Introducing geometric degree of freedom in structural stability

A geometric degree of freedom, GDOF, is introduced as a means of reducing the size of the problem of structural stability of large multiple DOF frames. GDOFs will be defined as DOFs that are associated with nodes that are associated with members that carry axial loads. It has been shown that the structural stability of frames with a large number of DOF can be reduced to a much smaller size and can be expressed in terms of these declared GDOFs only. These GDOFs may be viewed as analogous to the dynamic DOFs in structural dynamics and carry all the benefits that are associated with them. It has been proven that the behavior of the structure in structural stability using only GDOFs is identical to the behavior of the structural stability using the entire DOFs of the original structure. It has also been shown that the effective basic buckling loads will be equal to the number of GDOFs. The buckling modes higher than the effective basic modes are shown to be too large in order of magnitude to take place, and hence, it would be a waste of resources to obtain them.