arXiv subjects

Alexander Saccani

Publications and source records attributed to Alexander Saccani.

3 recordsLinked to original sources

arXiv2026

Craig-Bampton-based Quadratic Manifold for Nonlinear Substructuring

Component Mode Synthesis methods, such as the Craig-Bampton (CB) approach, are widely used in structural dynamics due to their modularity and compatibility with substructuring workflows. While highly effective for linear systems, extending these methods to geometrically nonlinear structures remains a significant challenge. In this work, we propose a nonlinear extension of the CB method tailored to such contexts. The approach is based on the construction of a quadratic reduction manifold, derived via perturbation analysis, in which high-frequency fixed-interface modes are statically condensed onto a reduced set of low-frequency modes and interface coordinates. This formulation enables the representation of geometric nonlinear effects without increasing the number of reduced degrees of freedom.The resulting Nonlinear Craig-Bampton (NL-CB) reduced-order model is obtained through Galerkin projection onto the tangent space of the manifold and admits a polynomial structure that is efficient for time integration. The formulation preserves the Lagrangian structure of the underlying finite element model, ensuring consistent energetic behavior and numerical stability.The proposed method is demonstrated on representative nonlinear structural systems of increasing complexity. The results show that the NL-CB model captures the essential nonlinear dynamic response while retaining the modularity and computational efficiency of classical substructuring approaches.

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arXiv2025

Non-Intrusive Data-Free Parametric Reduced Order Model for Geometrically Nonlinear Structures

We present a fully non-intrusive parametric reduced-order modeling (PROM) framework for geometrically nonlinear structures subject to geometric variations. The method builds upon equation-driven Galerkin ROMs constructed from vibration modes and modal-derivative companion vectors, while nonlinear reduced tensors are identified from standard finite element outputs. A database of such ROMs is generated over a set of training samples, and all reduced operators-including the linear stiffness matrix, the quadratic and cubic nonlinear tensors, the Rayleigh damping parameters, and the reduction basis-are interpolated using Radial Basis Functions (RBFs). A global reduced basis is obtained through a two-level POD compression, combined with a MAC-guided reordering strategy to ensure parametric smoothness. The resulting PROM preserves the symmetry and polynomial structure of the reduced equations, enabling robust and efficient adaptation to new parameter values. Analytical parameter sensitivities follow directly from the interpolation model. The approach is demonstrated on a parametrically curved panel and a wing-box with geometric variations, showing excellent agreement with high-fidelity simulations and enabling substantial reductions in computational cost for parametric analyses.

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arXiv2024

Accelerating Construction of Non-Intrusive Nonlinear Structural Dynamics Reduced Order Models through Hyperreduction

We present a novel technique to significantly reduce the offline cost associated to non-intrusive nonlinear tensors identification in reduced order models (ROMs) of geometrically nonlinear, finite elements (FE)-discretized structural dynamics problems. The ROM is obtained by Galerkin-projection of the governing equations on a reduction basis (RB) of Vibration Modes (VMs) and Static Modal Derivatives (SMDs), resulting in reduced internal forces that are cubic polynomial in the reduced coordinates. The unknown coefficients of the nonlinear tensors associated with this polynomial representation are identified using a modified version of Enhanced Enforced Displacement (EED) method which leverages Energy Conserving Sampling and Weighting (ECSW) as hyperreduction technique for efficiency improvement. Specifically, ECSW is employed to accelerate the evaluations of the nonlinear reduced tangent stiffness matrix that are required within EED. Simulation-free training sets of forces for ECSW are obtained from displacements corresponding to quasi-random samples of a nonlinear second order static displacement manifold. The proposed approach is beneficial for the investigation of the dynamic response of structures subjected to acoustic loading, where multiple VMs must be added in the RB, resulting in expensive nonlinear tensor identification. Superiority of the novel method over standard EED is demonstrated on FE models of a shallow curved clamped panel and of a nine-bay aeronautical reinforced panel modelled, using the commercial finite element program Abaqus.

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