Miscellaneous Efficient formulation for nonlinear dynamics of steel frames

Abstract

Crisfield et al. used the constant Timoshenko mass matrix, although they used local cubic interpolations to derive the elastic force vector and tangent stiffness matrix. The same approach was adopted in (Iura, M. & Atluri, S.N. 1995). In (Masuda, N. 1987; Oran, C. & Kassimli, A. 1976; Xue, Q; & Meek, J.L. 2001), the authors used a constant lumped mass matrix without any attempt to check its accuracy. In (Behdinan, K. et al., 1998), Behdinan et al. proposed a corotational dynamic formulation. However, the cubic shape functions were used to describe the global displacements, which is not consistent with the idea of the corotational method.