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Численное моделирование теплового расширения композиционных материалов…
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Numerical simulation of composite material thermal
expansion by homogenization method
© Yu.I. Dimitrienko, E.A. Gubareva, S.V. Sborschikov
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article considers a variant of the asymptotic homogenization method for calculation
of effective thermal expansion coefficients of composite materials with thermoelastic
properties.
We formulate
problems of local thermoelasticity over a periodicity cell of
composites
.
A variational formulation of the thermoelasticity problem over a periodicity
cell is proposed. A finite element method for computational solving of these problems of
thermoelasticity is applied
.
For software implementation of the finite element method we
use the software package developed by the Scientific and Educational Center of the
BMSTU.
We also give
examples of numerical solution of the local problems of
thermoelasticity for composites based on ceramic fibers and the polymer matrix. Effective
coefficients of thermal expansion for composite materials with spatial arrangement of
ceramic fibers and a polymer matrix were calculated for different temperatures.
We
show that processes of thermal decomposition of polymer matrix result in nonmonotonic
dependence of the thermal expansion coefficient on temperature. The proposed algorithm
allows to calculate
the thermal expansion coefficients for composites with almost any
structures of fiber reinforced matrices undergoing physicochemical transformations at
high temperatures. Unlike a large number of the well-known approximate methods for
calculating thermal expansion coefficients the proposed method allows to obtain the
mathematically accurate values for these coefficients.
Ключевые слова:
multilayer thin shell, asymptotic homogenization method, asymptotic
theory of shells
.
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