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Расчет полного тензора напряжений в тонких моноклинных композитных оболочках…
Инженерный журнал: наука и инновации
# 12·2016 23
Explicit formulas for the calculation of the complete tensor
of the stresses in the monoclinic thin composite shells
based on the asymptotic homogenization method
© Yu.I. Dimitrienko, Е.A. Gubareva, Yu.V. Yurin
Bauman Moscow State Technical University, Moscow, 105005, Russia
The article presents the results of further development of the previously proposed by the
authors’ new asymptotic theory of thin multilayer anisotropic shells. The theory is con-
structed on the equations of the general three-dimensional theory of elasticity by intro-
ducing small geometric parameter asymptotic expansions without any hypotheses on
stresses and displacements distribution over the thickness. The case of monoclinic layers
having at the most 13 independent elastic constants is considered. An algorithm for ob-
taining explicit analytic formulas for the calculation of the complete stress tensor compo-
nent distribution over the shell is proposed. The algorithm is based on solving specific
local problems of the first, second and third approximations. It allows obtaining expres-
sions for all six components of the stress tensor in a compact closed form, as a function
of strain, curvature of the middle surface of the shell, as well as their derivatives with re-
spect to the longitudinal coordinates. These formulas allow calculating all stress tensor
components in the shell without additional tasks, using only the solutions of the averaged
problem of shell theory.
Keywords:
stress tensor, multilayer thin monoclinic shells, composites, the method of as-
ymptotic averaging, asymptotic theory of shells
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