• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.

• Journal of Korean Society of Steel Construction
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• v.18 no.6
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• pp.687-696
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• 2006

An efficient numerical method is developed to estimate the elasto-plastic post-buckling strength of space-framed structures. The inelastic ultimate strength of beam-columns and frames is evaluated by the parametric study. Applying the improved plastic hinge analysis that evaluate the gradual stiffness decrease effects due to spread of plasticity, elasto-plastic post-buckling behavior of steel frames is investigated considering the various residual stress distributions. Introducing the plastification parameter that represent pread of plasticity in the element and performing parametric study of equivalent element force and member idealization, finite-element solutions for the elasto-plastic analysis of space frames are compared with the results by plastic region analysis, shell elements and experimental results.

• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.339-361
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• 2012

Large amplitude free vibration and thermal post-buckling of shear flexible Functionally Graded Material (FGM) beams is studied using finite element formulation based on first order Timoshenko beam theory. Classical boundary conditions are considered. The ends are assumed to be axially immovable. The von-Karman type strain-displacement relations are used to account for geometric non-linearity. For all the boundary conditions considered, hardening type of non-linearity is observed. For large amplitude vibration of FGM beams, a comprehensive study has been carried out with various lengths to height ratios, maximum lateral amplitude to radius of gyration ratios, volume fraction exponents and boundary conditions. It is observed that, for FGM beams, the non-linear frequencies are dependent on the sign of the vibration amplitudes. For thermal post-buckling of FGM beams, the effect of shear flexibility on the structural response is discussed in detail for different volume fraction exponents, length to height ratios and boundary conditions. The effect of shear flexibility is observed to be predominant for clamped beam as compared to simply supported beam.

• Journal of the Architectural Institute of Korea Structure & Construction
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• v.35 no.8
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• pp.139-148
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• 2019

The lightweight structures such as domes are particularly vulnerable when it has been subjected to high temperature induced by the fire. It is therefore crucial to predict the possible instability path of structures exposed to the fire in structural design process. In this study, the instabilities of single-layer domes is investigated by using finite element technologies with the consideration of high temperature. The material properties of members under high temperature are considered by using the reduction factors which is provided in Eurocodes 3. Some damage patterns are assumed with use of a structural unit which is symmetric in radial direction. For numerical evaluations, the geometrically nonlinear truss element is implemented and the arch-length control method is employed to trace the post-buckling behaviour of domes. From numerical results, it is found to be that a significant change of post-buckling behaviour is detected in dome structures when structural members are exposed to the fire.

• Advances in nano research
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• v.13 no.4
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• pp.393-406
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• 2022

In the present article, functionally graded small-scaled plates based on modified strain gradient theory (MSGT) are studied for analyzing the nonlinear bending and post-buckling responses. Von-Karman's assumptions are applied to incorporate geometric nonlinearity and the first-order shear deformation theory is used to model the plates. Modified strain gradient theory includes three length scale parameters and is reduced to the modified couple stress theory (MCST) and the classical theory (CT) if two or all three length scale parameters become zero, respectively. The Ritz method with Legendre polynomials are used to approximate the unknown displacement fields. The solution is found by the minimization of the total potential energy and the well-known Newton-Raphson technique is used to solve the nonlinear system of equations. In addition, numerical results for the functionally graded small-scaled plates are obtained and the effects of different boundary conditions, material gradient index, thickness to length scale parameter and length to thickness ratio of the plates on nonlinear bending and post-buckling responses are investigated and discussed.

• Advances in nano research
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• v.16 no.6
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• pp.623-638
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• 2024

This study investigates the thermal post-buckling behavior of concrete eccentric annular sector plates reinforced with graphene oxide powders (GOPs). Employing the minimum total potential energy principle, the plates' stability and response under thermal loads are analyzed. The Haber-Schaim foundation model is utilized to account for the support conditions, while the transform differential quadrature method (TDQM) is applied to solve the governing differential equations efficiently. The integration of GOPs significantly enhances the mechanical properties and stability of the plates, making them suitable for advanced engineering applications. Numerical results demonstrate the critical thermal loads and post-buckling paths, providing valuable insights into the design and optimization of such reinforced structures. This study presents a machine learning algorithm designed to predict complex engineering phenomena using datasets derived from presented mathematical modeling. By leveraging advanced data analytics and machine learning techniques, the algorithm effectively captures and learns intricate patterns from the mathematical models, providing accurate and efficient predictions. The methodology involves generating comprehensive datasets from mathematical simulations, which are then used to train the machine learning model. The trained model is capable of predicting various engineering outcomes, such as stress, strain, and thermal responses, with high precision. This approach significantly reduces the computational time and resources required for traditional simulations, enabling rapid and reliable analysis. This comprehensive approach offers a robust framework for predicting the thermal post-buckling behavior of reinforced concrete plates, contributing to the development of resilient and efficient structural components in civil engineering.

• Advances in nano research
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• v.4 no.1
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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.

• Earthquakes and Structures
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• v.16 no.5
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• pp.589-599
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• 2019

Conventional buckling restrained braces used in concentrically braced frames are expected to yield in both tension and compression without major degradation of capacity under severe seismic ground motions. One of the weakness points of a standard buckling restrained braced frame is the low post-yield stiffness and thus large residual deformation under moderate to severe ground motions. This phenomenon can be attributed to low post-yield stiffness of core member in a BRB. This paper introduces a multi-core buckling restrained brace. The multi-core term arises from the use of more than one core component with different steel materials, including high-performance steel (HPS-70W) and stainless steel (304L) with high strain hardening properties. Nonlinear dynamic time history analyses were conducted on variety of diagonally braced frames with different heights, in order to compare the seismic performance of regular and multi-core buckling restrained braced frames. The results exhibited that the proposed multi-core buckling restrained braces reduce inter-story and especially residual drift demands in BRBFs. In addition, the results of seismic fragility analysis designated that the probability of exceedance of residual drifts in multi-core buckling restrained braced frames is significantly lower in comparison to standard BRBFs.

• Journal of Korean Society of Steel Construction
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• v.19 no.6
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• pp.725-735
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• 2007

The local buckling strength and post-local buckling strength of thin steel plates in the steel-concrete composite column were evaluated by nonlinear finite element analyses. The proposed width-to-thickness limit ratio was based on elastic buckling analyses, in which the increased local buckling capacity of the plate due to the in-filled concrete was considered by the boundary conditions of the thin plate. Considering the initial imperfections and residual stresses, we determined the initial local buckling strength and post-local buckling strength of the thin plates with various width-to-thickness ratios. The formula to evaluate the compressive capacity of the steel-concrete composite column based on the effective width of the plate was proposed. For verification, values determined by the formula were compared with the experimental results.

• Journal of Korean Society of Steel Construction
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• v.20 no.3
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• pp.377-387
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• 2008

The post-buckling behavior of slender members, such as the chord of truss structures generally implies extreme strength degradation. The buckling strength is usually determined as the performance of the compressed steel members, so it is important to understand the exact buckling behavior of a member in order to design the entire structure. A target analytical model is usually divided by beam or shell element when we simulate the buckling behavior of a compressed steel member such as atruss member. In this case, it is possible to accurately obtain the behavior, but such would be expensive and would require experience inanalysis even in monotonic loading. In this paper, we propose a consistent and convenient method to analyze the post-buckling behavior of elastoplastic compression members. The present methods are formulated to satisfy the second law of thermodynamics. Three numerical examples were tested to determine the validity of the proposed model in cyclic loading with comparable F.E.M results.