TY - JOUR
T1 - Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements
AU - Vizzaccaro, Alessandra
AU - Givois, Arthur
AU - Longobardi, Pierluigi
AU - Shen, Yichang
AU - Deü, Jean François
AU - Salles, Loïc
AU - Touzé, Cyril
AU - Thomas, Olivier
PY - 2020/12/2
Y1 - 2020/12/2
N2 - 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.
AB - 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.
KW - reduced order modeling
KW - geometric nonlinearities
KW - three-dimensional effect
KW - thickness modes
KW - Modified STiffness Evaluation Procedure
KW - nonlinear modes
KW - modal derivatives
UR - http://www.scopus.com/inward/record.url?scp=85090134255&partnerID=8YFLogxK
U2 - 10.1007/s00466-020-01902-5
DO - 10.1007/s00466-020-01902-5
M3 - Article (Academic Journal)
SN - 0178-7675
VL - 66
SP - 1293
EP - 1319
JO - Computational Mechanics
JF - Computational Mechanics
IS - 6
ER -