Geometrically Nonlinear Structural Modal Analysis Using Fictitious Masses

In this paper, a new method to obtain a geometrically nonlinear structural dynamics model based on the full linear finite element model of slender structures is presented. For this purpose, a finite element model is divided into multiple segments along its span. For each segment, a modal analysis is carried out. Boundary grid points are defined on each segment and loaded by fictitious masses. The modal analysis produces a set of elastic modes and six rigid-body modes that have significant deformations near the boundary. These deformations facilitate high-accuracy integration of the segments into a coupled model, in which the fictitious masses are removed. The elastic modes are used as master modes that describe the deformation, whereas the rigid-body modes are used as slave modes to establish displacement compatibility between the segments. The modal analysis is carried out with the local segment attached to its own reference frame, yielding a local linear solution that is part of a global nonlinear analysis. Large rotations and displacements are provided by the rigid-body modes in a corotational framework.