• Title/Summary/Keyword: buckling mode

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Frequency, bending and buckling loads of nanobeams with different cross sections

  • Civalek, Omer;Uzun, Busra;Yayli, M. Ozgur
    • Advances in nano research
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    • v.9 no.2
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    • pp.91-104
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    • 2020
  • The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bernoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter e0a, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

Buckling characteristics and static studies of multilayered magneto-electro-elastic plate

  • Kiran, M.C.;Kattimani, S.C.
    • Structural Engineering and Mechanics
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    • v.64 no.6
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    • pp.751-763
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    • 2017
  • This article deals with the buckling behaviour of multilayered magneto-electro-elastic (MEE) plate subjected to uniaxial and biaxial compressive (in-plane) loads. The constitutive equations of MEE material are used to derive a finite element (FE) formulation involving the coupling between electric, magnetic and elastic fields. The displacement field corresponding to first order shear deformation theory (FSDT) has been employed. The in-plane stress distribution within the MEE plate existing due to the enacted force is considered to be equivalent to the applied in-plane compressive load in the pre-buckling range. The same stress distribution is used to derive the potential energy functional. The non-dimensional critical buckling load is accomplished from the solution of allied linear eigenvalue problem. Influence of stacking sequence, span to thickness ratio, aspect ratio, load factor and boundary condition on critical buckling load and their corresponding mode shape is investigated. In addition, static deflection of MEE plate under the sinusoidal and the uniformly distributed load has been studied for different stacking sequences and boundary conditions.

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

  • Khalaf, Basima Salman;Fenjan, Raad M.;Faleh, Nadhim M.
    • Advances in materials Research
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    • v.8 no.3
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    • pp.219-235
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    • 2019
  • This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

Buckling and Optimum Reinforcement of Axially Stiffened Cylindrical Shells (보강(補剛) 원통 Shell의 좌굴(挫屈) 및 최적보강(最適補强))

  • Jang, Chang-Doo;Nho, Wan
    • Bulletin of the Society of Naval Architects of Korea
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    • v.24 no.1
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    • pp.42-50
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    • 1987
  • The energy expressions are formulated for the axially stiffened shell treating the stiffeners as discrete elements. The principle of minimum potential energy is employed to formulate the buckling equations for a simply supported, axially stiffened shell under uniform axial compression. The displacement functions are expended into double trigonometric series. The mode assuming method employed in this paper makes it possible to reduce the matrix size of the eigenvalue problem considerably. Effects are made to investigate the transition from overall buckling to local buckling and to verify the existence of the minimum stiffness ratio of stiffener as in the case of stiffened plate. The results of the calculation show that the critical stiffener size increase linearly as the length of the shell increases. The results also show that the overall buckling load decreases and the local buckling load has a nearly constant value as the length of the shell increases. The results show very good agreements with other computational available.

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Effects of imperfection shapes on buckling of conical shells under compression

  • Shakouri, Meisam;Spagnoli, Andrea;Kouchakzadeh, M.A.
    • Structural Engineering and Mechanics
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    • v.60 no.3
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    • pp.365-386
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    • 2016
  • This paper describes a systematic numerical investigation into the nonlinear elastic behavior of conical shells, with various types of initial imperfections, subject to a uniformly distributed axial compression. Three different patterns of imperfections, including first axisymmetric linear bifurcation mode, first non-axisymmetric linear bifurcation mode, and weld depression are studied using geometrically nonlinear finite element analysis. Effects of each imperfection shape and tapering angle on imperfection sensitivity curves are investigated and the lower bound curve is determined. Finally, an empirical lower bound relation is proposed for hand calculation in the buckling design of conical shells.

Modal Analysis of Sandwich Plate Structure Considering Buckling (좌굴을 고려한 샌드위치형 판 구조물의 모드해석)

  • Han, Geun-Jo;Ahn, Chan-Woo;Ahn, Seong-Chan;Hong, Do-Kwan;Han, Dong-Seop
    • Journal of the Korean Society for Precision Engineering
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    • v.19 no.6
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    • pp.104-108
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    • 2002
  • Sandwich plate structure is widely used in various fields of industry due to its excellent strength and stiffness compared with weight. In this paper, the mechanical behavior of sandwich plate structure with honeycomb core considering buckling is investigated in detail. The focus of the analysis is to evaluate strength and stiffness of the plate structure with critical stress, natural frequency, and mode shapes. The results of this investigation are obtained from detailed finite element analysis for various parameters, such as length, height ratio, and thickness ratio of honeycomb core.

Nonlinear dynamic stability and vibration analysis of sandwich FG-CNTRC shallow spherical shell

  • Kamran Foroutan;Akin Atas;Habib Ahmadi
    • Advances in nano research
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    • v.17 no.2
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    • pp.95-107
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    • 2024
  • In this article, the semi-analytical method was used to analyze the nonlinear dynamic stability and vibration analysis of sandwich shallow spherical shells (SSSS). The SSSS was considered as functionally graded carbon nanotube-reinforced composites (FG-CNTRC) with three new patterns of FG-CNTRC. The governing equation was obtained and discretized utilizing the Galerkin method by implementing the von Kármán-Donnell nonlinear strain-displacement relations. The nonlinear dynamic stability was analyzed by means of the fourth-order Runge-Kutta method. Then the Budiansky-Roth criterion was employed to obtain the critical load for the dynamic post-buckling. The approximate solution for the deflection was represented by suitable mode functions, which consisted of the three modes of transverse nonlinear oscillations, including one symmetrically and two asymmetrical mode shapes. The influences of various geometrical characteristics and material parameters were studied on the nonlinear dynamic stability and vibration response. The results showed that the order of layers had a significant influence on the amplitude of vibration and critical dynamic buckling load.

Contact buckling behaviour of corrugated plates subjected to linearly varying in-plane loads

  • Dong, Jianghui;Ma, Xing;Zhuge, Yan;Mills, Julie E.
    • Steel and Composite Structures
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    • v.29 no.3
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    • pp.333-348
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    • 2018
  • An analytical method is developed for analysing the contact buckling response of infinitely long, thin corrugated plates and flat plates restrained by a Winkler tensionless foundation and subjected to linearly varying in-plane loadings, where the corrugated plates are modelled as orthotropic plates and the flat plates are modelled as isotropic plates. The critical step in the presented method is the explicit expression for the lateral buckling mode function, which is derived through using the energy method. Simply supported and clamped edges conditions on the unloaded edges are considered in this study. The acquired lateral deflection function is applied to the governing buckling equations to eliminate the lateral variable. Considering the boundary conditions and continuity conditions at the border line between the contact and non-contact zones, the buckling coefficients and the corresponding buckling modes are found. The analytical solution to the buckling coefficients is also expressed through a fitted approximate formula in terms of foundation stiffness, which is verified through previous studies and finite element (FE) method.

Finite element simulation for steel tubular members strengthened with FRP under compression

  • El-Kholy, Ahmed M.;Mourad, Sherif A.;Shaheen, Ayman A.;Mohamed, Yomna A.
    • Structural Engineering and Mechanics
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    • v.72 no.5
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    • pp.569-583
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    • 2019
  • Tubular steel sections are widespread all over the world because of their strength and aesthetic appearance. Tubular steel members may exhibit local buckling such as elephant foot or overall buckling under extreme compression load. Recently, external bonding of fiber reinforced polymers (FRP) sheets for strengthening these members has been explored through experimental research. This paper presents three-dimensional nonlinear finite element analysis (FEA) to investigate the structural behavior of strengthening tubular steel members with FRP against local and overall buckling phenomena. Out-of-roundness and out-of-straightness imperfections were introduced to the numerical models to simulate the elephant foot and overall buckling, respectively. The nonlinear analysis preferences such as the integration scheme of the shell elements, the algorithm for solution of nonlinear equations, the loading procedure, the bisection limits for the load increments, and the convergence criteria were set, appropriately enough, to successfully track the sophisticated buckling deformations. The agreement between the results of both the presented FEA and the experimental research was evident. The FEA results demonstrated the power of the presented rigorous FEA in monitoring the plastic strain distribution and the buckling phenomena (initiation and propagation). Consequently, the buckling process was interpreted for each mode (elephant foot and overall) into three sequential stages. Furthermore, the influence of FRP layers on the nonlinear analysis preferences and the results was presented.

Reinforcement Effects of Buckling Member for Single-layer Latticed Dome (단층래티스 돔의 좌굴부재 보강효과에 관한 연구)

  • Jung, Hwan-Mok;Yoon, Seok-Ho;Lee, Dong-Woo
    • Journal of Korean Association for Spatial Structures
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    • v.16 no.4
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    • pp.45-52
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    • 2016
  • The single layer latticed domes have attracted many designers and researchers's attention all of the world, because these structures as spatial structure are of great advantage in not only mechanical rationality but also function, fabrication, construction and economic aspect. But single layer latticed domes are apt to occur the unstable phenomena that are called "buckling" because of the lack of strength of members, instability of structural shape, etc. In the case of latticed dome, there are several types of buckling mode such as overall buckling, local buckling, and member buckling according to the shape of dome, section type of member, the size of member, junction's condition of member and so on. There are many methods to increase the buckling strength of the single layer latticed dome, that is, with the change of geometrical shape of dome, the reinforcement of buckled member, etc. Therefore, the purpose of this study is to verify the reinforcement effect of buckled member when designers reinforce the buckled member to increase the buckling strength of single layer latticed dome with 3-way grid.