A Mathematical Study for Investigation the Problems of Soft Shells Materials

The current study investigates the problems of soft shells theory for manufacturing composite products by superimposition on each 2D layers. Analytical and numerical methods are considered to study the layers imposing winding around the halffinished materials or pulling some additional shells on the surface of materials which are partly made. Based on this, the smoothness of layers, and the criteria of the absence of wrinkles and folds are obtained. Methods for calculation the deformations and residual stresses of the textile structure of used materials were established. The results obtained by the analytical and numerical methods indicated that it is possible to establish mathematical equations which can be applied to find the strains and stresses developed in the shells and bands and their pressure on the surfaces of covered solid. The results of the present work can also be implemented for manufacturing composite materials having complex geometric forms