539.3 Modeling of stresses in a composite nonlinear elastic panel under cylindrical bending

Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University), Kolzhanova D. Y. (Bauman Moscow State Technical University)


doi: 10.18698/2309-3684-2021-1-330

The problem of calculating the stress–strain state of a composite laminated panel during cylindrical bending under conditions of finite deformations is considered. To solve the problem, the method of asymptotic averaging of periodic nonlinear elastic structures with finite deformations was applied, which was developed in detail earlier in the previous works of the authors. A feature of this problem is the use of universal models of constitutive relations for isotropic components of the composite, as well as for the composite as a whole, which is a transversely isotropic nonlinear elastic medium. Universal models make it possible to obtain solution of problems within the framework of a single solution algorithm simultaneously for several classes of models of nonlinear elastic media corresponding to different conjugate pairs of stress tensors–deformation. An analytical solution is obtained for the problem of cylindrical bending of a composite panel. A numerical analysis of the solution is carried out using the example of a composite, the periodicity cell of which consists of two layers: polyurethane and rubber. It is shown that for thin panels the stresses, both averaged and true, practically do not depend on the class of the model of the constitutive relations. At the same time, for thicker panels, the stresses differ significantly for different classes of models of composite layers.

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