Analysis of rectangular thin plates and plate structures basing on the Vlasov's variational procedure1

  • Johannes Altenbach Förderstedter Str. 28
  • Konstantin Naumenko Martin-Luther- Universität Halle- Wittenberg
  • Vladimir K. Naumenko Ukrainian Engineering-Educational Academy


The solution procedure proposed by Vlasov based on the reduction of the basic two-dimensional boundary value problems into ordinary differential equations provides a good accuracy in the case of rectangular domains with small size ratios. The paper presents an extension of this method applied to rectangularKirchhoff's plates in connection with the iterational scheme. The results are compared with analytical solutions available for rectangular plates with simplified boundary conditions and loading. The possibilities of application of the solutions for simple plate geometry to complex plate problems (e.g. complex geometry, boundary conditions) are discussed and illustrated by numerical examples.



[1] J. Altenbach, W. Kissing, H. Altenbach. Dünnwandige Stab- und Stabschalentragwerke. Vieweg, Braunschweig/ Wiesbaden, 1994.
[2] J. Altenbach. Die Berechnung ebener Flächentragwerke mit Hilfe von Einfluƥfunktionen zugeordneter vereinfachter Grundaufgaben. ZAMM, 52:T288-T292, 1972.
[3] J. Altenbach. Beitrag zur Berechnung regelmiiBiger polygonaler Behlter. Wissenschaftliche Zeitschrift der TH Otto von Guericke Magdeburg, 14(5): 441-457, 1970.
[4] J. Altenbach, K. Naumenko, V. Naumenko. On application of Vlasov's solution for rectangular thin plates to complex plate problems. In: V. Kompis, ed., Proceedings of the International Conference on Numerical Methods in Continuum Mechanics, 141-145, UTC Ed., Zilina, 1996.
[5] H. Altenbach, K. Naumenko. Creep bending of thin-walled shells and plates by consideration of finite deflections. Comp. Mech., 19: 490-495, 1997.
May 31, 2023
How to Cite
ALTENBACH, Johannes; NAUMENKO, Konstantin; NAUMENKO, Vladimir K.. Analysis of rectangular thin plates and plate structures basing on the Vlasov's variational procedure1. Computer Assisted Methods in Engineering and Science, [S.l.], v. 5, n. 2, p. 115-128, may 2023. ISSN 2956-5839. Available at: <>. Date accessed: 18 july 2024.