Optimization of mass effectiveness of axisymmetric pressure vessels

The optimization problems taken into consideration in this paper consist in finding the shape and the thickness distribution of elastic axisymmetric shells in the frame of membrane theory, loaded by fixed statical forces in such a way that the cost functional reaches a maximum, while satisfying some strength mechanics constraints. In this paper the mass effectiveness of the shell is considered as a cost function and as constraint we use the bounds on the maximum normal stress which is typical for shells made from brittle or quasi-brittle materials. The paper gives some possible formulations of optimal structural design problems. Analytical investigations and corresponding solutions are presented.