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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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