Mistakes and paradoxes in solutions of spatial, geometrically nonlinear problems and equilibrium stability problems
The object of consideration comprises geometrically nonlinear (second-order) problems and equilibrium stability problems for spatial bar structures. Unlike that in planar problems, the matrix of geometric stiffness for particular bars here depends both on the longitudinal forces and the distribution of the bending and torsion moments. Besides that, a traditional point of view becomes erroneous: that the components of an ordinary moment vector can be used as generalized forces that correspond to the slope components in the structure’s nodes.
*Anatoly Perelmuter, Vladimir Slivker