A Fourier based reduced model for wrinkling analysis of circular membranes

Huang, Wei; Huang, Qun; Liu, Yin; Yang, Jie; Hu, Heng; Trochu, F.; Causse, Philippe

doi:10.1016/j.cma.2018.09.012

Cited by 18 publications

(7 citation statements)

References 58 publications

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“…The solid blue line represents our numerical results, while the dots represent those obtained by the Fourier series based method. 45 A good agreement can be found between the two methods. It is worth noting that if two or more integration points are used to evaluate the boundary integral in Equation ( 54) of out-of-plane displacement, direction derivate of w along radial direction vanishes, 𝜕w∕𝜕n = 0, on the boundaries, that is, clamped boundary condition, as illustrated in Figure 11, though only penalty term corresponding to the simply supported condition is considered.…”

Section: Radial Stretching Of Annular Membranementioning

confidence: 65%

“…Eventually, all unknowns ( u p , w p , 𝜆 p ) , 1 ≤ p ≤ m, can be determined by successively solving the system of Equations ( 25), ( 44) and ( 42), (45) at each order. We should point out that only the displacement vector ( u p , w p ) , 1 ≤ p ≤ m, will be discretized by the Powell-Sabin B-splines.…”

Section: Asymptotic Numerical Methodsmentioning

confidence: 99%

“…We compare our numerical results with those obtained by other approaches. 28,29,45 For all the numerical examples, we truncate the series Equation ( 17) at the order m = 15 and set the accuracy parameter 𝜖 = 10 −8 to control the step-length of the asymptotic solution.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…The third example explores a more complex domain, square membrane with a central circular hole under diagonal radial tensile displacement load. We compare our numerical results with those obtained by other approaches 28,29,45 . For all the numerical examples, we truncate the series Equation (17) at the order

m=15

and set the accuracy parameter

\epsilon =1{0}^{-8}

to control the step‐length of the asymptotic solution.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Stretch‐induced wrinkling analysis of thin sheets with splines

Tian

Chen

2023

Numerical Meth Engineering

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Numerical simulation of stretch-induced wrinkling in thin elastic sheets is a challenging problem due to a vanishing bending stiffness and the coexistence of superabundant equilibrium solutions. In this work, we present a computational framework to capture the morphological evolution of stretch-induced wrinkles. The application of modified Föppl-von Kármán plate model results in a fourth-order partial differential equation. The convergence of finite-element solutions necessitates C 1 -continuous approximations. Herein, Powell-Sabin B-splines, which are based on triangles, are utilized for both the approximation of the field variables and the description of the geometry. To trace the wrinkling behavior in thin sheets, a path-following technique using asymptotic numerical method is considered. The advantage of this method is an adaptive step length, which works incredibly well near the bifurcation points and allows for the computation of the post-bifurcation diagrams with a quite small perturbation. The versatility and accuracy of the developed computational approach are assessed in three case studies, featuring wrinkling in highly stretched rectangular and annular thin sheets.

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Section: Radial Stretching Of Annular Membranementioning

confidence: 65%

Section: Asymptotic Numerical Methodsmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

m=15

and set the accuracy parameter

\epsilon =1{0}^{-8}

to control the step‐length of the asymptotic solution.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

Stretch‐induced wrinkling analysis of thin sheets with splines

Tian

Chen

2023

Numerical Meth Engineering

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show abstract

“…12. It is evident that both the long-and short-wavelength modes are captured accurately by the proposed method which is normally a challenge issue for computational mechanics, see e.g., [69][70][71] .…”

Section: Applications To More Practical Structuresmentioning

confidence: 99%

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Xiang

Sun

Banerjee

et al. 2021

Mechanical Systems and Signal Processing

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An exact dynamic stiffness method is proposed for the free vibration analysis of multi-body systems consisting of flexible beams and rigid bodies. The theory is sufficiently general in that the rigid bodies can be of any shape or size, but importantly, the theory permits connections of the rigid bodies to any number beams at any arbitrary points and oriented at any arbitrary angles. For beam members, a range of theories including the Bernoulli-Euler and Timoshenko theories are applied. The assembly procedure for the beam and rigid body properties is simplified without resorting to matrix inversion. The difficulty generally encountered in computing the problematic J0 count when applying the Wittrick-Williams algorithm for modal analysis has been overcome. Applications of different beam theories for both axial and bending vibrations have enabled the examination of the role played by rigid-body parameters on the multibody system's dynamic behaviour. Some exact benchmark results are provided and compared with published results and with finite element solutions. This research provides an exact and highly efficient analysis tool for multibody system dynamics which is for the free vibration analysis, ideally suited for optimization and inverse problems such as modal parameter identification.

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Wrinkling prediction of laminated composite panels under in-plane shear deformation

Sabri

Meguid

2020

Acta Mech

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A Fourier based reduced model for wrinkling analysis of circular membranes

Cited by 18 publications

References 58 publications

Stretch‐induced wrinkling analysis of thin sheets with splines

Stretch‐induced wrinkling analysis of thin sheets with splines

An exact dynamic stiffness method for multibody systems consisting of beams and rigid-bodies

Wrinkling prediction of laminated composite panels under in-plane shear deformation

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