Incrementally small-deformation theory for nonlinear analysis of structural frames

An incrementally small-deformation theory that is physically self-explainable is presented for the large-displacement nonlinear analysis of structural frames. Strictly based on the assumption of small strains, small rotations, and small displacements within each incremental step, the elastic and geometric stiffness matrices for the beam element are derived from the force–displacement relations. Due consideration is taken of the 3D rotational behavior of nodal moments. The geometric stiffness matrix derived for the element is asymmetric. However, by enforcing all the joints to remain in equilibrium in the deformed configuration, the antisymmetric parts of the geometric stiffness matrices cancel out, resulting in a symmetric stiffness matrix for the structure. Also described is the procedure for updating the element forces and geometry in an incremental-iterative analysis. The present approach in its entire set is demonstrated to be robust and efficient for solving the nonlinear, postbuckling response of structural frames.