Optimization of thick-walled shells based on solutions of inverse problems of the elastic theory for inhomogeneous bodies

Abstract

An inverse problem of elastic theory for inhomogeneous bodies is normally used for identification of the dependencies of a material’s mechanical properties of coordinates where the stress state of the body will be specified. It is known that in thick-walled cylindrical or spherical shells under internal or external pressure the highest stresses are close to the inner surface of the shell. Several solutions of inverse problems (depending on the elastic modulus along the radius at which the equivalent stress in the shell will be constant) are obtained in this paper with the use of conventional strength theories. Corresponding shells could be called equal stress shells. If an investigator changes the elastic modulus of the material its mechanical properties change as well. It is shown that for some materials the investigator can create a model of an equal strength shell with an equivalent stress at each point, which is equal to the strength of the material. This paper is devoted to creating multi-layered shells in which the elastic modulus in each layer is determined by the results of solving inverse problems.