems, obtaining equations in the incremental form [8] and finding several novel solutions to particular problems [10, 11], he contributed to raising the linear and nonlinear mechanics of thin-walled structures from the level of technical theories towards an established branch of continuum mechanics. His bright thinking and advanced techniques of analysis allowed him to obtain novel results related to composites and fracture [12], magneto- and electroelasticity [6], fluid–structure interaction [13], rotor dynamics [14], contact problems [15], dynamics and stability of axially moving material structures [16], and many others. Colleagues of Prof. Yeliseyev made a collection of his printed works available at

The present volume of Acta Mechanica contains outstanding contributions on various aspects of structural mechanics. Many of them feature structural theories in the form developed by Prof. Yeliseyev, or are closely related to his research. We are hoping that this special issue will further attract attention to his bright scientific heritage.



  1. 1.
    Yeliseyev, V.V.: Mechanics of Elastic Bodies. St. Petersburg State Polytechnical University Publishing House, St. Petersburg (1999). (in Russian)Google Scholar
  2. 2.
    Yeliseyev, V.V.: Mechanics of Deformable Solid Bodies. St. Petersburg State Polytechnical University Publishing House, St. Petersburg (2006). (in Russian)Google Scholar
  3. 3.
    Yeliseyev, V.V., Zinovieva, T.V.: Fundamentals of Mechanics of Materials. Lan’, St. Petersburg (2016). (in Russian)Google Scholar
  4. 4.
    Eliseev, V.V.: Constitutive equations for elastic prismatic bars. Mech. Solids 24(1), 70–75 (1989)MathSciNetGoogle Scholar
  5. 5.
    Eliseev, V.V.: Saint-Venant problem and elastic moduli for bars with curvature and torsion. Mech. Solids 26(2), 167–176 (1991)Google Scholar
  6. 6.
    Yeliseyev, V.V., Orlov, S.G.: Asymptotic splitting in the three-dimensional problem of linear elasticity for elongated bodies with a structure. J. Appl. Math. Mech. 63(1), 85–92 (1999)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Eliseev, V.V.: The non-linear dynamics of elastic rods. J. Appl. Math. Mech. (PMM) 52(4), 493–498 (1988)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Eliseev, V.V., Vetyukov, Yu.: Finite deformation of thin shells in the context of analytical mechanics of material surfaces. Acta Mech. 209(1–2), 43–57 (2010)CrossRefGoogle Scholar
  9. 9.
    Eliseev, V., Vetyukov, Y.: Theory of shells as a product of analytical technologies in elastic body mechanics. In: Pietraszkiewicz, W., Górski, J. (eds.) Shell Structures: Theory and Applications, vol. 3, pp. 81–84. CRC Press/Balkema, Taylor & Francis Group, London (2014)Google Scholar
  10. 10.
    Belyaev, A.K., Eliseev, V.V.: Flexible rod model for the rotation of a drill string in an arbitrary borehole. Acta Mech. 229, 841–848 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Eliseev, V., Zinovieva, T.: Lagrangian mechanics of classical shells: theory and calculation of shells of revolution. In: Pietraszkiewicz, W., Witkowski, W. (eds.) Shell Structures: Theory and Applications, vol. 4, pp. 73–76. Taylor & Francis Group, London (2018)Google Scholar
  12. 12.
    Eliseev, V.V., Piskunov, V.A.: Composite gas-turbine blades. Rus. Eng. Res. 36(10), 819–822 (2016)CrossRefGoogle Scholar
  13. 13.
    Eliseev, V.V., Vetyukov, Yu., Zinovieva, T.V.: Divergence of a helicoidal shell in a pipe with a flowing fluid. J. Appl. Math. Tech. Phys. (Zhurnal Prikladnoi Matematiki i Tehnicheskoi Fiziki) 52(3), 450–458 (2011)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Eliseev, V.V., Moskalets, A.A.: Computational technique of plotting Campbell diagrams for turbine blades. In: Evgrafov, A. (ed.) Advances in Mechanical Engineering. Lecture Notes in Mechanical Engineering, pp. 37–44. Springer, Berlin (2017)Google Scholar
  15. 15.
    Belyaev, A.K., Eliseev, V.V., Irschik, H., Oborin, E.A.: Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod. Acta Mech. 228, 4425–4434 (2017)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Eliseev, V., Vetyukov, Yu.: Effects of deformation in the dynamics of belt drive. Acta Mech. 223, 1657–1667 (2012). MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.TU WienViennaAustria
  2. 2.Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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