A reduced order model for nonlinear time history seismic analyzes of elasto-plastic 3D frame structures

A reduced order model for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame structures is presented. It is based on an approximated solution space for the displacement field that is assumed as the sum of two subspaces. The first subspace is generated by the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue problem in terms of participation factor. The second one is defined by collapse mechanisms associated to appropriate static load distributions. The time history analyzes are carried out within the reduced solution space, while the internal forces are evaluated on the full model to guarantee an accurate description of the constitutive laws. The proposed reduction method was tested for different structural geometries varying frequency content, direction and amplitude of the ground motion. Numerical results show accuracy and robustness also employing a few tens of modes, including elastic modes and plastic collapse mechanisms. In particular, the need for plastic modes in capturing the structural dynamics in case of seismic actions leading to significant plastic excursions is emphasized. This highlights the limits of simplified approaches based on the hypothesis of shape conservation in nonlinear problems, regardless of the building regularity.