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Reduction Method Applied to Viscoelastically Damped Finite Element Models
[chapter]
2013
Lecture Notes in Mechanical Engineering
We propose in this paper to combine the GHM (Golla-Hughes-Mc Tavish) method with model reduction technique, especially direct condensation methods to resolve the problem of increased model order of viscoelastically structures. In fact, modeling structures using the GHM method leads to global systems of equation of motion whose numbers of degrees-offreedom largely exceeds the order of the associated undamped system. As result, the numerical resolution of such equations can require prohibitive
doi:10.1007/978-3-642-37143-1_15
fatcat:3pdz6naapnfina4ngozsiklzhy
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... putational (CPU) time. So, to overcome this problem, both Static and Dynamic methods are used to reduce the order of finite elements matrices while preserving its capability to represent the dynamic behavior of viscoelastically damped structures. This paper intends to compare these two methods in direct reduction. Numerical example applied to cantilever beam structure is presented. This example will highlight the domain of validity of the studied methods. Results obtained from these two reduction methods are compared with the full model in order to illustrate its performances and its practical interest in the dynamic analysis of viscoelastically damped structures.
Dynamics of convective slippery constraints on hybrid radiative Sutterby nanofluid flow by Galerkin finite element simulation
2022
Nanotechnology Reviews
The heat transport and entropy formation of an unsteady Sutterby hybrid nanofluid (SBHNF) are investigated in this work. SBHNF's flowing and thermal transport properties are investigated by exposing the nanofluid to a slippery hot surface. This analysis includes the influences of solid-shaped nanoparticles, porous materials, radiative flux, and viscous dissipative flow. The Galerkin finite element technique (G-FEM) is used to find self-similar solutions to equations that are then transformed
doi:10.1515/ntrev-2022-0070
fatcat:mwi4u5aatjez5ccm6kvs5wjnue
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... o ODEs using appropriate transformations. This research considers two diverse kinds of nanosolid-particles, copper (Cu) and graphene oxide (GO), using non-Newtonian engine-oil (EO) as the working fluid. In the flowing, energy, skin friction, Nusselt number, and entropy production, important findings for the various variables are visually depicted. The most notable finding of the analysis is that when SBHNF (GO–Cu/EO) is compared to a typical nanofluid (Cu–EO), the thermal transmission rate of SBHNF (GO–Cu/EO) gradually increases. Furthermore, heat transfer is greatest for spherical-shaped nanoparticles and lowest for lamina-shaped nanoparticles. The entropy in the model is increased when the size of the nanoparticles ϕ \phi is increased. The comparable impact is noticed once the radiation flowing N r {N}_{\text{r}} and Deborah number λ \lambda increase.
Model reduction methods for viscoelastic sandwich structures in frequency and time domains
2015
Finite elements in analysis and design
Generation of Reference Softgauges for Minimum Zone Fitting Algorithms: Case of Aspherical and Freeform Surfaces
2021
Nanomaterials
Optical aspherical lenses with high surface quality are increasingly demanded in several applications in medicine, synchrotron, vision, etc. To reach the requested surface quality, most advanced manufacturing processes are used in closed chain with high precision measurement machines. The measured data are analysed with least squares (LS or L2-norm) or minimum zone (MZ) fitting (also Chebyshev fitting or L∞-norm) algorithms to extract the form error. Performing data fitting according to L∞-norm
doi:10.3390/nano11123386
pmid:34947735
pmcid:PMC8703870
fatcat:uw7w2spejvfxhfhdybod3e2xrm
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... is more accurate and challenging than L2-norm, since it directly minimizes peak-to-valley (PV). In parallel, reference softgauges are used to assess the performance of the implemented MZ fitting algorithms, according to the F1 algorithm measurement standard, to guarantee their traceability, accuracy and robustness. Reference softgauges usually incorporate multiple parameters related to manufacturing processes, measurement errors, points distribution, etc., to be as close as possible to the real measured data. In this paper, a unique robust approach based on a non-vertex solution is mathematically formulated and implemented for generating reference softgauges for complex shapes. Afterwards, two implemented MZ fitting algorithms (HTR and EPF) were successfully tested on a number of generated reference pairs. The evaluation of their performance was carried out through two metrics: degree of difficulty and performance measure.
Traceable Reference Full Metrology Chain for Innovative Aspheric and Freeform Optical Surfaces Accurate at the Nanometer Level
2021
Sensors
The design of innovative reference aspheric and freeform optical elements was investigated with the aim of calibration and verification of ultra-high accurate measurement systems. The verification is dedicated to form error analysis of aspherical and freeform optical surfaces based on minimum zone fitting. Two thermo-invariant material measures were designed, manufactured using a magnetorheological finishing process and selected for the evaluation of a number of ultra-high-precision measurement
doi:10.3390/s21041103
pmid:33562598
pmcid:PMC7915810
fatcat:tjmu7gk65zdfrfe2mq6e4yueoe
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... machines. All collected data sets were analysed using the implemented robust reference minimum zone (Hybrid Trust Region) fitting algorithm to extract the values of form error. Agreement among the results of several partners was observed, which demonstrates the establishment of a traceable reference full metrology chain for aspherical and freeform optical surfaces with small amplitudes.
REPUBLIQUE TUNISIENNE MINISTERE DE L'ENSEIGNENMENT SUPERIEUR ET DE LA RECHERCHE SCIENTIFIQUE Mémoire Pour l'obtention d'un Diplôme de Mastère Professionnel Réalisé par Mohamed Mehdi MAMLOUK Business Plan pour la création d'une Agence maritime de Consignation de navire
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