• Steel and Composite Structures
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• 제20권1호
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• pp.57-70
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• 2016

The predominant type of buckling that I-steel concrete composite beams experience in the negative moment area is distortional buckling. The key factors that affect distortional buckling are the torsional and lateral restraints by the bottom flange. This study thoroughly investigates the equivalent lateral and torsional restraint stiffnesses of the bottom flange of an I-steel concrete composite beam under negative moments. The results show a coupling effect between the applied forces and the lateral and torsional restraint stiffnesses of the bottom flange. A formula is proposed to calculate the critical buckling stress of the I-steel concrete composite beams under negative moments by considering the lateral and torsional restraint stiffnesses of the bottom flange. The proposed method is shown to better predict the critical bending moment of the I-steel composite beams. This article introduces an improved method to calculate the elastic foundation beams, which takes into account the lateral and torsional restraint stiffnesses of the bottom flange and considers the coupling effect between them. The results show a close match in results from the calculation method proposed in this paper and the ANSYS finite element method, which validates the proposed calculation method. The proposed calculation method provides a theoretical basis for further research on distortional buckling and the ultimate resistance of I-steel concrete composite beams under a variable axial force.

• 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.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.525-534
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• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Steel and Composite Structures
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• 제45권3호
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• pp.349-367
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• 2022

In this research, an approach combining a semi-analytical method and an analytical method is presented to investigate the static and dynamic post-buckling behavior of the sandwich functionally graded (FG) porous cylindrical shells exposed to external pressure. The sandwich cylindrical shell considered is composed of a viscoelastic core and two FG porous (FGP) face layers. The viscoelastic core is made of Kelvin-Voigt-type material. The material properties of the FG porous face layer are considered continuous through each face thickness according to a porosity coefficient and a volume fraction index. Two types of sandwich FG porous viscoelastic cylindrical shells named Type A and Type B are considered in the research. Type A shell has the porosity evenly distributed across the thickness direction, and Type B has the porosity unevenly distributes across the thickness direction. The FG face layers are considered in two cases: outside metal surface, inside ceramic surface (OMS-ICS), and inside metal surface, outside ceramic surface (IMS-OCS). According to Donnell shell theory, von-Karman equation, and Galerkin's method, a discretized nonlinear governing equation is derived for analyzing the behavior of the shells. The explicit expressions for static and dynamic critical buckling loading are thus developed. To study the dynamic buckling of the shells, the governing equation is examined via a numerical approach implementing the fourth-order Runge-Kutta method. With a procedure presented by Budiansky-Roth, the critical load for dynamic post-buckling is obtained. The effects of various parameters, such as material and geometrical parameters, on the post-buckling behaviors are investigated.

• Steel and Composite Structures
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• 제3권1호
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• pp.1-12
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• 2003

Cantilevers are unique statically determinate structural elements with respect to their mode of overall buckling, in that the tension flange is the critical flange under gravity loading, and is the flange that deflects greatest during overall buckling. While this phenomenon does not complicate the calculation of the lateral buckling load, either theoretically or in structural design codes, it has been shown in previous research that the influence of distortion in the elastic buckling of cantilevers is not the same as that experienced in the elastic buckling of simply supported beams. This paper extends the study of the distortional buckling of cantilevers into the hitherto unconsidered inelastic range of structural response. A finite element method for studying the inelastic bifurcative instability of members whose cross-sections may distort during buckling is described, and the efficacy of the method is demonstrated. It is then used to study the inelastic distortional buckling of hot-rolled I-section cantilevers with two common patterns of residual stresses, and which may be restrained elastically from buckling by other structural elements.

• Steel and Composite Structures
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• 제29권3호
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• pp.405-422
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• 2018

In this research, experimental tensile test and manufacturing of carbon nanotube reinforced composite beam (CNTRC) is presented. Also, bending, buckling, and vibration analysis of CNTRC based on various beam theories such as Euler-Bernoulli, Timoshenko and Reddy beams are considered. At first, the experimental tensile tests are carried out for CNTRC and composite beams in order to obtain mechanical properties and then using Hamilton's principle the governing equations of motion are derived for Euler Bernoulli, Timoshenko and Reddy theories. The results have a good agreement with the obtained results by similar researches and it is shown that adding just two percent of carbon nanotubes increases dimensionless fundamental frequency and critical buckling load as well as decreases transverse deflection of composite beams. Also, the influences of different manufacturing processes such as hand layup and industrial methods using vacuum pump on composite properties are investigated. In these composite beams, glass fibers used in an epoxy matrix and for producing CNTRC, CNTs are applied as reinforcement particles. Applying two percent of CNTs leads to increase the mechanical properties and increases natural frequencies and critical buckling load and decreases deflection. The obtained natural frequencies and critical buckling load by theoretical method are higher than other methods, because there are some inevitable errors in industrial and hand layup method. Also, the minimum deflection occurs for theoretical methods, in bending analysis. In this study, Young's and shear modulli as well as density are obtained by experimental test and have not been used from the results of other researches. Then the theoretical analysis such as bending, buckling and vibration are considered by using the obtained mechanical properties of this research.

• Composites Research
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• 제12권3호
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• pp.55-65
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• 1999

형상기억합금 선을 삽입한 복합적층 보의 열좌굴 및 좌굴후 거동을 해석 및 실험적으로 고찰하였다. 균일한 온도분포, 양단고정 상태에서 형상기억합금 선을 삽입한 복합적층 보의 열좌굴 거동을 나타내었고 검토하였다. 삽입한 형상기억합금 선의 형상회복력은 복합적층 보의 열팽창 변형률을 감소시킴으로써 임계좌굴온도를 증가시키고 좌굴후 거동에서 횡방향 변형을 감소시키는 결과를 얻을 수 있었다. 형상회복력이 열좌굴에 미치는 영향을 온도-하중-횡방향 변위의 거동결과에서 세장비, 기하학적 초기결함, 형상기억합금 선의 삽입 위치 등의 설계변수를 고려하여 정량적으로 나타내었다. 온도-횡방향 변형의 결과로부터 임계좌굴온도를 구하는 접선교차점의 방법을 제안하였다. 열좌굴 및 좌굴후 거동에서 실험결과의 해석을 바탕으로 형상회복력이 임계좌굴온도에 미치는 영향을 나타내는 이론적인 식을 제시하였다.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.439-455
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• 2019

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

• 해양환경안전학회지
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• 제20권4호
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• pp.451-460
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• 2014

본 연구에서 해양플랜트 구조물에 주로 사용하고 있는 알루미늄 합금 A6082-T6의 재료특성을 반영한 사각형 판에 대한 패치 로딩의 구조 안정성 문제를 검토하였다. 구조 안정성 문제를 검토 시 네 가지 패치 로딩 형태와 종횡비 효과, 주변지지조건을 적용하여 임계 탄성 좌굴하중을 산출하였다. 고유치 좌굴해석 간 사용한 요소는 4절점 쉘요소 shell181을 적용하였다. 패치 로딩을 받는 판은 균일 축 압축하중과 비교 시 상이한 탄성 좌굴거동이 발생되는 것을 관찰할 수 있었으며 하중형태와 위치, 종횡비 효과 등과 같은 변수에 대해 상당히 영향을 받고 있는 것을 확인할 수 있다. 또한, 종횡비(a/b) 1.0, 하중길이(${\gamma}b$) 200 mm 단순지지 사각형 판에서 패치 로딩 형태에 따른 임계 탄성좌굴하중은 67 %(하중 I), 119 %(하중 II), 76 %(하중 III), 160 %(하중 IV)이 각각 산출되었으며 하중 I과 III은 하중 II와 IV보다 훨씬 더 탄성 좌굴거동에 강한 것으로 판단할 수 있다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2009년도 춘계학술대회 논문집
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• pp.161-162
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• 2009