A continuum-based mixed shell element for shakedown analysis

• A new CB mixed finite element is devised for limit and shakedown analysis of shells.
• The use of generalized stresses in shakedown formulation is avoided with the element.
• We focus on the ability of the element to provide accurate critical load domains.
• Numerical tests confirm the accuracy and convergence of the element.

The objective of this paper is to present a new triangular shell element for shakedown analysis. The element is based on a mixed variational formulation with displacement/velocity and stress fields independently interpolated. We also employ the continuum based (CB) approach which allows the definition of the yield function at the continuum level without any approximation in terms of generalized stresses. The formulation of the proposed element is presented in details after a brief review of relevant classical shakedown theory concepts. The performance of the element is assessed by means of a set of selected representative examples. The numerical tests include: (i) analyses of thin and thick-walled straight pipes under combined loads, (ii) the shakedown analysis of a pipe bend under internal pressure and in-plane bending and (iii) limit analysis of a cylinder–cylinder intersection subjected to bending and internal pressure.