Considerations for Indirect Parameter Estimation in Nonlinear Reduced Order Models

Abstract

Over the past few decades, there have been many developments in techniques that extract a reduced order model (ROM) from a geometrically nonlinear finite element model. The enforced displacement ROM strategy that is of interest in this work is known as an indirect approach because it does not require altering the finite element code. Instead, one uses a series of static displacement fields applied to the nonlinear finite element model to estimate the nonlinear stiffness coefficients in the reduced equations. Geometric nonlinearity causes the bending and membrane displacements to become coupled, and the enforced displacements method requires that the kinematics of the membrane motion be explicitly included in the basis using either axial vibration modes or dual modes. This work explores the accuracy of the enforced displacements ROM strategy by comparing the efficiency of these basis vectors, as well as the use of three different parameter estimation procedures and the effect of scaling factors on the static load cases used to generate the ROM. The different modeling decisions are shown to have a very significant effect on the accuracy of the ROMs, and the comparisons are used to suggest best practices that result in the most accurate ROMs. These issues are explored using finite element models of a flat geometrically nonlinear beam with fixed-fixed boundary conditions and a flat geometrically nonlinear exhaust cover plate. The effect of each of the modeling decisions on the resulting enforced displacement ROM is evaluated by computing the Nonlinear Normal Modes (NNMs) of the full finite element model and comparing them with the NNMs calculated from the ROMs. The NNMs offer a powerful metric that indicates whether or not the ROM captures a variety of important physics in the original model.