Design of Equi-Strength Nonhomogeneous Rotating Shafts

The article is devoted to the design of an equi-strength rotating cylinder under conditions of plane or generalized plane strain. Both solid and hollow cylinders are investigated. The problem statement is based on the equations of the linear theory of elasticity. The lateral surfaces of the cylinder are assumed to be traction-free. It is supposed that Young’s modulus is an unknown function of the radial coordinate, and the other physical and mechanical parameters of the material are constant. The dependencies of Young’s modulus are established, at which the desired stress state is achieved in the cylinder. As such a state, a constant hoop stress, a constant difference between the hoop and radial stress, and a constant linear combination of the hoop and radial stresses are considered.