Optimization of composite revolution shell by methods of theory of the optimal process

Abstract

We considered the problem of weight optimization of parameters of multi-layer composite shell produced by the method of continuous cross-winding under axisymmetric loading. Shell layers are placed symmetrically relative to the middle surface. The angles of the reinforcing material winding variable along the meridian and the thickness of layers are taken as the variation parameters. We propose an algorithm of the automated determination of the elastic constants of a composite material variable along the shell meridian anisotropy. The connection of the composite structure with the technological process of shell manufacturing by winding with a reinforcing tape under different angles to the axis of rotation is taken into account. The values of four elastic constants obtained as a result of experimental testing of witness specimens of the composite material along and orthogonal to the reinforcement are used as output. The equations of state of the moment theory of shells of the variable along the meridian orthotropy and wall thickness are obtained as a boundary value problem for a system of ordinary differential equations with variable coefficients. The use of the necessary optimality conditions in the form of the principle maximum of Pontryagin in the presence of arbitrary phrasal restraints made it possible to reduce the emerging multiparameter problem to a sequence of extreme problems of a significantly smaller dimension. This approach greatly simplifies taking into account the conditions of strength reliability, and technological and structural requirements of real design, and the process of finding an optimal project as a whole. The results of the optimization of a two-layer fiberglass shell of rotation are presented in the form of a change in the distribution of layers’ thickness and the glass fiber winding angle. Materials of research can be used to reduce the material consumption of structural elements in rocket and space technology and other branches.