Ultimate load theorems for rigid plastic solids with internal degrees of freedom and their application in continual lattice shells

• Ultimate load theorems are extended to solids with internal degrees of freedom.
• Ultimate load theorems are used for shells with shape memory hinges.
• The behavior of the rigid plastic rotating shells is analyzed.

This paper studies solids with internal degrees of freedom using the method of Cartan moving hedron. Strain compatibility conditions are derived in the form of structure equations for manifolds. Constitutive relations are reviewed and ultimate load theorems are proved for rigid plastic solids with internal degrees of freedom. It is demonstrated how the above theorems can be applied in behavior analysis of rigid plastic continual shells of shape memory materials. The ultimate loads are estimated for rotating shells under external forces and in case of shape recovery from heating.