Postbuckling of a uniformly compressed simply supported plate with free in-plane translating edges
V. B. Myntiuk
Zhukovsky National Aerospace University “Kharkiv Aviation Institute” (KhAI),
ul. Chkalova 17, Kharkov 61070, Ukraine
The postbuckling of a Kirchhoff isotropic simply supported plate
is considered in detail.
The in-plane displacements on the edges of the plate
are not constrained.
The solution is obtained using the principle
of the total potential energy stationarity.
The expression for energy is written in the three versions:
in terms of the Biot strain,
the Cauchy–Green strain,
and the strain corresponding
to Föppl–von Kármán plate theory.
Some approximate solution is constructed by the classical Ritz method.
The basis functions are taken in the form of Legendre polynomials
and their linear combinations.
The obtained equilibrium path is rather similar
to the classical equilibrium path of compressed shells.
We show the failure of Föppl–von Kármán theory
under large deflections.
Using the Biot strain and the Cauchy–Green strain
leads to the discrepancy between the results of at most 5%.
We demonstrate the high accuracy and convergence of the approximate solution.
postbuckling, plate, limit point, Biot strain, Cauchy–Green strain.
PDF file (703 kB)
First page: PDF file
V. B. Myntiuk, “Postbuckling of a uniformly compressed simply supported plate with free in-plane translating edges”, Sib. Zh. Ind. Mat., 23:1 (2020), 143–154
Citation in format AMSBIB
\paper Postbuckling of a uniformly compressed simply supported plate with free in-plane translating edges
\jour Sib. Zh. Ind. Mat.
Citing articles on Google Scholar:
Related articles on Google Scholar:
|Number of views:|