Session: 02-04-01: Computer Methods and Reduced Order Modeling

Paper Number: 152315

152315 - Substructuring of Non-Intrusive Nonlinear Reduced-Order Models With
Thickness-Varying Constraint Modes 

Non-intrusive nonlinear reduced-order models (NLROMs) have been used extensively over the past two decades to predict the dynamic response of thin structures. However, limited research exists on the inclusion of over-the-thickness modes to capture the full-field response of structures modeled with continuum finite elements. In this research, longitudinal over-the-thickness modes are included in the modal basis of a deep beam modeled using plane elasticity elements, and the restoring force function is identified non-intrusively using a displacement-based procedure. The resulting NLROM is used as a substructure and coupled to an adjacent beam finite element (FE) model along the cross section described by the over-the-thickness modes. The FE subdomain uses full-order nodal displacement degrees-of-freedom (DOFs), while the nodal displacements of the NLROM subdomain are expressed as an expansion of modal variables.

The Craig-Bampton (CB) method of substructuring has been used to couple NLROMs by including characteristic constraint modes (CCMs) to describe the rotations and displacements of the interface between two substructures. The NLROM in this study captures the longitudinal displacements on the interface using the over-the-thickness constraint modes, and the transverse displacements on the interface are computed as a nonlinear expansion of the modal variables. The coefficients of the nonlinear expansion function are identified using a least-squares procedure with the displacement data available from the non-intrusive identification test cases, similar to the approach used in the implicit condensation and expansion (ICE) method.

The displacement and stress results obtained from the substructured model closely align with those from the truth model under uniform loading at the beam midline. The maximum errors in the transverse and axial displacements are less than 0.3% and 0.03%, respectively, compared to the corresponding maximum displacements in the beam. The maximum error in the bending stress is 0.094%, and the maximum error in the shear stress is 2.4%. The NLROM achieves a 90% reduction in the number of degrees-of-freedom when compared to the original finite element model in the NLROM subdomain.

Presenting Author: Jordan Seawright Simpson Gumpertz & Heger

Presenting Author Biography: Jordan received his PhD in Civil Engineering from the University of Washington, where he conducted research on non-intrusive nonlinear reduced order models of geometrically nonlinear structures. He now works at Simpson Gumpertz & Heger (SGH) with a focus on the analysis and design of nuclear facilities.