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  1. Book ; Online: Reduced order models for the buckling of hyperelastic beams

    Pichi, Federico / Rozza, Gianluigi

    2023  

    Abstract: In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications on their design ...

    Abstract In this paper, we discuss reduced order modelling approaches to bifurcating systems arising from continuum mechanics benchmarks. The investigation of the beam's deflection is a relevant topic of investigation with fundamental implications on their design for structural analysis and health. When the beams are exposed to external forces, their equilibrium state can undergo to a sudden variation. This happens when a compression, acting along the axial boundaries, exceeds a certain critical value. Linear elasticity models are not complex enough to capture the so-called beam's buckling, and nonlinear constitutive relations, as the hyperelastic laws, are required to investigate this behavior, whose mathematical counterpart is represented by bifurcating phenomena. The numerical analysis of the bifurcating modes and the post-buckling behavior, is usually unaffordable by means of standard high-fidelity techniques such (as the Finite Element method) and the efficiency of Reduced Order Models (ROMs), e.g.\ based on Proper Orthogonal Decomposition (POD), are necessary to obtain consistent speed-up in the reconstruction of the bifurcation diagram. The aim of this work is to provide insights regarding the application of POD-based ROMs for buckling phenomena occurring for 2-D and 3-D beams governed by different constitutive relations. The benchmarks will involve multi-parametric settings with geometrically parametrized domains, where the buckling's location depends on the material and geometrical properties induced by the parameter. Finally, we exploit the acquired notions from these toy problems, to simulate a real case scenario coming from the Norwegian petroleum industry.
    Keywords Mathematics - Numerical Analysis
    Subject code 621
    Publishing date 2023-05-31
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  2. Article: Model order reduction for bifurcating phenomena in fluid-structure interaction problems.

    Khamlich, Moaad / Pichi, Federico / Rozza, Gianluigi

    International journal for numerical methods in fluids

    2022  Volume 94, Issue 10, Page(s) 1611–1640

    Abstract: This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid- ... ...

    Abstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.
    Language English
    Publishing date 2022-06-04
    Publishing country England
    Document type Journal Article
    ZDB-ID 1491176-0
    ISSN 1097-0363 ; 0271-2091
    ISSN (online) 1097-0363
    ISSN 0271-2091
    DOI 10.1002/fld.5118
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  3. Book ; Online: A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

    Pichi, Federico / Moya, Beatriz / Hesthaven, Jan S.

    2023  

    Abstract: The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations of parametric ...

    Abstract The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real-time and many-query evaluations of parametric Partial Differential Equations (PDEs). Linear techniques such as Proper Orthogonal Decomposition (POD) and Greedy algorithms have been analyzed thoroughly, but they are more suitable when dealing with linear and affine models showing a fast decay of the Kolmogorov n-width. On one hand, the autoencoder architecture represents a nonlinear generalization of the POD compression procedure, allowing one to encode the main information in a latent set of variables while extracting their main features. On the other hand, Graph Neural Networks (GNNs) constitute a natural framework for studying PDE solutions defined on unstructured meshes. Here, we develop a non-intrusive and data-driven nonlinear reduction approach, exploiting GNNs to encode the reduced manifold and enable fast evaluations of parametrized PDEs. We show the capabilities of the methodology for several models: linear/nonlinear and scalar/vector problems with fast/slow decay in the physically and geometrically parametrized setting. The main properties of our approach consist of (i) high generalizability in the low-data regime even for complex regimes, (ii) physical compliance with general unstructured grids, and (iii) exploitation of pooling and un-pooling operations to learn from scattered data.

    Comment: https://github.com/fpichi/gca-rom
    Keywords Mathematics - Numerical Analysis ; Computer Science - Machine Learning ; 65M22 ; 65M60 ; 68T07
    Subject code 006
    Publishing date 2023-05-15
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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  4. Book ; Online: An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

    Pichi, Federico / Ballarin, Francesco / Rozza, Gianluigi / Hesthaven, Jan S.

    2021  

    Abstract: This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, ... ...

    Abstract This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we study the Navier-Stokes equations describing: (i) the Coanda effect in a channel, and (ii) the lid driven triangular cavity flow, in a physical/geometrical multi-parametrized setting, considering the effects of the domain's configuration on the position of the bifurcation points. Finally, we propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution. Exploiting such detection tool, we are able to efficiently obtain information about the pattern flow behaviour, from symmetry breaking profiles to attaching/spreading vortices, even at high Reynolds numbers.

    Comment: 28 pages, 22 figures
    Keywords Physics - Fluid Dynamics ; Computer Science - Machine Learning ; Mathematics - Numerical Analysis ; Physics - Computational Physics
    Subject code 532
    Publishing date 2021-09-22
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

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