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large deflection of clamped circular plate and accuracy of its approximate analytical solutions

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Science China(Physics,Mechanics & Astronomy) 2016年第2期59卷 67-77页

作者： Yin Zhang State Key Laboratory of Nonlinear Mechanics(LNM) Institute of Mechanics Chinese Academy of Sciences

A different set of governing equations on the large deflection of plates are derived by the principle of virtual work(PVW), which also leads to a different set of boundary conditions. Boundary conditions play an important role in determining the computation accuracy of the large deflection of plates. Our boundary conditions are shown to be more appropriate by analyzing their difference with the previous ones. The accuracy of approximate analytical solutions is important to the bulge/blister tests and the application of various sensors with the plate structure. Different approximate analytical solutions are presented and their accuracies are evaluated by comparing them with the numerical results. The error sources are also analyzed. A new approximate analytical solution is proposed and shown to have a better approximation. The approximate analytical solution offers a much simpler and more direct framework to study the plate-membrane transition behavior of deflection as compared with the previous approaches of complex numerical integration.

关键词： approximate analytical solutions large deflection plate membrane bulge and blister tests

large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes

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Applied Mathematics and Mechanics(English Edition) 2020年第8期41卷 1227-1250页

作者： S.ZGHAL A.FRIKHA F.DAMMAK Laboratory of Electromechanical Systems National Engineering School of SfaxUniversity of SfaxB.P W3038SfaxTunisia

This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates and panels using a finite element *** on the first-order shear deformation theory(FSDT),the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type.A C^0 isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite *** adopting the extended rule of mixture,the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency *** carbon nanotube(CNT)distributions,labeled uniformly distributed(UD)-CNT,FG-VCNT,FG-O-CNT,and FG-X-CNT,are *** solution procedure is carried out via the Newton-Raphson incremental *** numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present *** effects of the CNT distributions,their volume fractions,and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

关键词： carbon nanotube(CNT) functionally graded material(FGM) geometrical nonlinearity large deflection

large deflection THEORY OF NANOBEAMS

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Acta Mechanica Solida Sinica 2010年第5期23卷 394-399页

作者： Dujuan Zeng Quanshui Zheng 1(Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China) [a] Department of Engineering Mechanics Tsinghua University Beijing 100084 China

One-dimensional nanostructured materials are often used as beams in many applications such as ultrahigh-frequency resonators and ultrasensitive sensors. Compared with usual macroscopic beams, nanobeams have much higher surface/volume ratios so that their surface energies may play a significant role. Besides, they often bear large deflections due to their typically large slenderness ratios and larger elastic ranges. There is, however, lack of a theory that takes into account of both the above two features owned by nanobeams. In this paper, we present such a theory and give applied examples to show that surface energy and large deflection may individually or jointly have notable effects.

关键词： nanobeam surface energy large deflection

large deflection of annular throttle-slices in shock absorbers

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Journal of Beijing Institute of Technology 2012年第2期21卷 258-263页

作者：贺李平顾亮肖介平 Beijing Institute of Radio Measurement School of Mechanical Engineering Beijing Institute of Technology Department of CAE and Performance Integration Beijing Automotive Technology Center

method was used to derive the stiffness curve equation of a single throttle-slice in shock absorbers. The analytical formula of large deflection for superposed throttle-slices was deduced directly and generalized. The undetermined coefficients of analytical for- mula were obtained through the finite element method （FEM） and curve fitting. Numerical results show that the analytical formula has satisfactory accuracy.

关键词： superposed annular throttle-slices large deflection perturbation method finite ele-ment method (FEM) curve fitting

Buckling and large deflection behaviors of radially functionally graded ring-stiffened circular plates with various boundary conditions

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Applied Mathematics and Mechanics(English Edition) 2016年第9期37卷 1131-1152页

作者： M.E.GOLMAKANI M.EMAMI Department of Mechanical Engineering Mashhad BranchIslamic Azad University

The buckling and large deflection behaviors of axis-symmetric radially functionally graded （RFG） ring-stiffened circular plates are investigated by the dynamic relaxation （DR） method combined with the finite difference discretization technique. The material properties of the constituent components of the RFG plate are assumed to vary continuously according to the Mori-Tanalka distribution along the radial direction. The nonlinear governing equations are obtained in the incremental form based on the firstorder shear deformation plate theory （FSDT） and the von Karman relations for large deflection. In the buckling analysis, an external in-plane load is applied to the plate in- crementally so that, in each load-step, the incremental form of the governing equations can be solved by a numerical code prepared based on the DR method. After converging the DR code in the first increment, the latter load-step is added to the previous one, and the program is repeated again. The critical buckling load is determined from the compressive load-displacement curve obtained by solving the incremental form of the governing equations. Based on the present incremental form of formulation, a bending analysis can also be conducted if the whole load is applied simultaneously. Finally, a detailed parametric study is carried out to investigate the influences of various boundary conditions, grading indices, thickness-to-radius ratios, stiffener＇s positions and depths on the critical buckling load, and displacements and stresses resulted from the bending analysis. It is observed that the effect of the stiffener on the results is much greater in the functionally graded plate with higher material grading indices. The results also reveal that, by increasing the depth of the stiffer, the values of ascending the critical buckling load are approximately identical for both simply supported and clamped boundary conditions.

关键词： buckling large deflection functionally graded stiffened plate dynamicrelaxation method

large deflection PROBLEM OF A CLAMPED ELLIPTICAL PLATE SUBJECTED TO UNIFORM PRESSURE

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Applied Mathematics and Mechanics(English Edition) 1992年第10期13卷 891-908页

作者：钱伟长潘立宙刘晓明 Shanghai University of Technology

In this paper, the perturbation solution of large deflection problem of clampedelliptical plate subjected to uniform pressure is given on the basis of the perturbationsolution of large deflection problem of similar clamped circular plate (1948)[1], (1954)[2]. The analytical solution of this problem was obtained in 1957. However, due to social difficulties, these results have never been published. Nash and Cooley (1959)[3] published a brief note of similar nature, in which only the case λ=a/b=2 is given. In this paper, the analytical solution is given in detail up to the 2nd approximation. The numerical solutions are given for various Poisson ratios v =0.25, 0.30, 0.35 and for various eccentricities λ= 1, 2, 3, 4, 5, which can be used in the calculation of engineering designs.

关键词： elliptical plate large deflection perturbation method

Numerical Solution of Membrane Forces for A Free-Free Floating Plate with large deflection

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海洋工程：英文版 2003年第2期17卷 163-176页

作者：陈徐均崔维成宋皓汤雪峰 School of Naval Architecture and Ocean Engineering Shanghai Jiao Tong University Engineering Institute of Engineering Crops PLA University of Science and Technology

Considering that the thickness of a pontoon-type very large floating structure (VLFS) is very small in comparison with the length and width, VLFS can be modeled as a thin plate. In theory, the displacements and the membrane forces of a plate with large deflection are all the functions of the second-order differentials of the Ariy stress function. With these characteristics considered, the Ariy stress function of a floating free-free plate is calculated by setting the virtual values of three of the corner points. The finite difference method is chosen to solve the problem. When the Ariy stress function of the plate is obtained, the membrane forces can easily be calculated. Comparisons between the forces induced by the membrane forces and by the fluid are considered. It is shown that the membrane forces can not be neglected in many cases.

关键词： membrane forces VLFS large deflection finite difference method

ITERATIVE METHOD FOR large deflection NONLINEAR PROBLEM OF LAMINATED COMPOSITE SHALLOW SHELLS AND PLATES

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Applied Mathematics and Mechanics(English Edition) 1999年第7期20卷 72-79页

作者：尹邦信 Department of Civil Engineering Southwest Institute of Technology 621000 Mianyang P R China

Based on the results by Wang,in this paper, the iterative method is presented for the study of large deflection nonlinear problem of laminated composite shallow shells and plates. The rectangular laminated composite shallow shells have been analyzed. The results have been compared with the small deflection linear analytical solution and finite element nonlinear solution. The results proved that the solution coincide with small deflection linear analytical solution in the condition of the low loads and finite element nonlinear solution in the condition of the high loads.

关键词： laminated composite shallow shells and plates large deflection iterative method

APPLICATION OF THE MODIFIED METHOD OF MULTIPLE SCALES TO THE BENDING PROBLEMS FOR CIRCULAR THIN PLATE AT VERY large deflection ANDTHE ASYMPTOTICS OF SOLUTIONS (Ⅰ)

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Applied Mathematics and Mechanics(English Edition) 1998年第10期19卷 937-950页

作者：江福汝 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University 200072 Shanghai P. R. China

In this paper, the modified method of multiple scales is applied to study the bending problems for circular thin plate with large deflection under the hinged and simply supported edge conditions. Theseries solutions a... 详细信息

关键词： circular plate large deflection boundary layer effect,asymptotics modified method of multiple scales