Multiscale analysis of membrane instability by using the Arlequin method

Huang, Qun; Kuang, Zengtao; Hu, Heng; Potier‐Ferry, Michel

doi:10.1016/j.ijsolstr.2018.11.023

Cited by 13 publications

(5 citation statements)

References 50 publications

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“…In sequential analysis, a 3D model of circular membrane is set up in ABAQUS/standard with the geometrical parameters as: R=500mm, h=1mm. When studying membrane, many scholars modeled in ABAQUS using shell element [27,28], such as S4R, S8R5. However, shell elements (S4R) cannot give a nice simulation to real deformation of circular membrane subjected to a load at central point shown as Fig.…”

Section: Numerical Simulation Using Abaqus 31 Finite-element Modelmentioning

confidence: 99%

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

Huang

Song

et al. 2020

IEEE Access

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In this study, the deformation of circular orthotropic membranes subjected to a central concentrated force is investigated. An orthotropic membrane equation indicating load-deflection behavior based on Föppl-von Kármán membrane theory is obtained and the numerical solutions are gotten by using MATLAB. A variable k, which is the most influential parameter on the load-deflection behavior, is proposed. In isotropic membrane, the change of material parameters mainly influences the deflection of membranes subjected to a concentrated force; however, when studying for orthotropic membrane, the shape of membrane after deformation can be controlled by changing the value of k. Only change in elastic modulus and Poisson's ratio, with k constant, mainly influence the deflection of curves, instead of the shape of curves. Then, four numerical simulations by ABAQUS are conducted and the membrane element M3D4R is used to set up a finite-element model. By comparing these simulation results with the solutions from orthotropic membrane equation, it is shown that the orthotropic membrane equation gives a good estimation of load-deflection behavior. INDEX TERMS load-deflection curve, orthotropic membrane, central concentrated load, membrane element M3D4R.

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Section: Numerical Simulation Using Abaqus 31 Finite-element Modelmentioning

confidence: 99%

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

Huang

Song

et al. 2020

IEEE Access

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“…Due to its robustness and ability to predict post buckling behavior, the bifurcation analysis approach has been the method of choice in several recent efforts focused on elucidating wrinkling behavior of thin membranes. [16][17][18][19] Wrinkling has an undesirable effect in many applications as it might undermine the capability and performance of structures. An example to realize the seriousness of this undesired effect could be that of a membrane reflector.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wrinkling suppression in thin membranes using designed geometrical features

Nazzal

Alkhader

Agha

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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The rapidly increasing use of thin membranes; especially in the fabrication of flexible electronics, has motivated investigating the wrinkling behavior of these membranes. Wrinkling has an undesirable effect since wrinkles degrade the surface accuracy of structures incorporating thin membranes. This work introduces and evaluates an approach based on including optimized geometric features in thin membranes to suppress their wrinkling behavior. The ability of the optimized geometric features to suppress wrinkling in a 25 μm thick polyimide membrane subjected to uniaxial stretching is investigated computationally and experimentally in this work. A finite element model is developed to predict the wrinkling behavior of the membrane. An experimental setup equipped with 3D digital image correlation system is used to determine the wrinkles pattern, amplitude, and wavelength. Symmetric circular holes are introduced in the membrane to redistribute the stress field, eliminate the fluctuation in the minor principal stress in the membrane, and suppress wrinkles. The location and size of the circular holes are determined by coupling the Non-Linear Programming by Quadratic Largrangian technique and finite element simulations. An optimal design is obtained and the experimental results show that the optimally designed holes effectively suppressed the wrinkling behavior.

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“…Steigmann [ 10 ] derived a partial differential equation for the membrane tension trajectory to avoid the membrane deformation in uncertainty. The Kármán theory is commonly used to analyze the amplitude and wavelength of thin membranes [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ], and it takes into account the effects of membrane bending in the analysis of wrinkles. Fu et al [ 21 ] established a solution framework for compressible and incompressible materials under the Föppl–von Kármán Theory.…”

Section: Introductionmentioning

confidence: 99%

“…Fu et al [ 21 ] established a solution framework for compressible and incompressible materials under the Föppl–von Kármán Theory. Huang et al [ 22 ] used the Föppl–von Kármán theory to improve the accuracy and efficiency of membrane instability calculations by transitioning the Fourier-approximated membrane model to a multiscale model through the Arlequin method. Koiter’s theory is based on the three-dimensional elastic theory, which simulates the fold mode by combining the stretching and bending effects of the thin plate [ 23 , 24 ].…”

Section: Introductionmentioning

confidence: 99%

Stress Superposition Method and Mechanical Properties Analysis of Regular Polygon Membranes

Tao

Lin

et al. 2021

Materials

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In this paper, the stress superposition method (SSM) is proposed to solve the stress distribution of regular polygon membranes. The stress-solving coefficient and the calculation formula of arbitrary point stress of regular polygon membrane are derived. The accuracy of the SSM for calculating stresses in regular polygonal membranes is verified by comparing the calculation results of the SSM with the finite element simulation results. This article is the first to propose a method to investigate the response of the arch height of the membrane curved edge to the membrane’s mechanical properties while keeping the effective area constant. It is found that the equivalent stress and the second principal stress at the midpoint of the membrane curved edge are effectively increased with the increase of the arch height of the curved edge. The second principal stress at the edge region of the membrane is relatively small, leading to the occurrence of wrinkles. When the stress at the midpoint of the curved edge is equal to that at the center of the membrane, the membrane plane attains the maximum stiffness and reduces the possibility of wrinkling at the edge.

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Multiscale analysis of membrane instability by using the Arlequin method

Cited by 13 publications

References 50 publications

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

A Theoretical Study of Circular Orthotropic Membrane Under Concentrated Load: The Relation of Load and Deflection

Wrinkling suppression in thin membranes using designed geometrical features

Stress Superposition Method and Mechanical Properties Analysis of Regular Polygon Membranes

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