• Steel and Composite Structures
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• v.6 no.5
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• pp.401-415
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• 2006

Based on a non-linear model taking into account flexural-torsional couplings, analytical solutions are derived for lateral buckling of simply supported I beams under some representative load cases. A closed form is established for lateral buckling moments. It accounts for bending distribution, load height application and pre-buckling deflections. Coefficients $C_1$ and $C_2$ affected to these parameters are then derived. Regard to well known linear stability solutions, these coefficients are not constant but depend on another coefficient $k_1$ that represents the pre-buckling deflection effects. In numerical simulations, shell elements are used in mesh process. The buckling loads are achieved from solutions of eigenvalue problem and by bifurcations observed on non linear equilibrium paths. It is proved that both the buckling loads derived from linear stability and eigenvalue problem lead to poor results, especially for I sections with large flanges for which the behaviour is predominated by pre-buckling deflection and the coefficient $k_1$ is large. The proposed solutions are in good agreement with numerical bifurcations observed on non linear equilibrium paths.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.215-219
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• 2003

Buckling and post-buckling Analysis of Ludwick type and modified Ludwick type elastic materials was carried out. Because the constitutive equation, or stress-strain relationship is different from that of linear elastic one, a new governing equation was derived and solved by $4^{th}$ order Runge-Kutta method. Considered as a special case of combined loading, the buckling under both point and distributed load was selected and researched. The final solution takes distinguished behavior whether the constitutive relation is chosen to be modified or non-modified Ludwick type as well as linear or non-linear. We also derived strain energy function for non-linear elastic constitutive relationship. By doing so, we calculated the criterion function which estimates the stability of the equilibrium solutions and determines critical buckling load for non-linear cases. We applied this theory to the constitutive relationship of fabric, which also is the non-linear equation between the applied moment and curvature. This results has both technical and mathematical significance.

• Steel and Composite Structures
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• v.13 no.1
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• pp.71-89
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• 2012

The paper investigates beam lateral buckling stability according to linear and non-linear models. Closed form solutions for single-symmetric cross sections are first derived according to a non-linear model considering flexural-torsional coupling and pre-buckling deformation effects. The closed form solutions are compared to a beam finite element developed in large torsion. Effects of pre-buckling deflection and gradient moment on beam stability are not well known in the literature. The strength of singly symmetric I-beams under gradient moments is particularly investigated. Beams with T and I cross-sections are considered in the study. It is concluded that pre-buckling deflections effects are important for I-section with large flanges and analytical solutions are possible. For beams with T-sections, lateral buckling resistance depends not only on pre-buckling deflection but also on cross section shape, load distribution and buckling modes. Effects of pre-buckling deflections are important only when the largest flange is under compressive stresses and positive gradient moments. For negative gradient moments, all available solutions fail and overestimate the beam strength. Numerical solutions are more powerful. Other load cases are investigated as the stability of continuous beams. Under arbitrary loads, all available solutions fail, and recourse to finite element simulation is more efficient.

• Steel and Composite Structures
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• v.14 no.6
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• pp.571-586
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• 2013

This paper focuses on the buckling capacity of a hybrid grid shell. The eigenvalue buckling, geometrical non-linear elastic buckling and elasto-plastic buckling analyses of the hybrid structure were carried out. Then the influences of the shape and scale of imperfections on the elasto-plastic buckling loads were discussed. Also, the effects of different structural parameters, such as the rise-to-span ratio, beam section, area and pre-stress of cables and boundary conditions, on the failure load were investigated. Based on the comparison between elastic and elasto-plastic buckling loads, the effect of material non-linearity on the stability of the hybrid barrel vault is found significant. Furthermore, the stability of a hybrid barrel vault is sensitive to the anti-symmetrical distribution of loads. It is also shown that the structures are highly imperfection sensitive which can greatly reduce their failure loads. The results also show that the support conditions pose significant effect on the elasto-plastic buckling load of a perfect hybrid structure.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.33 no.4
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• pp.35-40
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• 2005

There are many methods to reinforce the cylindrical structure for light weight design like skin-stringer and semi-monocoque. Isogrid is one of the reinforced structures to improve buckling load. Isogrid has many advantages for complex load case, internal pressure and concentrated load.In this paper, compressive buckling test and non-linear FE analysis of the isogrid panel are described. Diameter of panel is 2.4m and thickness of plate is 11.43mm. The angle which the panel accomplish is about 70 degrees and, its height is about 660mm. Local buckling, global buckling and variation of stiffness after local buckling were observed during buckling test of the panel. MSC/MARC is used for non-linear FE analysis. When analysis, initial imperfection of panel which occurred during plastic forming is considered. The results of analysis for buckling mode and buckling load have good agreements with test.

• Steel and Composite Structures
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• v.42 no.5
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• pp.711-722
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• 2022

In this paper, hyperbolic shear deformation plate theory is developed for thermal buckling of functionally graded plates with porosity by dividing transverse displacement into bending and shear parts. The present theory is variationally consistent, and accounts for a quadratic variation of the transverse shearstrains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Three different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. The logarithmic-uneven porosities for first time is mentioned. Equilibrium and stability equations are derived based on the present theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, aspect ratio and side-to-thickness ratio on the buckling temperature difference of imperfect FG plates.

• Advances in nano research
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• v.9 no.3
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• pp.211-220
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• 2020

This paper investigates the effect of linear and non-linear distribution of carbon nanotube volume fraction in the FG-CNTRC beams on the critical buckling by using higher-order shear deformation theories. Here, the material properties of the CNTRC beams are assumed to be graded in the thickness direction according to a new exponential power law distribution in terms of the carbon nanotube volume fractions. The single-walled carbon nanotube is aligned and distributed in the polymeric matrix with different patterns of reinforcement; the material properties of the CNTRC beams are described by using the rule of mixture. The governing equations are derived through using Hamilton's principle. The Navier solution method is used under the specified boundary conditions for simply supported CNTRC beams. The mathematical models provided in this work are numerically validated by comparison with some available results. New results of critical buckling with the non-linear distribution of CNT volume fraction in different patterns are presented and discussed in detail, and compared with the linear distribution. Several aspects of beam types, CNT volume fraction, exponent degree (n), aspect ratio, etc., are taken into this investigation. It is revealed that the influences of non-linearity distribution in the beam play an important role to improve the mechanical properties, especially in buckling behavior. The results show that the X-Beam configuration is the strongest among all different types of CNTRC beams in supporting the buckling loads.

• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.621-640
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• 2017

This paper reports the numerical investigation conducted to study the influence of Local-Distortional (L-D) interaction mode buckling on post buckling strength erosion in fixed ended lipped channel cold formed steel columns. This investigation comprises of 81 column sections with various geometries and yield stresses that are carefully chosen to cover wide range of strength related parametric ratios like (i) distortional to local critical buckling stress ratio ($0.91{\leq}F_{CRD}/F_{CRL}{\leq}4.05$) (ii) non dimensional local slenderness ratio ($0.88{\leq}{\lambda}_L{\leq}3.54$) (iii) non-dimensional distortional slenderness ratio ($0.68{\leq}{\lambda}_D{\leq}3.23$) and (iv) yield to non-critical buckling stress ratio (0.45 to 10.4). The numerical investigation is carried out by conducting linear and non-linear shell finite element analysis (SFEA) using ABAQUS software. The non-linear SFEA includes both geometry and material non-linearity. The numerical results obtained are deeply analysed to understand the post buckling mechanics, failure modes and ultimate strength that are influenced by L-D interaction with respect to strength related parametric ratios. The ultimate strength data obtained from numerical analysis are compared with (i) the experimental tests data concerning L-D interaction mode buckling reported by other researchers (ii) column strength predicted by Direct Strength Method (DSM) column strength curves for local and distortional buckling specified in AISI S-100 (iii) strength predicted by available DSM based approaches that includes L-D interaction mode failure. The role of flange width to web depth ratio on post buckling strength erosion is reported. Then the paper concludes with merits and limitations of codified DSM and available DSM based approaches on accurate failure strength prediction.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.689-696
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• 2006

This paper deals with the geometrical non-linear analyses of the buckled columns. Differential equations governing elasticas of the buckled columns are derived, in which both effects of taper type and shear deformation are included. Three kinds of taper types such as breadth, depth and square tapers are considered. Differential equations are solved numerically to obtain the elasticas and buckling loads of such columns. End constraint of both clamped ends and both hinged ends are considered. The effects of shear deformation on the elastica of the buckled column and buckling load of column are investigated extensively. Experimental studies are presented that complement theoretical results of non-linear responses of the elasticas.

• Structural Engineering and Mechanics
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• v.45 no.5
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• pp.613-629
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• 2013

In this article we will present a method to directly evaluate the critical point of a non-linear system by using the solution of a polynomial eigenvalue approximation as a starting point for an iterative non-linear system solver. This method will be used to evaluate out-of-plane buckling properties of truss structures for which the lateral displacement of the upper chord has been prevented. The aim is to assess for a number of example structures whether or not the linearized eigenvalue solution gives a relevant starting point for an iterative non-linear system solver in order to find the minimum positive critical load.