Nonlinear Modal Condensation of Large Finite Element Models: Application of Hodges’s Intrinsic Theory

Abstract

A method to obtain geometrically nonlinear reduced-order descriptions of structures defined by a large finite element model is presented. The full model is used to identify all the coefficients in a modal projection of Hodges’s intrinsic beam equations, with the geometric reduction introduced through static or dynamic condensation along the main load paths on the original structure. The only information retrieved from the full model is the linear normal modes as well as condensed mass and stiffness and nodal coordinates. The approach aims to solve geometrically nonlinear problems of industrial complexity in an efficient manner, while preserving the linear model under small displacements. Examples of increasing complexity will be shown with the built-up finite element models made with beams and shells and both lumped and distributed masses. Nonlinear static and dynamic analyses, including rigid-body dynamics, are then demonstrated using the resulting nonlinear modal description.