scholarly journals Prediction of transmission, reflection and absorption coefficients of periodic structures using a hybrid Wave Based – Finite Element unit cell method

2018 ◽  
Vol 356 ◽  
pp. 282-302 ◽  
Author(s):  
Elke Deckers ◽  
Stijn Jonckheere ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Wim Desmet
Keyword(s):  
Finite Element ◽  
Periodic Structures ◽  
Unit Cell ◽  
Hybrid Wave ◽  
Absorption Coefficients ◽  
Cell Method

scholarly journals WANG TILES LOCAL TILINGS CREATED BY MERGING EDGE-COMPATIBLE FINITE ELEMENT MESHES

2017 ◽  
Vol 13 ◽  
pp. 161
Author(s):  
Lukáš Zrůbek ◽  
Anna Kučerová ◽  
Martin Doškář
Keyword(s):  
Finite Element ◽  
Mechanical Response ◽  
Unit Cell ◽  
Cell Method ◽  
Mechanical Field ◽  
Wang Tiles ◽  
Small Set ◽  
Finite Element Meshes ◽  
Heterogeneous Microstructures ◽  
Periodic Unit Cell

In this contribution, we present the concept of Wang Tiles as a surrogate of the periodic unit cell method (PUC) for modelling of materials with heterogeneous microstructures and for synthesis of micro-mechanical fields. The concept is based on a set of specifically designed cells that compresses the stochastic microstructure into a small set of statistical volume elements – tiles. Tiles are placed side by side according to matching edges like in a game of domino. Opposite to the repeating pattern of PUC the Wang Tiles method with the stochastic tiling algorithm preserves the randomness for reconstructed microstructures. The same process is applied to obtain the micro-mechanical response of domains where the evaluation as one piece would be time consuming. Therefore the micro-mechanical quantities are evaluated only on tiles (with surrounding layers of tiles of each addressed tile included into the evaluation) and then synthesized to the micro-mechanical field of whole domain.

Analysis of Vibration and Wave Propagation in Cylindrical Grid-Like Structures

2003 ◽  
Author(s):  
Sang Min Jeong ◽  
Massimo Ruzzene
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Periodic Structures ◽  
Dynamic Properties ◽  
Unit Cell ◽  
Element Formulation ◽  
Two Dimensional ◽  
Curved Beams ◽  
Cylindrical Grid ◽  
Phase Constant

The wave propagation in and the vibration of cylindrical grid structures are analyzed. The considered grids are composed of a sequence of identical elementary cells repeating along the axial and circumferential directions to form a two-dimensional (2D) periodic structure. Two-dimensional periodic structures are characterized by wave propagation patterns that are strongly frequency dependent and highly directional. Such unique characteristics can be utilized to design structures able to confine external perturbations to specified regions. The wave propagation characteristics of 2D periodic structures are determined through the analysis of the dynamic properties of the unit cell, which is described by its Finite Element mass and stiffness matrices. The cell is composed of curved beams to form a cylindrical grid. The combined application of the Finite Element formulation and the theory of 2D periodic structures yields the phase constant surfaces, which define, for the considered cell lay-out, the directions of wave propagation for assigned frequency values. The predictions from the phase constant surfaces analysis are verified by estimating the forced harmonic response of the complete grid. The results demonstrate the unique characteristics of this class of grid structures, and suggest how they may be designed to enhance attenuation capabilities of shell structures commonly used in aerospace or naval applications. Design configurations can be identified so that the transmission of vibrations towards specified locations and at certain frequencies is minimized. The study can be extended to include the optimization of the geometry and topology of the unit cell to achieve desired transmissibility levels in specified directions and for given excitation frequencies.

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

2015 ◽  
Vol 07 (02) ◽  
pp. 1550018 ◽  
Author(s):  
C. W. Zhou ◽  
J. P. Lainé ◽  
M. N. Ichchou ◽  
A. M. Zine
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Numerical Approach ◽  
Unit Cell ◽  
Cell Dynamics ◽  
One Dimensional ◽  
Ill Conditioning ◽  
Selection Of ◽  
Element Method

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

Edge finite element method for periodic structures using random meshes

2021 ◽  
pp. 1-19
Author(s):  
Ouail Ouchetto ◽  
Brahim Essakhi ◽  
Said Jai-Andaloussi ◽  
Saad Zaamoun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Element Method

scholarly journals Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method

Materials ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 271
Author(s):  
Jun-Jun Zhai ◽  
Xiang-Xia Kong ◽  
Lu-Chen Wang
Keyword(s):  
Finite Element ◽  
Cell Model ◽  
Structural Parameters ◽  
Thermal Relaxation ◽  
Viscoelastic Behavior ◽  
Unit Cell ◽  
Time Dependent ◽  
3D Braided Composites ◽  
Equivalent Time ◽  
Representative Unit Cell

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

scholarly journals A numerical study of a size-dependent finite-element based unit cell with primary and secondary voids

2021 ◽  
pp. 104493
Author(s):  
Vetle Espeseth ◽  
David Morin ◽  
Jonas Faleskog ◽  
Tore Børvik ◽  
Odd Sture Hopperstad
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Unit Cell ◽  
Size Dependent

The Effectiveness of the Unit Cell Method in Numerically Modeling and Designing Liquid Cooled Heatsinks

2019 ◽  
Vol 11 (6) ◽  
Author(s):  
Ali C. Kheirabadi ◽  
Dominic Groulx
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Parametric Design ◽  
Unit Cell ◽  
Liquid Cooling ◽  
Cell Method ◽  
Numerical Predictions ◽  
Finite Element Package ◽  
Parametric Studies ◽  
Relative Differences

This study compares two numerical strategies for modeling flow and heat transfer through mini- and microchannel heatsinks, the unit cell approximation, and the full 3D model, with the objective of validating the former approach. Conjugate heat transfer and laminar flow through a 2 × 2 cm2 copper–water heatsink are modeled using the finite element package COMSOL Multiphysics 5.0. Parametric studies showed that as the heatsink channels’ widths were reduced, and the total number of channels increased, temperature and pressure predictions from both models converged to similar values. Relative differences as low as 5.4% and 1.6% were attained at a channel width of 0.25 mm for maximum wall temperature and channel pressure drop, respectively. Due to its computational efficiency and tendency to conservatively overpredict temperatures relative to the full 3D method, the unit cell approximation is recommended for parametric design of heatsinks with channels’ widths smaller than 0.5 mm, although this condition only holds for the given heatsink design. The unit cell method is then used to design an optimal heatsink for server liquid cooling applications. The heatsink has been fabricated and tested experimentally, and its thermal performance is compared with numerical predictions. The unit cell method underestimated the maximum wall temperature relative to experimental results by 3.0–14.5% as the flowrate rose from 0.3 to 1.5 gal/min (1.1–5.7 l/min).

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