An Improved Stability Matrix for Co-Rotational Formulation

Abstract

Geometrically nonlinear analysis of 3D framed structures has focused on the treatment of the difficulties associated with finite nodal rotations. The Co-rotational formulation excludes the rigid body rotation of the element, and to account for this aspect the addition of a stability matrix is required to the natural tangent stiffness matrix. This spatial beam element stability matrix needs to fully account for the behaviour of the nodal forces and moments on the rigid body rotation. In the context of the Co-rotational formulation, the correct stability matrix is used in conjunction with the natural tangent stiffness matrix. The natural finite element concept used for the numerical analysis of nonlinear structural problems is extended to the Co-rotational formulation. It is shown through numerical examples that fully account for the rotational behaviour of nodal moments, that the Co-rotational formulation can accurately predict the flexural-torsional buckling loads for spatial structures in which the members are not connected collinearly.