Finite element analysis of buckling of structures at special prebuckling states

The consistently linearized eigenproblem is used to derive mathematical conditions in the frame of the Finite Element Method (FEM) for loss of static stability of elastic structures at prebuckling states characterized by a constant percentage bending energy of the strain energy in the prebuckling regime. Special cases of such prebuckling states are membrane stress states and pure bending. Buckling from a membrane stress state as a special case within sensitivity analysis of buckling at a constant non-zero percentage bending energy in the prebuckling regime is one of two examples serving the purpose to verify the existence of hitherto unknown subsidiary conditions of buckling in the context of the FEM.