Probabilistic-Guaranteed Optimal Design of Membrane Shells Against Quasi-brittle Fracture

摘要

The problems described in this article concern the shape optimization of brittle or quasi-brittle (axisymmetric) elastic shells. The optimization problem takes into consideration the possibilities of cracks arising and consists in finding the shape of the shell loaded by external forces in such a way that the cost function (volume of the shell material) reaches a minimum, while satisfying some prescribed bounds on stress intensity factors. The questions discussed are characterized by incomplete information concerning crack size, crack location, and its orientation. In this context, the article presents some formulations of optimal shell design problems based on probabilistic-guaranteed approach and provides some results of analytical investigation for thin-walled shells with a through cracks.