Abstract
Physical components of effective tangential stiffness and temperature stress tensors of a multilayer reinforced in different directions composite were obtained in the coordinate system not related to the material microstructure. The structural approach was used in estimating its physical and mechanical properties. It is based on the assumption that there exists a characteristic environment heterogeneity dimension of a regular structure which makes it possible to define the representative element and to describe the averaging procedure. For example, in a fiber composite the representative length equals the distance between fibers. Physical components of effective tangential stiffness and thermal stresses tensors for one-directional reinforced layer were obtained in the coordinate system related to the material microstructure based on the following assumptions:
1. A multireinforced layer constitutes an elastic isotropic homogenous matrix and a regular grid of one-directional elastic fibers is incorporated into the matrix. Reinforcing fibers sustain both stretching and compression.
2. The number of reinforcing fibers is big enough to assume that the multireinforced layer is quasihomogenous.
3. The external force and heat field gradients are “not too big” and we can consider that there is no variation of the thermal field and stress-strain behavior of the representative volume.
4. Both the matrix and reinforcing material follow Duhamel-Neumann’s law.
5. The increment of temperature is small enough not to affect the elastic and thermophysical properties of composite compounds. We will assume that they do not depend on temperature.
6. The heat flux vector and temperature gradient follow the Fourier law in both composite compounds.
7. The reinforcing fiber cross-section is rectangular and has an ideal heat contact with the matrix. The stress vector on the phase division surface of the heterogeneous mediun is continuous and the heat field follows the ideal heat contact law.
A closed system of equations of multilayer hyperboloid shells of revolution statics, the order of which does not depend on the number of layers or the method of reinforcement, is given.
Keywords: One-directional reinforced layer,multireinforced layer, Duhamel-Neumann’s la, Fourier law of heat transfer, ideal heat contac, heterogeneous environment, multilayered shell, one-sheeted hyperboloid of revolution, non-coupled thermoelastic problem
Authors:
Iu.V. NEMIROVSKY
Khristianovich Institute of Theoretical and Applied Mechanics, D. Sc. (Phys. & Math., professor.) 4/1, Institutskaya Street, Novosibirsk, 630090, Russian Federation.E-mail:yur.nemi-rowscky@yandex.ru
A.I. BABIN
Kuzbass State Technical University, senior lecturer, 28 Spring Street, Kemerovo, 650000, Russian Federation. Е-mail:anbabin@yandex.ru
E.A. SAL'SKII
Kemerovo State University,graduate student, 6 Krasnaya Street,Kemerovo, 650043,Russian Federation. Е-mail:e_s_@mail.ru
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