Axisymmetric shell optimization under fracture mechanics and geometric constraints

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The shell is made from quasi-brittle materials, and through crack arising is admitted. It is supposed that the shell is loaded by cyclic forces. A crack propagation process related to the stress intensity factor is described by Paris fatigue law. The problem of finding the meridian shape and the thickness distribution (geometric design variables) of the shell having the smallest mass subject to constraints on the cyclic number for fatigue cracks and geometrical con- straint on the shell volume is investigated. Special attention is devoted to different possibilities of problem transforma- tion andanalytical methodsoftheir solution.Using minimax approach, optimal shapes of the shells and their thickness distributions have been found analytically.