Conceptual issues in geometrically nonlinear analysis of 3D framed structures Original Research Article

This paper aims to clarify some of the conceptual issues which are related to the geometrically nonlinear analysis of 3D framed structures, and which have been a source of previous confusion. In particular, the paper discusses the symmetry of the tangent stiffness matrix and the nature of the element end moments. It is shown that a symmetric tangent stiffness matrix can always be achieved for a conservative system if the nodal equilibrium equations, including the equations which describe moment equilibrium, are identical to those derived from a variational energy approach. With regard to the element end moments, it is suggested that any definition can be adopted in formulating the geometrically nonlinear element response. Furthermore, it is proposed that any definition for nodal rotations expressing a unique vector transformation may be adopted without compromising modelling accuracy. The argument of this paper is validated with reference to three variants of a large displacement analysis method for 3D frames, where several illustrative examples are utilised.