Optimal shape design of axisymmetric shells for crack initiation and propagation under cyclic loading

This paper describes a problem of axisymmetric shell optimization under fracture mechanics and geometric constraints. The problem is formulated as the weight ( volume of a shell material) minimization and the meridional contour of the shell is taken as the design variable. The shell is made from quasi-brittle materials and through cracks arising are 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 the Paris fatigue law. The problem of. finding the meridian shape ( geometric design variable), of the shell having the smallest mass subject to constraint on the cyclic number for fatigue cracks, is investigated using a minimax ( guaranteed) approach worked out in the theory of optimization under incomplete information. Optimal designs of the shells are found numerically with the application of genetic algorithms.