Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements

TL;DR

This paper improves non-intrusive reduced-order modeling of geometrically nonlinear flat structures by addressing slow convergence issues in 3D finite element applications, introducing efficient methods like static modal derivatives and a modified STEP.

Contribution

It demonstrates that static modal derivatives and a modified STEP method enhance convergence and computational efficiency in non-intrusive reduced-order modeling of nonlinear flat structures.

Findings

Static modal derivatives achieve the same accuracy with fewer calculations.

A modified STEP method improves convergence by applying prescribed displacements selectively.

Convergence issues in 3D elements are linked to high-frequency mode couplings.

Abstract

Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory. We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.