The design of nonhomogeneous equi-strength annular discs of variable thickness under internal and external pressures

Abstract

The optimal distributions of Young's modulus and thickness which guarantee satisfaction of the Tresca yield criterion simultaneously at all points within the annular discs are presented. The prescribed stress state takes place when the quasistatic pressures upon the contours reach their limit values. An analytical solution has been obtained for the case of an arbitrary distribution of thickness (Young's modulus) by means of a semireciprocal method. Assuming the disc thickness (Young's modulus) to be a power function of radius relations between the limit values of pressures and the optimal distributions of Young's modulus (thickness) have been presented. For the case of prescribed linear distributions of radial stress, formulae for the determination of optimal distributions of thickness and Young's modulus by means of a reciprocal method have been obtained. The regions of variation of pressures in which homogeneous or annular discs of optimal distributions of Young's modulus and thickness respectively will remain elastic, are determined. The advantages of discs of optimal distributions of Young's modulus and thickness compared with homogeneous discs and discs with constant thickness are discussed.