Symplectic superposition method-based new analytic bending solutions of cylindrical shell panels

Zheng, Xinran; Sun, Yuwen; Huang, Ming-Qiu; An, Dongqi; Li, Peng; Wang, Bo; Li, Rui

doi:10.1016/j.ijmecsci.2019.01.012

Cited by 34 publications

(10 citation statements)

References 17 publications

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“…. ) are obtained by solving the nonhomogeneous equations (47)(48)(49)(50) for the case of uniform load or incorporating Eqs. (51)(52)(53)(54) for the case of concentrated load.…”

Section: Analytic Solutions For Rectangular Nanoplates With Combinations Of Clamped and Simply Supported Edgesmentioning

confidence: 99%

“…For the buckling (free vibration) problem, equating q u , q c , N x , N y , k w , and k p ( q u , q c , ω , k w , and k p ) with zero, the buckling loads (natural frequencies) are determined by equating with zero the determinant of the coefficient matrix of the homogeneous simultaneous equations of Eqs. (47)(48)(49)(50). Substituting the nonzero constant solutions into the Eqs.…”

Section: Analytic Solutions For Rectangular Nanoplates With Combinations Of Clamped and Simply Supported Edgesmentioning

confidence: 99%

“…In recent years, we have proposed an analytic symplectic superposition method for mechanics problems of plates and shells based on classical theories, which proved to be widely applicable to bending 46,47 , buckling 48 , and vibration 49,50 problems. The solution procedure involves three main steps, i.e., converting an original problem into several elaborated subproblems, solving the subproblems within the Hamiltonian system by the symplectic approach, and superposition of the subproblems for the final solution.…”

mentioning

confidence: 99%

“…).For a CCCC nanoplate under concentrated load, the only differences are on the right-hand sides of Eqs. (47-50), which become for Eqs (47)(48)(49)(50),. respectively.…”

mentioning

confidence: 99%

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New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

Zheng

Huang

et al. 2021

Sci Rep

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New analytic bending, buckling, and free vibration solutions of rectangular nanoplates with combinations of clamped and simply supported edges are obtained by an up-to-date symplectic superposition method. The problems are reformulated in the Hamiltonian system and symplectic space, where the mathematical solution framework involves the construction of symplectic eigenvalue problems and symplectic eigen expansion. The analytic symplectic solutions are derived for several elaborated fundamental subproblems, the superposition of which yields the final analytic solutions. Besides Lévy-type solutions, non-Lévy-type solutions are also obtained, which cannot be achieved by conventional analytic methods. Comprehensive numerical results can provide benchmarks for other solution methods.

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“…. ) are obtained by solving the nonhomogeneous equations (47)(48)(49)(50) for the case of uniform load or incorporating Eqs. (51)(52)(53)(54) for the case of concentrated load.…”

Section: Analytic Solutions For Rectangular Nanoplates With Combinations Of Clamped and Simply Supported Edgesmentioning

confidence: 99%

Section: Analytic Solutions For Rectangular Nanoplates With Combinations Of Clamped and Simply Supported Edgesmentioning

confidence: 99%

mentioning

confidence: 99%

“…).For a CCCC nanoplate under concentrated load, the only differences are on the right-hand sides of Eqs. (47-50), which become for Eqs (47)(48)(49)(50),. respectively.…”

mentioning

confidence: 99%

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New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

Zheng

Huang

et al. 2021

Sci Rep

Self Cite

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“…e symplectic superposition method is developed which is the combination of superposition method as stated above and symplectic elasticity approach [22][23][24][25], and applied systematically to the bending [26,27], buckling [28,29], and free vibration [30,31] problems of plate. is method has attracted wide attention, including plate; it is also applicable to solve shell problems [32]. However, the method involves complex mathematical manipulations, which require skilled personnel in the fields of mathematics and mechanics.…”

Section: Introductionmentioning

confidence: 99%

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Zhong

Ullah

et al. 2020

Advances in Civil Engineering

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For the first time, the finite integral transform method is introduced to explore the accurate bending analysis of orthotropic rectangular thin plates with two adjacent edges free and the others clamped or simply supported. Previous solutions mostly focused on plates with simply supported and clamped edges, but the existence of free corner makes the solution procedure much complex to solve by conventional inverse/semi-inverse methods. Compared with the conventional methods, the employed method eliminates the need to preselect the deflection function, which makes it more reasonable and theoretical for calculating the mechanical responses of the plates. Moreover, the approach used can also analyze static problems of moderately thick plates and thick plates with the same boundary conditions investigated in this article. Finally, comprehensive analytical results obtained in this paper illuminate the validity of the proposed approach by comparing with the previous literature and finite element method by using (ABAQUS) software.

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Analytical solution of the bending problem of free orthotropic rectangular thin plate on two‐parameter elastic foundation

et al. 2021

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The bending problem of free orthotropic rectangular thin plate (RTP) on two‐parameter elastic foundation under a concentrated load is studied by the symplectic superposition method. Firstly, the original bending problem is decomposed into three subproblems by analyzing load effects and boundary conditions, each of which is the bending problem of the plate with two opposite edges slidingly supported. In order to solve the three sub‐problems based on the separation of variables method in Hamiltonian system, the Hamiltonian system for the orthotropic RTP with two opposite edges slidingly supported is studied, and then the eigenvalues and eigenfunctions of the Hamiltonian operator are obtained by combining the separation of variables and symbolic computation. Secondly, according to the symplectic orthogonality and the completeness of the eigenfunctions, the general solution of the Hamiltonian system with the two opposite edges slidingly supported is obtained. Furthermore, the solutions in the form of series of the three subproblems are obtained respectively. Finally, the symplectic superposition solution of the original bending problem is obtained by superposing the solutions of the three subproblems and the correctness of the symplectic superposition solution is verified by two numerical examples.

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Symplectic superposition method-based new analytic bending solutions of cylindrical shell panels

Cited by 34 publications

References 17 publications

New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

Analytical Bending Solutions of Orthotropic Rectangular Thin Plates with Two Adjacent Edges Free and the Others Clamped or Simply Supported Using Finite Integral Transform Method

Analytical solution of the bending problem of free orthotropic rectangular thin plate on two‐parameter elastic foundation

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