arXiv subjects

Paolo Tiso

Publications and source records attributed to Paolo Tiso.

15 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.

math.NA↗

arXiv2026

A scalability benchmark study of model order reduction techniques for very large, strongly coupled vibroacoustic problems

Model Order Reduction (MOR) can significantly reduce the computational cost of vibroacoustic simulations. While most MOR research focuses on single-domain systems (e.g., structural dynamics or computational fluid mechanics), this work compares MOR techniques for large multi-domain problems to identify methods that remain efficient and accurate at very large scales. In particular, harmonic response simulations of vibroacoustic fluid-structure coupled systems used to compute transfer functions from an input force to either structural acceleration or pressure in the heavy fluid domain are of high interest. To achieve this, the most common MOR techniques based on modal methods and Krylov subspace methods are compared for multi-material systems. To assess the feasibility and accuracy of these techniques for different system sizes, a scalable benchmark model of a water-filled Plexiglass cylinder is developed, with mesh sizes from 10,000 to 1,000,000 Degrees of Freedom (DOF). The quality of the models is assured by validation against experimental data. The geometry, model data, and experimental results are made available so that they can be used as a benchmark for further studies. For systems larger than 100,000 DOF, the investigated modal methods become impractical due to memory limitations, even on powerful workstations. Among the tested techniques, a Krylov subspace two-level orthogonal Arnoldi reduction, combined with symmetrization and conditioning of the system matrices, provides the most accurate and efficient approximation of the target transfer functions - particularly for large-scale models up to 1,000,000 DOF. This approach achieves a speedup of up to 600 times compared to the full model.

physics.app-ph↗

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.

math.NA↗

arXiv2025

Matching frequency response measurements and reduced order models for the inverse identification of viscoelastic properties

3D-printed materials are used in many different industries (automotive, aviation, medicine, etc.). Most of these 3D-printed materials are based on ceramics or polymers whose mechanical properties vary with frequency. For numerical modeling, it is crucial to characterize this frequency dependency accurately to enable realistic finite-element simulations. At the same time, the damping behavior plays a key role in product development, since it governs a component's response at resonance and thus impacts both performance and longevity. In current research, inverse material characterization methods are getting more and more popular. However, their practical validation and applicability on real measurement data have not yet been discussed widely. In this work, we show the identification of two different materials, POM and additively manufactured sintered ceramics, and validate it with experimental data of a well-established measurement technique (dynamic mechanical analysis). The material identification process considers state-of-the-art reduced-order modeling and constrained particle swarm optimization, which are used to fit the frequency response functions of point measurements obtained by a laser Doppler vibrometer. This work shows the quality of the method in identifying the parameters defining the viscoelastic fractional derivative model, including their uncertainty. It also illustrates the applicability of this identification method in the presence of practical difficulties that come along with experimental data such as boundary conditions and noise.

physics.app-ph↗

arXiv2025

AquaROM: shape optimization pipeline for soft swimmers using parametric reduced order models

The efficient optimization of actuated soft structures, particularly under complex nonlinear forces, remains a critical challenge in advancing robotics. Simulations of nonlinear structures, such as soft-bodied robots modeled using the finite element method (FEM), often demand substantial computational resources, especially during optimization. To address this challenge, we propose a novel optimization algorithm based on a tensorial parametric reduced order model (PROM). Our algorithm leverages dimensionality reduction and solution approximation techniques to facilitate efficient solving of nonlinear constrained optimization problems. The well-structured tensorial approach enables the use of analytical gradients within a specifically chosen reduced order basis (ROB), significantly enhancing computational efficiency. To showcase the performance of our method, we apply it to optimizing soft robotic swimmer shapes. These actuated soft robots experience hydrodynamic forces, subjecting them to both internal and external nonlinear forces, which are incorporated into our optimization process using a data-free ROB for fast and accurate computations. This approach not only reduces computational complexity but also unlocks new opportunities to optimize complex nonlinear systems in soft robotics, paving the way for more efficient design and control.

cs.RO↗

arXiv2025

Embodying computation in nonlinear perturbative metamaterials

Designing metamaterials that carry out advanced computations poses a significant challenge. A powerful design strategy splits the problem into two steps: First, encoding the desired functionality in a discrete or tight-binding model, and second, identifying a metamaterial geometry that conforms to the model. Applying this approach to information-processing tasks requires accurately mapping nonlinearity -- an essential element for computation -- from discrete models to geometries. Here we formulate this mapping through a nonlinear coordinate transformation that accurately connects tight-binding degrees of freedom to metamaterial excitations in the nonlinear regime. This transformation allows us to design information-processing metamaterials across the broad range of computations that can be expressed as tight-binding models, a capability we showcase with three examples based on three different computing paradigms: a coherent Ising machine that approximates combinatorial optimization problems through energy minimization, a mechanical racetrack memory exemplifying in-memory computing, and a speech classification metamaterial based on analog neuromorphic computing.

cond-mat.mes-hall↗

arXiv2025

Higher-order transmissibility and its linear approximation for in-service crack identification in train wheelset axles

In-service structural health monitoring is a so far rarely exploited, yet potent option for early-stage crack detection and identification in train wheelset axles. This procedure is non-trivial to enforce on the basis of a purely data-driven approach and typically requires the adoption of numerical, e.g. finite element-based, simulation schemes of the dynamic behavior of these axles. Damage in this particular case can be formulated as a breathing crack problem, which further complicates simulation by introducing response-dependent nonlinearities into the picture. In this study, first, a new crack detection feature based on higher-order harmonics of the breathing crack is proposed, termed Higher-Order Transmissibility (HOTr), and, secondly, its sensitivity and efficacy are assessed within the context of crack identification. Next, the mentioned feature is approximated via use of linear system theory, delivering a surrogate model which facilitates the computation and speeds up the crack identification procedure. The accuracy of the proposed method in reproducing the delivered HOTr is compared against the nonlinear simulation model. The obtained results suggest that the approximation of the HOTr can significantly reduce the computational burden by eliminating the need for an iterative solution of the governing nonlinear equation of motion, while maintaining a high level of accuracy when compared against the reference model. This implies great potential for adoption in in-service damage identification for wheelset axles, feasibly within a near real-time context.

cs.CE↗

arXiv2024

Data-Driven Reduction of the Finite-Element Model of a Tribomechadynamics Benchmark Problem

Bolted joints can exhibit nonsmooth and significantly nonlinear dynamics. Finite Element Models (FEMs) of this phenomenon require fine spatial discretizations, inclusion of nonlinear contact and friction laws, as well as geometric nonlinearity. Owing to the nonlinearity and high dimensionality of such models, full-order dynamic simulations are computationally expensive. In this work, we use the theory of Spectral Submanifolds (SSMs) to construct a data-driven, smoothed reduced model for a 187,920-dimensional FEM model of a broadly studied Tribomechadynamics benchmark structure with bolted joints. We train the 4-dimensional reduced model using only a few transient trajectories of the full unforced FEM model. We show that this smooth model accurately predicts the experimentally observed nonlinear forced response of the full nonsmooth benchmark problem.

math.DS↗

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.

math.NA↗

arXiv2022

A Reduced Order Model for Joint Assemblies by Hyper-Reduction and Model-Driven Sampling

The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models (HFMs) of the contact interfaces are required. However, the high computational cost of such HFMs impedes the feasibility of the simulations. To this end, we propose a model-driven method for constructing hyper-reduced order models of such assemblies. Focusing on steady-state analysis, we use the Multi-Harmonic Balance Method (MHBM) to formulate the equations of motion in frequency domain. The reduction basis is constructed through solving a set of vibration problems corresponding to fictitious interface conditions. Subsequently, a Galerkin projection reduces the order of the model. Nonetheless, the necessary fine discretization of the interfaces represents a bottleneck for achieving high speedups. For this reason, we implement an adapted Energy Conserving Weighing and Sampling (ECSW) technique for Hyper Reduction (HR), thereby allowing significant speedups for meshes of arbitrary fineness. This feature is particularly advantageous since analysts typically encounter a trade-off between accuracy and computational cost when deciding on the mesh size, whose estimation is particularly challenging for problems of this type. To assess the accuracy of our method without resorting to the HF solution, we propose an error indicator with thresholds that have proven reliable in our analyses. Finally, the accuracy and efficiency of the method are demonstrated by two case studies.

cs.CE↗

arXiv2021

An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion

We present an enhanced version of the parametric nonlinear reduced order model for shape imperfections in structural dynamics we studied in a previous work [1]. The model is computed intrusively and with no training using information about the nominal geometry of the structure and some user-defined displacement fields representing shape defects, i.e. small deviations from the nominal geometry parametrized by their respective amplitudes. The linear superposition of these artificial displacements describe the defected geometry and can be embedded in the strain formulation in such a way that, in the end, nonlinear internal elastic forces can be expressed as a polynomial function of both these defect fields and the actual displacement field. This way, a tensorial representation of the internal forces can be obtained and, owning the reduction in size of the model given by a Galerkin projection, high simulation speed-ups can be achieved. We show that by adopting a rigorous deformation framework we are able to achieve better accuracy as compared to the previous work. In particular, exploiting Neumann expansion in the definition of the Green-Lagrange strain tensor, we show that our previous model is a lower order approximation with respect to the one we present now. Two numerical examples of a clamped beam and a MEMS gyroscope finally demonstrate the benefits of the method in terms of speed and increased accuracy.

cs.CE↗

arXiv2019

Model Order Reduction for Temperature-Dependent Nonlinear Mechanical Systems: A Multiple Scales Approach

The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a slowly-varying temperature distribution in a systematic manner. In the process, we construct a reduction basis that adapts according to the instantaneous temperature distribution of the structure, facilitating an efficient reduction in the number of unknown. As a proof of concept, we demonstrate the method on a range of linear and nonlinear beam examples and obtain a consistently better accuracy and reduction in the number of unknowns than standard the Galerkin projection using a constant basis.

cs.CE↗

arXiv2019

Hyper-reduction over nonlinear manifolds for large nonlinear mechanical systems

Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed by Galerkin projection of the governing equations onto a constant reduction basis. Though this reduces the number of unknowns in the system, the computational cost for obtaining the solution could still be high due to the prohibitive computational costs involved in the evaluation of nonlinear terms. Hyper-reduction methods are then seen as a fast way of approximating the nonlinearity in the system of equations. In the finite element context, the energy conserving sampling and weighing (ECSW) method has emerged as a stability and structure-preserving method for hyper-reduction. Classical hyper-reduction techniques, however, are applicable only in the context of linear mappings into the reduction subspace. In this work, we extend the concept of hyper-reduction using ECSW to general nonlinear mappings, while retaining its desirable stability and structure-preserving properties. As a proof of concept, the proposed hyper-reduction technique is demonstrated over models of a flat plate and a realistic wing structure, whose dynamics has been shown to evolve over a nonlinear (quadratic) manifold. An online speed-up of over one thousand times relative to the full system has been obtained for the wing structure using the proposed method, which is higher than its linear counterpart using the ECSW.

cs.CE↗

arXiv2017

Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifolds

We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a linear modal subspace, is then used to further reduce the beam equations within the slow manifold. This two-stage, mathematically exact procedure results in a drastic reduction of the finite-element beam model to a one-degree-of freedom nonlinear oscillator. We also introduce the technique of spectral quotient analysis, which gives the number of modes relevant for reduction as output rather than input to the reduction process.

math.DS↗

arXiv2017

A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics

This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and its curvature is provided by modal derivatives obtained by sensitivity analysis of the eigenvalue problem, or its static approximation, along the vibration modes. The construction of the quadratic manifold requires minimal computational effort once the vibration modes are known. The reduced order model is then obtained by Galerkin projection, where the configuration-dependent tangent space of the manifold is used to project the discretized equations of motion.

cs.CE↗