Open AccessNUMERICAL METHOD OF CALCULATION OF ROUND PLATES IN A GEOMETRICALLY NONLINEAR STATEMENT
Author(s) -
Габбасов Радек Фатыхович,
Уварова Наталья Борисовна
Publication year - 2017
Publication title -
vestnik mgsu
Language(s) - English
Resource type - Journals
eISSN - 2304-6600
pISSN - 1997-0935
DOI - 10.22227/1997-0935.2017.6.631-635
Subject(s) - nonlinear system , mathematics , classification of discontinuities , mathematical analysis , resolvent , function (biology) , differential equation , physics , quantum mechanics , evolutionary biology , biology
The article considers the axisymmetric problem about the calculation of round plates with dead loading in a geometrically nonlinear system. To solve the problem some generalized equations of finite difference method (FMD) are needed that allow to solve tasks within intergrable scope taking into account discontinuities of the required function, its first-order derivative and the right-hand side of the primitive differential equation. Resolvent differential equations of the question comprised fractionally the required function of the inflection and stresses are reduced to four differential equations, two of which are linear of the first-order and two are nonlinear of the second order. The obtained system of differential equations is solved numerically. The proposed method is shown with the example of calculation of a round plate; the given data are taken from work [1]. The calculation data with the minimum number of partitions are compared to the known solution of A.S. Vol’mir [1] and they indicate the possibility of using a numerical method for handling the problem in nonlinear statement.