Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations

Yu, Qiang; Xu, Hang; Liao, Shijun

doi:10.1016/j.apm.2018.04.022

Cited by 18 publications

(6 citation statements)

References 34 publications

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“…Here the Coiflet wavelet modification technique suggested by Yu et al [27] is employed to solve Eq. (12).…”

Section: Generalized Coiflets Wavelet Expressionmentioning

confidence: 99%

“…Their modified technique not only holds the advantages of strong nonlinear processing capability inherited by the homotopy analysis method and excellent local expression characteristics originated from the Coiflet wavelet, but also is very efficient and accurate for nonlinear equations with homogenous boundary conditions. Yu and Xu [25][26][27] established a generalized boundary modification approach based on the Coiflet wavelet which is suitable for both ordinary and partial differential equations subjected to non-homogenous boundary conditions. Their idea was further adopted by Wang et al [28] for a electrohydro-dynamic flow problem and Chen [29] for a channel flow problem, respectively.…”

Section: Introductionmentioning

confidence: 99%

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Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Ahmed¹,

Xu²,

Wang³

et al. 2021

Preprint

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The magnetised Jeffery-Hamel flow due to a point sink or source in convergent and divergent channels is studied. The simplified governing equation ruled by the Reynolds number, the Hartmann number and the divergent-convergent angle with appropriate boundary conditions are solved by the newly proposed Coiflet wavelet-homotopy method. Highly accurate solutions are obtained, whose accuracy is rigidly checked. As compared with the traditional homotopy analysis method, our proposed technique has higher computational efficiency and larger applicable range of physical parameters. Results show that our proposed technique is very convenient to handle strong nonlinear problems without special treatment. It is expected that this technique can be further applied to study complex nonlinear problems in science and engineering involving into extreme physical parameters. Besides, the influence of physically important quantities on the flow is discussed. It is found that wall stretching and shrinking exhibits totally different roles on the flow development. The enhanced Lorenz force affects the flow behaviours significantly for both convergent and divergent cases.

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“…Here the Coiflet wavelet modification technique suggested by Yu et al [27] is employed to solve Eq. (12).…”

Section: Generalized Coiflets Wavelet Expressionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Ahmed¹,

Xu²,

Wang³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Taking the boundary conditions (4) into consideration, it is known that F(η) satisfies the inhomogeneous Dirichlet and homogeneous Neumann types of boundary conditions. Hence, following Yu et al [37,38,[41][42][43], by modifying the coefficient matrices, the Coiflet wavelet basis is selected as…”

Section: Coiflet Wavelet Expressionmentioning

confidence: 99%

“…One-dimensional and two-dimensional Bratus equations subjected to homogeneous boundary conditions were considered in their work as illustrative examples. eir proposed technique was then extended by Yu and his collaborators to solve the nonlinear plate bending problem [37] and cavity flow problem [38] with nonhomogeneous boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Coiflet Wavelet-Homotopy Solution of Channel Flow due to Orthogonally Moving Porous Walls Governed by the Navier–Stokes Equations

Chen

2020

Journal of Mathematics

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A newly computational method based on the Coiflet wavelet and homotopy analysis method is developed, which inherits the great nonlinear treatment of the homotopy analysis technique and the local high-precision capability of the wavelet approach, to give solutions to the classic problem of channel flow with moving walls. The basic principle of this suggested technique and the specific solving process are presented in detail. Its validity and efficiency are then checked via rigid comparisons with other computational approaches. It is found that the homotopy-based convergence-control parameter and the wavelet-based resolution level of Coiflet are two effective ways to improve on accuracies of solutions.

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“…Flexibility in the choice of this auxiliary parameter as well as linear operator and initial guess is another great advantage of the method. The Homotopy Analysis Method has been successfully applied to solve many problems in biology [26][27][28], chemistry [29][30][31], physics [32][33][34], optimal control theory [35][36][37], fluid mechanics [38][39][40][41], and solid mechanics [42][43][44]. More specifically, HAM successfully solved static and dynamic problems of isotropic beams.…”

Section: Introductionmentioning

confidence: 99%

Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

Doeva

Masjedi

2021

Acta Mech

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New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problems.

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Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations

Cited by 18 publications

References 34 publications

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Highly Accurate Coiflet wavelet-Homotopy Solution of Jeffery-Hamel Problem at Extreme Parameters

Coiflet Wavelet-Homotopy Solution of Channel Flow due to Orthogonally Moving Porous Walls Governed by the Navier–Stokes Equations

Static analysis of composite beams on variable stiffness elastic foundations by the Homotopy Analysis Method

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