Numerical solution to pneumatic forming problems of axisymmetric superplastic thin shells

A numerical method is presented for analysis of the pneumatic forming process of axisymmetric superplastic thin shells. The governing non-linear partial differential equations are derived from membrane shell theory, using total Lagrangian description and considering a hardening creep material model. The method of lines used in the computational algorithm, involves two steps: first the Cauchy problem in time is considered, then the boundary problem is solved by finite differences. The effectiveness of the proposed algorithm is illustrated by several examples.