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New analytic buckling solutions of rectangular thin plates with two free adjacent edges by the symplectic superposition method
Li R(李睿); Wang HY; Zheng XR; Xiong SJ; Hu ZY; Yan XY; Xiao Z; Xu HL; Li P
Corresponding AuthorLi, Rui(ruili@dlut.edu.cn)
Source PublicationEUROPEAN JOURNAL OF MECHANICS A-SOLIDS
2019-07-01
Volume76Pages:247-262
ISSN0997-7538
AbstractThis paper deals with a classic but very difficult type of problems, i.e., pursuing analytic buckling solutions of biaxially loaded rectangular thin plates with two free adjacent edges that are characterized by having both the free edges and a free corner. The primary challenge is to find the solutions satisfying both the governing high-order partial differential equations (PDEs) and non-Levy-type boundary constraints. Here, an up-to-date symplectic superposition method is developed for the issues, which yields the analytic solutions by converting the problems to be solved into the superposition of two elaborated subproblems that are solved by the symplectic elasticity approach. The distinctive merit of the method is that a direct rigorous derivation helps to access the analytic solutions without any assumptions/prior knowledge of the solution forms, which is attributed to the implementation in the symplectic space-based Hamiltonian system rather than in the classic Euclidean space-based Lagrangian system. As the important outputs, comprehensive new analytic results are obtained, with 1200 critical buckling loads and 100 buckling mode shapes presented, which are all well validated by the refined finite element analysis. The rapid convergence and favorable accuracy of the present method make it competent as a benchmark one for similar problems.
KeywordAnalytic solution Plate buckling Free edge Free comer Symplectic superposition method
DOI10.1016/j.euromechsol.2019.04.014
Indexed BySCI
Language英语
WOS IDWOS:000472691600020
WOS KeywordFREE-VIBRATION SOLUTIONS ; GRADED SANDWICH PLATES ; DISCRETE SINGULAR CONVOLUTION ; ELASTICITY APPROACH ; THERMAL-STABILITY ; EFFICIENT ; LOADS
WOS Research AreaMechanics
WOS SubjectMechanics
Funding ProjectYoung Elite Scientists Sponsorship Program by CAST[2015QNRC001] ; National Basic Research Program of China[2014CB049000] ; Opening Fund of State Key Laboratory of Nonlinear Mechanics ; Fundamental Research Funds for the Central Universities[DUT18GF101]
Funding OrganizationYoung Elite Scientists Sponsorship Program by CAST ; National Basic Research Program of China ; Opening Fund of State Key Laboratory of Nonlinear Mechanics ; Fundamental Research Funds for the Central Universities
Classification二类/Q1
Ranking1
Citation statistics
Document Type期刊论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/79404
Collection非线性力学国家重点实验室
Recommended Citation
GB/T 7714
Li R,Wang HY,Zheng XR,et al. New analytic buckling solutions of rectangular thin plates with two free adjacent edges by the symplectic superposition method[J]. EUROPEAN JOURNAL OF MECHANICS A-SOLIDS,2019,76:247-262.
APA 李睿.,Wang HY.,Zheng XR.,Xiong SJ.,Hu ZY.,...&Li P.(2019).New analytic buckling solutions of rectangular thin plates with two free adjacent edges by the symplectic superposition method.EUROPEAN JOURNAL OF MECHANICS A-SOLIDS,76,247-262.
MLA 李睿,et al."New analytic buckling solutions of rectangular thin plates with two free adjacent edges by the symplectic superposition method".EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 76(2019):247-262.
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