Limit and shakedown analysis of 3D steel frames via approximate ellipsoidal yield surfaces

This work concerns finite element limit and shakedown analysis of spatial steel frames under nonlinear yield criteria of steel sections. Inner and outer ellipsoidal approximations to the plastic interaction yield surfaces are systematically constructed. Under ellipsoidal yield criteria, the arising computational optimization problem becomes a second-order cone programming problem, for which free and commercial software packages are available, capable of treating large-scale problems. The present study is focused on approximations to the nonlinear plastic interaction provisions of Eurocode 3. Moreover, a well-known criterion due to Orbison is considered. Examples of limit and shakedown analysis of spatial frames under the aforementioned ellipsoidal approximations are presented and several aspects are discussed. For comparison, a fairly general interior point algorithm is also successfully applied to the limit and shakedown analysis under the original, non-ellipsoidal form of the Orbison criterion.