Mathematical modeling of processes of devising fibrous composite materials and thin-walled structural elements by forced winding

Conclusions With the aid of the method of averaging processes in regular media, on the assumption that the temperature field in the semiproduct of PM is homogeneous at all stages of the production of thin-walled articles of CM, we suggested averaged equations of equilibrium, and also constructive algorithms for calculating the effective moduli and defining relations of the material of the semiproduct of CM. On the basis of these equations and the boundary conditions corresponding to them, we showed that it is possible to determine the RTS in a finished product of CM, and also to predict the change of its shape after removal from the mandrel and cutting it up into separate elements. To determine the above-mentioned technological characteristics of thin-walled elements made of fibrous CM, it is necessary to know the physicomechanical characteristics of the fibers and of the PM before and after polymerization; the volume fraction of the reinforcing filler and of the PM during winding, and also the orientation of the reinforcement; the relative change of volume of the PM after heat treatment and cooling; the prestresses in the fibers in the process of winding. It should be noted that the obtained averaged equations make it possible to calculate only the components of the averaged RTS in products of CM. To determine the local stresses in PM and fibers at all stages of making the product, it would be necessary to investigate in detail the rheology of PM at different temperatures.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 513–527, May–June, 1990.