Графовый подход при построении конечно-элементной модели упругих тел в полярной системе координат

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Графовый подход при построении конечно-элементной модели упругих тел…
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 3 69
The graph of the whole body is built following the same
rule as in the elementary cell. The method is based on
transforming generalized coordinates of a solid body sepa-
rated into pieces to a system of generalized coordinates of
the initial solid body. The specific nature of the graph
model lies in the possibility to construct these matrices
with no need for their numerical inversion. With the use of
a unit cell having 8 degrees of freedom, the strain field is
approximated by linear polynomials (with corresponds to
approximated of the displacement fields by quadratic
polynomials). The standard finite-element method requires
16 degrees of freedom (elements with 8 nodes) for the same
purpose. The proposed graphical approach thus reduces
the number of equations that describe the model. We
provide numerical examples which prove the efficiency of
the method
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