New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework

Zheng, Xinran; Ni, Zhuofan; Xu, Dian; Wang, Zixuan; Li, Yihao; Du, Jingyu; Li, Rui

doi:10.1016/j.apm.2021.05.017

Cited by 18 publications

(2 citation statements)

References 53 publications

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“…In recent years, we have proposed a novel analytic symplectic superposition method (SSM) that has been successfully applied to bending [ 18 ], buckling [ 19 ], and vibration [ 20 ] of plate and shell structures as well as the mechanical analysis of flexible electronics [ 21 ]. The method involves a skillful combination of the superposition method and the symplectic approach [ 22 ], which is conducted within the Hamiltonian framework in the symplectic space rather than within the Lagrangian system in the Euclidean space where the conventional analytic methods are conducted.…”

Section: Introductionmentioning

confidence: 99%

An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition

Xiong

Meng

et al. 2022

Micromachines

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In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures.

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Section: Introductionmentioning

confidence: 99%

An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition

Xiong

Meng

et al. 2022

Micromachines

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“…Li et al 11 propose an analytical solution for evaluating the critical pressure of pipes under hydrostatic pressure. Zheng et al 12 provide some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. However, the analytical solution is difficult to realize the buckling research of complex frame structures, and the obtained information is also limited.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear buckling analysis of tower crane structure based on movable boundaries

Qin

Gao

et al. 2022

Advances in Mechanical Engineering

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The tower crane is a typical soaring and complex frame structure, and buckling is an important factor affecting its safety and carrying capacity. Considering the special characteristics of the boundary conditions for the boom structure, a numerical analysis method based on movable boundaries is proposed in this paper. In order to demonstrate the accuracy of the method, numerical analysis and stress tests are carried out on the tower crane. The results show that the numerical results are basically consistent with the experimental results. A geometric buckling analysis for extremely severe conditions is carried out in order to understand the buckling behaviors. The failure modes and complete load-response curves obtained for the tower crane are comprehensively analyzed. A dual (geometric and material) nonlinear buckling analysis of the tower crane is then investigated. Finally, the influences of the deflection load parameters on the buckling response of the tower crane are explored. It is demonstrated that bifurcation point buckling and limiting point buckling are excited by different deflection load parameters, respectively. The proposed method can accurately predict the buckling of the tower cranes, given the coupling of structure and mechanism, to ensure the safety of giant cranes in actual engineering use.

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An Extended Separation-of-Variable Method for the Eigenbuckling of Open Thin Circular Cylindrical Shells

Yuan,

Xing

2024

Lecture Notes in Mechanical Engineering

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New analytic buckling solutions of non-Lévy-type cylindrical panels within the symplectic framework

Cited by 18 publications

References 53 publications

An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition

An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition

Nonlinear buckling analysis of tower crane structure based on movable boundaries

An Extended Separation-of-Variable Method for the Eigenbuckling of Open Thin Circular Cylindrical Shells

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