• Steel and Composite Structures
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• 제16권1호
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• pp.45-58
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• 2014

EC3 provides several methodologies for the stability verification of members and frames. However, when dealing with the verification of non-uniform members in general, with tapered cross-section, irregular distribution of restraints, non-linear axis, castellated, etc., several difficulties are noted. Because there are yet no guidelines to overcome any of these issues, safety verification is conservative. In recent research from the authors of this paper, an Ayrton-Perry based procedure was proposed for the flexural buckling verification of web-tapered columns. However, in order to apply this procedure, Linear Buckling Analysis (LBA) of the tapered column must be performed for determination of the critical load. Because tapered members should lead to efficient structural solutions, it is therefore of major importance to provide simple and accurate formula for determination of the critical axial force of tapered columns. In this paper, firstly, the fourth order differential equation for non-uniform columns is derived. For the particular case of simply supported web-tapered columns subject to in-plane buckling, the Rayleigh-Ritz method is applied. Finally, and followed by a numerical parametric study, a formula for determination of the critical axial force of simply supported linearly web-tapered columns buckling in plane is proposed leading to differences up to 8% relatively to the LBA model.

• Structural Engineering and Mechanics
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• 제37권3호
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• pp.331-349
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• 2011

This study investigates the use of a vibration correlation technique (VCT) to identify the buckling load of a rectangular thin plate. It is proposed that the buckling load can be determined experimentally using the natural frequencies of plates under tensile loading. A set of rectangular plates was tested for natural frequencies using an impact test method. Aluminum and stainless steel specimens with CCCC, CCCF and CFCF boundary conditions were included in the experiment. The measured buckling load was determined from the plot of the square of a measured natural frequency versus an in-plane load. The buckling loads from the measured vibration data match the numerical solutions very well. For specimens with well-defined boundary conditions, the average percentage difference between buckling loads from VCT and numerical solutions is -0.18% with a standard deviation of 5.05%. The proposed technique using vibration data in the tensile loading region has proven to be an accurate and reliable method which might be used to identify the buckling load of plates. Unlike other static methods, this correlation approach does not require drawing lines in the pre-buckling and post-buckling regions; thus, bias in data interpretation is avoided.

• 한국공간구조학회논문집
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• 제10권1호
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• pp.119-126
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• 2010

쉘형 구조물의 동적 불안정 문제를 다룬 연구결과는 다소 발표되고 있으나 위상곡면을 이용하여 카오스 생성에 관한 기본적 현상을 다룬 연구는 거의 없는 실정이다. 동적 비선형 문제에서 여러 가지 초기조건에 의해 불안정 현상이 민감하게 발생하는 이유를 파악하기 위해서는 위상곡면에서 끌개의 특성을 조사하여 동적 불안정 생성과정을 검토하는 일은 매우 중요하다. 본 연구에서는 얕은 EP 쉘이 스텝하중을 받을 때, 직접 좌굴과 간접 좌굴의 발생 경로를 파악하기 위하여 Galerkin 법에 의해 전개된 이산화 방정식을 구한다. 이를 수치해석 기법으로 위상곡선과 연속응답스펙트럼을 구해 동적 불안정 특성을 규명한다.

• Structural Engineering and Mechanics
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• 제9권5호
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• pp.483-490
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• 2000

After manufacturing a structure, the assembly of structural components is often not as perfect as expected due to the immaturity of current engineering techniques. Thus the actual buckling load for an element is sometimes not consistent with that predicted in the design. For design considerations, it is necessary to establish an analytical method for determining the buckling load experimentally. In this paper, a dynamic method is described for determining the linear buckling loads for elastic, perfectly flat plates. The proposed method does not require the application of in-plane loads and is feasible for arbitrary types of boundary conditions. It requires only the vibrational excitation of the plate. The buckling load is determined from the measured natural frequencies and vibration mode shapes.

• Steel and Composite Structures
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• 제24권6호
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• pp.697-709
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• 2017

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.

• Structural Engineering and Mechanics
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• 제15권6호
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• pp.653-668
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• 2003

Many papers which deal with the dynamic instability of shell-like structures under the STEP load have been published. But, there have been few papers related to the dynamic instability of hybrid cable domes. In this study, the dynamic instability of hybrid cable domes considering geometric nonlinearity is investigated by a numerical method. The characteristic structural behaviour of a cable dome shows a strong nonlinearity, so we determine the shape of a cable dome by applying initial stress and examine the indirect buckling mechanism under dynamic external forces. The dynamic critical loads are determined by the numerical integration of the nonlinear equation of motion, and the indirect buckling is examined by using the phase plane to investigate the occurrence of chaos.

• 한국해양공학회지
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• 제23권5호
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• pp.71-78
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• 2009

In ship design or offshore structure design, the evaluation of buckling strength (or ultimate strength) is critical to the determination of scantling of stiffened plates. For this reason, it is useful to study the effect of applying different formula or the relationship between stiffened plate with buckling utilization factor (UF). It can facilitate a designer to decide how much the scantling should be reinforced or how much can be reduced for an optimal design. This paper conducts a comparative study for three buckling check methods; DNV-Ship-Rule, DNV-RP-C201, DNV-PULS. The capacity curves and 2D contour plot for utilization factors versus bi-axial in-plane stresses are compared. The contour plots of DNV-Ship-Rule and DNV-PULS show smoothly increasing trends of UF as the applied in-plane stresses increase, however that of DNV-RP-C201 shows rapidly increasing trend as the applied stresses go beyond transverse buckling stress. A sensitivity analysis is performed to investigate the influence level of each parameter of a stiffened plate on UF. Resulting from the analysis, plate thickness is identified to be the most affective parameter to UF regardless of the buckling check methods. Based on the addressed study, optimal designs for bottom plate of 165 K tanker corresponding to three formulas are compared with each other. DNV-PULS yields 1 mm and 2 mm less thickness than DNV-Ship-Rule and DNV-RP-C201, respectively.

• Structural Engineering and Mechanics
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• 제66권6호
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• pp.729-736
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• 2018

This paper studies thermal buckling and post-buckling behaviors of functionally graded materials (FGM) tubes subjected to a uniform temperature rise and resting on elastic foundations via a refined beam model. Compared to the Timoshenko beam theory, the number of unknowns of this model are the same and no correction factors are required. The material properties of the FGM tube vary continuously in the radial direction according to a power function. Two ends of the tube are assumed to be simply supported and in-plane boundary conditions are immovable. Energy variation principle is employed to establish the governing equations. A two-step perturbation method is adopted to determine the critical thermal buckling loads and post-buckling paths of the tubes with arbitrary radial non-homogeneity. Through detailed parametric studies, it can be found that the tube has much higher buckling temperature and post-buckling strength when it is supported by an elastic foundation.

• International Journal of Aerospace System Engineering
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• 제2권2호
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• pp.19-23
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• 2015

This work deals with the study of buckling and post buckling characteristics of laminated composite plates with and without localized regions of damage. The need of a detailed study on Finite Element Analysis of buckling and post buckling of laminated composite structures considering various aspects enhances the interest among researchers. Mathematical formulation is developed for damaged composite plates using a finite element technique based on Inverse Hyperbolic Shear Deformation Theory. This theory satisfies zero transverse shear stresses conditions at the top and bottom surfaces of the plate and provides a non-linear transverse shear stress distribution. Damage modeling is done using an anisotropic damage formulation, which is based on the concept of stiffness change. The structural elements are subjected to in-plane loading. The computer program is developed in MATLAB environment. The numerical results are presented after through validation of developed finite element code. The effect of damage on buckling and post buckling has been carried out for various parameters such as amount of percentage of damaged area, damage intensity, etc. The results show that the presence of internal flaws will significantly affect the buckling characteristics of laminated composite plates. The outcomes and remarks from this work will assist to address some key issues concerning composite structures.

• 한국전산구조공학회논문집
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• 제12권3호
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• pp.417-426
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• 1999

쉘형 구조물의 동적 불안정 문제를 다룬 연구결과는 다소 발표되고 있으나, 위상면을 이용하여 카오스 생성에 관해 기본적 현상을 다룬 연구는 아직 없는 실정이다. 동적 비선형 문제에서, 여러 가지 초기조건에 의해 불안정 현상이 민감하게 발생하는 이유를 파악하기 위해 위상면에서의 끌개의 특성을 조사하여 동적 불안정 생성과정을 검토하는 일은 매우 중요하다. 본 연구에서는 기하학적 비선형을 고려한 얕은 아치의 직접/간접 좌굴을 수치적 기법으로 조사하고, 이를 정적 좌굴하중과 비교한다.