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Ю.И. Димитриенко, И.О. Богданов
90
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2016. № 6
dimensional problems of buckling theory. Nowadays, nu-
merical methods of their solution are not known. The work
gives the variation statement of the three-dimensional prob-
lem of elastic structures buckling theory. According to this
statement, we proposed the final-element method for sol-
ving the buckling problems which is reduced to finding the
eigen values of the linear algebraic equations system with a
global symmetric stiffness matrix. As a result, we developed
the program module implementing the offered final-element
method within the SMCM program complex developed in
Scientific and Educational Center "SIMPLEX" at Bauman
Moscow State Technical University with the use of the CSIR
storage scheme of the sparse matrixes and a bi-conjugate
gradient method. We carried out the test calculation for the
rectangular plate buckling problem under the longitudinal
compression. The comparison of the final-element solution
of this problem according to the three-dimensional theory
and Timoshenko plates theory has shown high precision of
the developed numerical method when determining critical
loads. At the same time, the three-dimensional theory allows
for more exact forms of eigen functions of stability loss
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