Numerical solution to pneumatic forming problems of axisymmetric superplastic thin shells

Abstract

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.