• Bulletin of the Society of Naval Architects of Korea
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• v.21 no.2
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• pp.19-27
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• 1984

An extension of the finite element method to the stability analysis of shells of revolution under static axisymmetric loading is presented in this paper. A systematic procedure for the formulation of the problem is based upon the principle of virtual work. This procedure results in an eigenvalue problem. For solution, the shell of revolution is discretized into a series of conical frusta. The buckling mode in the circumferential direction is assumed, this assumption makes the problem economical for the computing time. The present method is applied to a number of shells of revolution, under axial compression or lateral pressure, and comparision are made with other theoretical results. The results show good agreement each other. The effects of aspect ratio, boundary conditions and buckling modes on the buckling strength of shells of revolution are studied. Also the optimum shape of cylindrical shell under uniform axial compression is obtained from the view point of structural stability.

• Computational Structural Engineering : An International Journal
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• v.3 no.1
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• pp.49-59
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• 2003

This paper discusses the enhancement of the buckling capacity of column strips by use of piezoelectric layer. The analytical model for obtaining the buckling capacity of the piezoelectric coupled column with general boundary conditions modelled with different types of springs applied at the ends of the column is derived the first time. Based on this proposed model, the buckling capacity of the column strips can be accurately predicted by solving an eigenvalue problem. The computational results show the great potential of the piezoelectric materials in enhancing the buckling capacity of the column strips. The optimal locations of the piezoelectric layer for higher buckling capacity are also obtained for the columns with. standard pinned-pinned, fixed-free, and fixed-pinned structures. In addition, the buckling capacity and the increase of buckling capacity are discussed for those columns with the general boundaries as well. This research may provide a benchmark for the buckling analysis of the piezoelectric coupled strips.

• Coupled systems mechanics
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• v.8 no.5
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• pp.459-471
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• 2019

This paper presents post-buckling analysis of a functionally graded beam under hygro-thermal effect. The material properties of the beam change though height axis with a power-law function. In the nonlinear kinematics of the post-buckling problem, the total Lagrangian approach is used. In the solution of the problem, the finite element method is used within plane solid continua. In the nonlinear solution, the Newton-Raphson method is used with incremental displacements. Comparison studies are performed. In the numerical results, the effects of the material distribution, the geometry parameters, the temperature and the moisture changes on the post-buckling responses of the functionally graded beam are presented and discussed.

• Journal of the Korean Society of Industry Convergence
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• v.13 no.2
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• pp.77-84
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• 2010

Recently, the concept of structural design against instability has been proposed in the chassis parts. The design considerations of lower control arm of chassis parts under the buckling and durability strengths are the general. More precisely, this paper considers a specific application and associated optimization problem for two strengths, where the design variables are the physical or geometric dimensions for skins and stiffeners. The objective is the minimization of the total weight, while optimization constrains involve reserve or improve factors for the buckling and durability strengths. The most important features are related to the numerical simulations for the estimation of buckling factor and their sensitivities by means of nonlinear and linear finite element analyses. The bucking and durability strength analyses, and the morping geometries are directly included in the optimization problem and the modified design is formulated. As a result, the optimal structure with stable behavior is obtained or increases the buckling and durability strengths of parts. Most of design problems for structures exposed to elastic instability can be formulated and solved.

• Steel and Composite Structures
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• v.45 no.4
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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.

• Smart Structures and Systems
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• v.26 no.2
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• pp.213-226
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• 2020

In this manuscript, static and dynamic behaviors of geometrically imperfect carbon nanotubes (CNTs) subject to different types of end conditions are investigated. The Doublet Mechanics (DM) theory, which is length scale dependent theory, is used in the analysis. The Euler-Bernoulli kinematic and nonlinear mid-plane stretching effect are considered through analysis. The governing equation of imperfect CNTs is a sixth order nonlinear integro-partial-differential equation. The buckling problem is discretized via the differential-integral-quadrature method (DIQM) and then it is solved using Newton's method. The equation of linear vibration problem is discretized using DIQM and then solved as a linear eigenvalue problem to get natural frequencies and corresponding mode shapes. The DIQM results are compared with analytical ones available in the literature and excellent agreement is obtained. The numerical results are depicted to illustrate the influence of length scale parameter, imperfection amplitude and shear foundation constant on critical buckling load, post-buckling configuration and linear vibration behavior. The current model is effective in designing of NEMS, nano-sensor and nano-actuator manufactured by CNTs.

• Steel and Composite Structures
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• v.29 no.3
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• pp.379-389
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• 2018

In this research, the explicit closed-form local buckling solution of steel plates in contact with concrete, with both loaded and unloaded edges elastically restrained against rotation and subjected to eccentric compression is presented. The Rayleigh-Rize approach is applied to establish the eigenvalue problem for the local buckling performance. Buckling shape which combines trigonometric and biquadratic functions is introduced according to that used by Qin et al. (2017) on steel plate buckling under uniform compression. Explicit solutions for predicting the local buckling stress of steel plate are obtained in terms of the rotational stiffness. Based on different boundary conditions, simply yet explicit local buckling solutions are discussed in details. The proposed formulas are validated against previous research and finite element results. The influences of the loading stress gradient parameter, the aspect ratio, and the rotational stiffness on the local buckling stress resultants of steel plates with different boundary conditions were evaluated. This work can be considered as an alternative to apply a different buckling shape function to study the buckling problem of steel plate under eccentric compression comparing to the work by Qin et al. (2018), and the results are found to be in consistent with those in Qin et al. (2018).

• Structural Engineering and Mechanics
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• v.51 no.6
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• pp.955-971
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• 2014

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.143-156
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• 2008

Elliptical tubes may buckle in an elastic local buckling failure mode under uniform compression. Previous analyses of the local buckling of these members have assumed that the cross-section is hollow, but it is well-known that the local buckling capacity of thin-walled closed sections may be increased by filling them with a rigid medium such as concrete. In many applications, the medium many not necessarily be rigid, and the infill can be considered to be an elastic material which interacts with the buckling of the elliptical tube that surrounds it. This paper uses an energy-based technique to model the buckling of a thin-walled elliptical tube containing an elastic infill, which elucidates the physics of the buckling phenomenon from an engineering mechanics basis, in deference to a less generic finite element approach to the buckling problem. It makes use of the observation that the local buckling in an elliptical tube is localised with respect to the contour of the ellipse in its cross-section, with the localisation being at the region of lowest curvature. The formulation in the paper is algebraic and it leads to solutions that can be determined by implementing simple numerical solution techniques. A further extension of this formulation to a stiffness approach with multiple degrees of buckling freedom is described, and it is shown that using the simple one degree of freedom representation is sufficiently accurate for determining the elastic local buckling coefficient.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.6
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• pp.173-181
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• 2000

The stability of a structural plate is a crucial problem which causes wrinkling and buckling. In this paper, the effect of the pattern of spot-welding points in the two rectangular plate on the shear buckling load is studied with respect to the thickness, the aspect ratio of plates, the number of welding spots. Buckling coefficient of the simple plate was compared with that of two plates with various conditions to extract the effect of buckling strength. The effect of the number of welding spots are studied in two directions, longitudinal and transverse directions. The concluded that the reinforcement effect was maximized when the aspect ratio was close to 1.5 and that the effect of number of welding spots in longitudinal direction was larger than that in transverse direction.