Paolo Tiso

Last Name

Tiso

First Name

Paolo

ORCID

0000-0002-8373-9286

Organisational unit

03973 - Haller, George / Haller, George

Show all metadata

Search Results

Publications 1 - 10 of 41

A non-intrusive model-order reduction of geometrically nonlinear structural dynamics using modal derivatives
Karamooz Mahdiabadi, Morteza; Tiso, Paolo; Brandt, Antoine; et al. (2021)
Mechanical Systems and Signal Processing
Non-intrusive model-order reduction methods are beneficial for reducing the computational costs of dynamic analysis of nonlinear finite element models, developed in programs that do not release nonlinear element forces and Jacobians (e.g., commercial software). One of the key aspects for developing a displacement-based non-intrusive reduced order model is a proper construction of the reduction basis, which has to be small in size, easy to compute, and must span the subspace in which the full solution lives. In this paper, we propose a non-intrusive model order reduction method based on modal derivatives stemming from a selected set of vibration modes of the linearized system. By definition, modal derivatives do not require the knowledge of the applied load. We name this load-independent basis. The method we propose is also simulation-free, meaning that no nonlinear dynamic simulations of the full model are required to construct the reduction basis. The method is tested with three examples of increasing complexity.
4 Modal methods for reduced order modeling
Tiso, Paolo; Karamooz Mahdiabadi, Morteza; Marconi, Jacopo (2021)
Model Order Reduction: Volume 1: System- and Data-Driven Methods and Algorithms
In this chapter, we present an overview of the so-called modal methods for reduced order modeling. The naming is loosely referring to techniques that aim at constructing the reduced order basis for reduction without resorting to data, typically obtained by full order simulations. We focus primarily on linear and nonlinear mechanical systems stemming from a finite element discretization of the underlying strong form equations. The nonlinearity is of a geometric nature, i. e. due to redirection of internal stresses due to large displacements. Intrusive vs non-intrusive techniques (i. e. requiring or not access to the finite element formulation to construct the reduced order model) are discussed, and an overview of the most popular methods is presented.
Numerical computation of nonlinear normal modes in a modal derivative subspace
Sombroek, Cees S.M.; Tiso, Paolo; Renson, Ludovic; et al. (2018)
Computers & Structures
Nonlinear normal modes offer a solid theoretical framework for interpreting a wide class of nonlinear dynamic phenomena. However, their computation for large-scale models can be time consuming, particularly when nonlinearities are distributed across the degrees of freedom. In this paper, the nonlinear normal modes of systems featuring distributed geometric nonlinearities are computed from reduced-order models comprising linear normal modes and modal derivatives. Modal derivatives stem from the differentiation of the eigenvalue problem associated with the underlying linearised vibrations and can therefore account for some of the distortions introduced by nonlinearity. The cases of the Roorda’s frame model, a doubly-clamped beam, and a shallow arch discretised with planar beam finite elements are investigated. A comparison between the nonlinear normal modes computed from the full and reduced-order models highlights the capability of the reduction method to capture the essential nonlinear phenomena, including low-order modal interactions.
Exact nonlinear model reduction for a von Karman beam: Slow-fast decomposition and spectral submanifolds
Jain, Shobhit; Tiso, Paolo; Haller, George (2018)
Journal of Sound and Vibration
We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Kármán 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.
A consistency analysis of phase-locked-loop testing and control-based continuation for a geometrically nonlinear frictional system
Abeloos, Gaëtan; Müller, Florian; Ferhatoglu, Erhan; et al. (2022)
Mechanical Systems and Signal Processing
Two of the most popular vibration testing methods for nonlinear structures are control-based continuation and phase-locked-loop testing. In this paper, they are directly compared on the same benchmark system, for the first time, to demonstrate their general capabilities and to discuss practical implementation aspects. The considered system, which is specifically designed for this study, is a slightly arched beam clamped at both ends via bolted joints. It exhibits a pronounced softening–hardening behavior as well as an increasing damping characteristic due to the frictional clamping. Both methods are implemented to identify periodic responses at steady-state constituting the phase-resonant backbone curve and nonlinear frequency response curves. To ensure coherent results, the repetition variability is thoroughly assessed via an uncertainty analysis. It is concluded that the methods are in excellent agreement, taking into account the inherent repetition variability of the system.
A higher-order parametric nonlinear reduced-order model for imperfect structures using Neumann expansion
Marconi, Jacopo; Tiso, Paolo; Quadrelli, Davide E.; et al. (2021)
Nonlinear Dynamics
We present an enhanced version of the parametric nonlinear reduced-order model for shape imperfections in structural dynamics we studied in a previous work. In this model, the total displacement is split between the one due to the presence of a shape defect and the one due to the motion of the structure. This allows to expand the two fields independently using different bases. The defected geometry is described by some user-defined displacement fields which can be embedded in the strain formulation. This way, a polynomial function of both the defect field and actual displacement field provides the nonlinear internal elastic forces. The latter can be thus expressed using tensors, and owning the reduction in size of the model given by a Galerkin projection, high simulation speedups can be achieved. We show that the adopted deformation framework, exploiting Neumann expansion in the definition of the strains, leads to better accuracy as compared to the previous work. 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.
Predicting the variability of the dynamics of bolted joints using polynomial chaos expansion
Morsy, Ahmed Amr; Tiso, Paolo (2025)
Mechanical Systems and Signal Processing
Friction and contact occurring in bolted joints can lead to highly nonlinear dynamics. Moreover, joints are prone to high sample-to-sample variability as well as low test-to-test repeatability. Notably, experimental work is increasingly highlighting the most influential sources of uncertainties. Nevertheless, randomness due to some uncertainties, such as surface imperfections, cannot be completely eliminated. Others, such as the actual applied bolt load, can be laborious to control. In this work, we aim to computationally predict the variability of numerical models of joints given such uncertainties. We perform the dynamic analysis using the Multi-Harmonic Balance Method (MHBM) to compute the forced, periodic response of the system. For probabilistic surrogate modeling, we use Polynomial Chaos Expansion (PCE). We show that PCE can be successful in studying the impact of ISO tolerances and uncertain bolt loads in the practical case where only a few numerical samples can be generated. We also show that an empirical error metric is unreliable and a validation error metric must be used. In addition, we assess using PCE to propagate uncertainties due to mesoscale imperfections, and highlight that unsuccessful PCE models indicate sensitive structural designs.
Data-Driven reduction of the finite-element model of a Tribomechadynamics benchmark problem
Morsy, Ahmed Amr; Xu, Zhenwei; Tiso, Paolo; et al. (2025)
Nonlinear Dynamics
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.
AquaROM: shape optimization pipeline for soft swimmers using parametric reduced order models
Dubied, Mathieu; Tiso, Paolo; Katzschmann, Robert K. (2025)
arXiv
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.
Accelerating Construction of Nonintrusive Nonlinear Structural Dynamics Reduced-Order Models Through Hyperreduction
Saccani, Alexander; Tiso, Paolo (2025)
AIAA Journal
We present a novel technique to reduce the offline cost associated with nonintrusive nonlinear tensor identification in reduced-order models of geometrically nonlinear, finite-element-discretized structural dynamics problems. The reduced-order model is obtained by Galerkin projection of the governing equations on a reduction basis of vibration modes and static modal derivatives, resulting in reduced internal forces that are cubic polynomials in the reduced coordinates. The unknown coefficients of the nonlinear tensors associated with this polynomial representation are identified using a modified version of the enhanced enforced displacement (EED) method that leverages energy-conserving sampling and weighting (ECSW) as a hyperreduction technique for efficiency improvement. Specifically, ECSW is employed to accelerate the evaluations of the 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 benefits the investigation of the dynamic response of structures subjected to acoustic loading, where multiple vibration modes must be added in the reduction basis, resulting in expensive tensor identification. The superiority of the novel method over standard EED is demonstrated on finite element models of a curved panel and of an aeronautical panel.

Publications 1 - 10 of 41

Paolo Tiso

Last Name

First Name

ORCID

Organisational unit

Filters

Search Results