Plastic Instability Pressure of Conical Shells

There several failure modes that are considered in the available codes and standards in field of pressure vessel and piping. One of these failure modes is plastic instability. This failure mode is defined as the pressure for which the components/structures approach dimensional instability (large deformation), i.e. unbounded displacement for a small increment in the applied load. In order to find this pressure both large deformation and strain hardening curve are considered. When the slope of numerically generated load-deformation curve approaching zero the corresponding applied load is considered as plastic instability load. Unlike cylindrical and spherical pressure vessels, available theoretical solution in range of plastic instability load for conical shells are very limited. Hence, it would be very useful to predict the behavior of these components with acceptable accuracy for design purposes. Analytical expressions are derived to determined plastic instability load of s conical shell subjected to internal pressure and when it is subjected to hydrostatic pressure (i.e., storage tanks). The geometrical changes can be estimated using the proposed solutions when considering the material strain hardening curve.