Finite integral transform method for analytical solutions of static problems of cylindrical shell panels

An, Dongqi; Xu, Dian; Ni, Zhuofan; Su, Yewang; Wang, Bo; Li, Rui

doi:10.1016/j.euromechsol.2020.104033

Cited by 20 publications

(5 citation statements)

References 26 publications

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“…Zhang et al (2019a) and Ullah et al (2019) proposed finite integral transform method to investigate the bending of rectangular thin plates with corner supports and buckling behavior of moderately thick clamped rectangular plates, respectively. An et al (2020) proposed a double finite integral transform method to solve the bending solutions of non-L evy-type cylindrical shell panels without a free edge. An et al (2016) employed the GITT in the bending analysis of fully clamped orthotropic rectangular plates by transforming only in one spatial coordinate.…”

Section: Introductionmentioning

confidence: 99%

“…(2019) proposed finite integral transform method to investigate the bending of rectangular thin plates with corner supports and buckling behavior of moderately thick clamped rectangular plates, respectively. An et al. (2020) proposed a double finite integral transform method to solve the bending solutions of non-Lévy-type cylindrical shell panels without a free edge.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, hybrid analytical-numerical approaches, the finite integral transform method and the generalized integral transform technique (GITT) (Cotta and Mikhailov, 1997;Cotta, 1998;An and Su, 2014), has been developed to solve the structural mechanics problems (Li et al, 2019;Zhang et al, 2019a;Ullah et al, 2019;An et al, 2020;Li et al, 2020;He et al, 2021), and heat and fluid problems (An et al, 2013;Fu et al, 2018;Lisboa et al, 2018Lisboa et al, , 2019Machado dos Santos et al, 2022). The GITT method essentially preserves the properties of partial differential equations, which is different from the physics-preserving schemes of the finite difference method and the finite element method (Zhao et al, 2017;Shen et al, 2018;Jiang et al, 2021Jiang et al, , 2022.…”

Section: Introductionmentioning

confidence: 99%

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Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

Tuo

Sun

et al. 2022

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PurposeThe purpose of this study is to propose a generalized integral transform technique (GITT) to investigate the bending behavior of rectangular thin plates with linearly varying thickness resting on a double-parameter foundation.Design/methodology/approachThe bending of plates with linearly varying thickness resting on a double-parameter foundation is analyzed by using the GITT for six combinations of clamped, simply-supported and free boundary conditions under linearly varying loads. The governing equation of plate bending is integral transformed in the uniform-thickness direction, resulting in a linear system of ordinary differential equations in the varying thickness direction that is solved by a fourth-order finite difference method. Parametric studies are performed to investigate the effects of boundary conditions, foundation coefficients and geometric parameters of variable thickness plates on the bending behavior.FindingsThe proposed hybrid analytical-numerical solution is validated against a fourth-order finite difference solution of the original partial differential equation, as well as available results in the literature for some particular cases. The results show that the foundation coefficients and the aspect ratio b/a (width in the y direction to height of plate in the x direction) have significant effects on the deflection of rectangular plates.Originality/valueThe present GITT method can be applied for bending problems of rectangular thin plates with arbitrary thickness variation along one direction under different combinations of loading and boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

Tuo

Sun

et al. 2022

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“…Similarly to the case of three-dimensional elasticity, the solution of the governing equations of shell theories requires numerical methods because analytical or semi-analytical techniques are limited to very few specific combinations of geometry, materials and boundary conditions as shown, for instance, in Refs. [11][12][13]. Among the computational approaches available in the literature, the Finite Element Method (FEM) has been used extensively in industry and it is still an active research area [14,15].…”

Section: Introductionmentioning

confidence: 99%

High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method

Guarino

Gulizzi

Milazzo

2021

Composite Structures

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“…5 An et al developed a double finite integral transform method for analytical bending solutions of non-Levytype cylindrical shell panels without a free edge that were not obtained by classical semi-inverse methods. 6 Numerous engineering calculation problems (e.g. arbitrary geometry, complex boundary conditions, diverse, and uneven material properties) can be obtained directly from the mathematical model by numerical methods.…”

Section: Introductionmentioning

confidence: 99%

R-Function and variation method for bending problem of clamped thin plate with complex shape

Xia

2021

Advances in Mechanical Engineering

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Solving ordinary thin plate bending problem in engineering, only a few analytical solutions with simple boundary shapes have been proposed. When using numerical methods (e.g. the variational method) to solve the problem, the trial functions can be found only it exhibits a simple boundary shape. The R-functions can be applied to solve the problem with complex boundary shapes. In the paper, the R-function theory is combined with the variational method to study the thin plate bending problem with the complex boundary shape. The paper employs the R-function theory to express the complex area as the implicit function, so it is easily to build the trial function of the complex shape thin plate, which satisfies with the complex boundary conditions. The variational principle and the R-function theory are introduced, and the variational equation of thin plate bending problem is derived. The feasibility and correctness of this method are verified by five numerical examples of rectangular, I-shaped, T-shaped, U-shaped, and L-shaped thin plates, and the results of this method are compared with that of other literatures and ANSYS finite element method (FEM). The results of the method show a good agreement with the calculation results of literatures and FEM.

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Finite integral transform method for analytical solutions of static problems of cylindrical shell panels

Cited by 20 publications

References 26 publications

Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

High-fidelity analysis of multilayered shells with cut-outs via the discontinuous Galerkin method

R-Function and variation method for bending problem of clamped thin plate with complex shape

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