DOI: 10.5937/jaes14-10454
This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.
Volume 14 article 357 pages: 84-92
Past studies on the stability of rectangular plates under the influence of variable loads were based on assumptions of simplified stress distributions, which put the question of the
accuracy of results thus obtained. The procedure of applying the exact stress
functions in the problem of elastic stability of the plate with different
boundary conditions under effects of patch and wheel loading is presented in
this paper. Mathieu (1890) obtained the exact solution for the plane-strain
state for a rectangular element for certain types of variable stresses on the
boundaries. Baker at al (1993), following Mathieus results, analyzed the general problem of a rectangular plate loaded by completely arbitrary distributions of (normal and/or shear) stresses along the
edges of the plate. Analytical approach used for determination of the critical
load is based on well known Ritz energy technique. The strain energy due to
bending of the plate is defined in the traditional way. On the other hand, the
exact stress distribution of Mathieus theory of elasticity is introduced through the potential energy of the plate associated with the work done by external loads. Results for the critical load
obtained by presented analytical approach are reaffirmed by numerical
finite-element (FE) runs.
Baker G.,
Pavlovic M. N., Tahan N. (1993): “An exact solution to the two-dimensional
elasticity problem with rectangular boundaries under arbitrary edge forces“,
Phil. Trans. R. Soc. London, A 393, pp. 307-336
Liu Y. G. (2006):
“Buckling of Plates under Non-Uniform Stresses, with Particular Emphasis on Shear“,
Ph. D Thesis, Imperial College, London
Mathieu E. (1890):
“Theorie de l’elasticite des corps solides“, Seconde
partie. Gauthier Villars, Paris
Mijuskovic O. (2008): “Analiza stabilnosti pravougaonih ploca
koriscenjem tacne
funkcije napona“, Doktorska disertacija, Gradjevinski fakultet Univerziteta u
Beogradu, Beograd
Mijuskovic
O., Coric B. (2013): “Patch loading analytical approach to critical load determination“, original scientific paper, Gradjevinar,
Journal of the Croatian Association of Civil Engineers, 65(1), pp. 1-10
Mijuskovic
O., Coric B., Scepanovic B. (2014):““Exact stress functions implementation in stability analysis of plates
with different boundary conditions under uniaxial and biaxial compression“, Thin-Walled Structures, 80, pp.
192-206
Mijuskovic O., Coric B., Scepanovic B.
(2015): “Accurate buckling
loads of plates with different boundary conditions under arbitrary edge compression“, International Journal of Mechanical Sciences,
101-102, pp.309-323
Mijuskovic O., Coric B., Scepanovi! B., Zugic
Lj. (2016): “Analytical model for buckling analysis of the plates
under patch and concentrated loads“, Thin-Walled Structures, 101, pp.26-42