• Computers and Concrete
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• 제25권3호
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• pp.205-214
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• 2020

Cytoskeleton components in living cell bear large compressive force and are responsible in maintaining the cell shape. Actually these filaments are surrounded by viscoelastic media within the cell. This surrounding, viscoelastic media affects the buckling behavior of these filaments when external force is applied on these filaments by exerting continuous pressure in opposite directions to the incipient buckling of the filaments. In this article a mechanical model is applied to account the effects of this media on the buckling behavior of intermediate filaments network of cytoskeleton. The model immeasurably associates; filament's bending rigidity, adjacent system elasticity, and cytosol viscosity with buckling wavelength, buckling growth rate and buckling amplitude of the filaments.

• Advances in nano research
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• 제4권1호
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• pp.51-64
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• 2016

This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.

• Steel and Composite Structures
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• 제45권4호
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Structural Engineering and Mechanics
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• 제16권5호
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• pp.533-556
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• 2003

The flutter and buckling analysis of a beam structure subjected to a static follower force is completely studied in the paper. The beam is fixed in the transverse direction and constrained by a rotational spring at one end, and by a translational spring and a rotational spring at the other end. The co-existence of flutter and buckling in this beam due to the presence of the follower force is an interesting and important phenomenon. The results from this theoretical analysis will be useful for the stability design of structures in engineering applications, such as the potential of flutter control of aircrafts by smart materials. The transition-curve surface for differentiating the two distinct instability regions of the beam is first obtained with respect to the variations of the stiffness of the springs at the two ends. Second, the capacity of the follower force is derived for flutter and buckling of the beam as a function of the stiffness of the springs by observing the variation of the first two frequencies obtained from dynamic analysis of the beam. The research in the paper may be used as a benchmark for the flutter and buckling analysis of beams.

• Structural Engineering and Mechanics
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• 제66권6호
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• pp.737-748
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• 2018

The current study presents a new technique in the framework of the nonlocal elasticity theory for a comprehensive buckling analysis of Euler-Bernoulli nano-beams made up of bidirectional functionally graded material (BDFGM). The mechanical properties are considered by exponential and arbitrary variations for axial and transverse directions, respectively. The various circumstances including tapering, resting on two-parameter elastic foundation, step-wise or continuous variations of axial loading, various shapes of sections with various distribution laws of mechanical properties and various boundary conditions like the multi-span beams are taken into account. As far as we know, for the first time in the current work, the buckling analyses of BDFGM nano-beams are carried out under mentioned circumstances. The critical buckling loads and mode shapes are calculated by using energy method and a new technique based on calculus of variations and collocation method. Fast convergence and excellent agreement with the known data in literature, wherever possible, presents the efficiency of proposed technique. The effects of boundary conditions, material and taper constants, foundation moduli, variable axial compression and small-scale of nano-beam on the buckling loads and mode shapes are investigated. Moreover the analytical solutions, for the simpler cases are provided in appendices.

• Structural Engineering and Mechanics
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• 제74권2호
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• pp.175-187
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• 2020

The theories having been developed thus far account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. A shear correction factor, therefore, is not required. In this paper, the effect of surface on the axial buckling and free vibration of nanobeams is studied using various refined higher-order shear deformation beam theories. Furthermore, these theories have strong similarities with Euler-Bernoulli beam theory in aspects such as equations of motion, boundary conditions, and expressions of the resultant stress. The equations of motion and boundary conditions were derived from Hamilton's principle. The resultant system of ordinary differential equations was solved analytically. The effects of the nanobeam length-to-thickness ratio, thickness, and modes on the buckling and free vibration of the nanobeams were also investigated. Finally, it was found that the buckling and free vibration behavior of a nanobeam is size-dependent and that surface effects and surface energy produce significant effects by increasing the ratio of surface area to bulk at nano-scale. The results indicated that surface effects influence the buckling and free vibration performance of nanobeams and that increasing the length-to-thickness increases the buckling and free vibration in various higher-order shear deformation beam theories. This study can assist in measuring the mechanical properties of nanobeams accurately and designing nanobeam-based devices and systems.

• 대한조선학회논문집
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• 제28권2호
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• pp.307-317
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• 1991

선체구조 및 해양구조물의 기본 구조요소로 사용되는 편심으로 보강된 평판이나 쉘 수조물의 기하하적 비선형 해석에 관한 논문으로서 사용된 유한요소는 격하 쉘요소와 편심된 격하보요소이며 total Lagrange(T.L.)수식과 updated Lagrange(U.L.)수식으로 정식화 하였다. 편심된 보강평판의 비선형 해석에서 사용된 모델은 보강재의 이상화 방법에 따라 평판과 보강재를 격하 쉘요소로 이상화한 모델과 평판은 격하 쉘요소로하고 보강재는 편심된 격하 보요소로 이상화한 모델로 각각 구분하여 비선형 해석을 수행하였으며 해석과정에서 편심 보강평판의 임계하중을 구하고 좌굴 후 비선형 거동을 조사하였다. 해석된 임계 좌굴하중은 선급에서 규정하고 있는 방식의 오일러의 좌굴하중값 보다는 낮게 조사되었다.

• Steel and Composite Structures
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• 제15권4호
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• Coupled systems mechanics
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• 제10권1호
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• pp.79-102
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• 2021

In this paper we deal with instability problems of structures under nonconservative loading. It is shown that such class of problems should be analyzed in dynamics framework. Next to analytic solutions, provided for several simple problems, we show how to obtain the numerical solutions to more complex problems in efficient manner by using the finite element method. In particular, the numerical solution is obtained by using a modified Euler-Bernoulli beam finite element that includes the von Karman (virtual) strain in order to capture linearized instabilities (or Euler buckling). We next generalize the numerical solution to instability problems that include shear deformation by using the Timoshenko beam finite element. The proposed numerical beam models are validated against the corresponding analytic solutions.

• 한국지반공학회논문집
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• 제22권11호
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• pp.123-131
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• 2006

지진 시 액상화에 의한 지반흐름은 말뚝파괴에 가장 큰 영향을 미치는 것으로 알려져 있다. 실제로 충분히 큰 정적 안전율을 갖도록 설계된 말뚝이 지진 시 좌굴에 의해 파괴되는 사례가 빈번히 발생하였다. 본 연구에서는 1-g 진동대 실험을 통해 액상화 지반에 근입된 말뚝의 좌굴에 의한 파괴거동을 분석하였다. 실험 결과, 좌굴하중에 근접한 연직하중을 받고 있는 말뚝은 지반의 액상화 발생 시 좌굴에 의해 쉽게 파괴될 수 있으며 액상화에 의한 지반흐름이 발생할 경우, 말뚝의 횡방향 변형이 증가하면서 좌굴파괴하중이 감소함을 알 수 있었다. 또한 파괴된 말뚝을 꺼내어 관찰한 결과, 액상화가 발생한 후라도 지반에 구속압이 존재하여 Euler 좌굴현상과 다르게 말뚝 하부가 아닌 중간위치에서 말뚝파괴가 발생하였으며 지반경사가 급해질수록 지반흐름에 의한 파괴 위치가 점점 말뚝하부로 낮아짐을 볼 수 있었다.