• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Journal of Mechanical Science and Technology
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• v.19 no.11
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• pp.2016-2024
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• 2005

In this work, a mixed beam approach that combines both the stiffness and the flexibility methods has been performed to analyze the coupled composite blades with closed, two-cell cross-sections. The Reissner's semi-complementary energy functional is used to derive the beam force-displacement relations. Only the membrane part of the shell wall is taken into account to make the analysis simple and also to deliver a clear picture of the mixed method. All the cross section stiffness coefficients as well as the distribution of shear across the section are evaluated in a closed-form through the beam formulation. The theory is validated against experimental test data, detailed finite element analysis results, and other analytical results for coupled composite blades with a two-cell airfoil section. Despite the simple kinematic model adopted in the theory, an accuracy comparable to that of two-dimensional finite element analysis has been obtained for cases considered in this study.

• Structural Engineering and Mechanics
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• v.13 no.5
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• pp.533-542
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• 2002

This paper considers the buckling and post-buckling behavior of empty metal storage tanks under wind load. The structures of such tanks may be idealized as cantilever cylindrical shells, and the structural response is investigated using a computational model. The modeling employs a doubly curved finite element based on a theory by Simo and coworkers, which is capable of handling large displacements and plasticity. Buckling results for tanks with four different geometric relations are presented to consider the influence of the ratios between the radius and the height of the shell (R/L), and between the radius and the thickness (R/t). The studies aim to clarify the differences in the shells regarding their imperfection-sensitivity. The results show that thin-walled short tanks, with R/L = 3, display high imperfection sensitivity, while tanks with R/L = 0.5 are almost insensitive to imperfections. Changes in the total potential energy of tanks that would buckle under the same high wind pressures are also considered.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.6
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• pp.133-139
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• 2000

Vibrational characteristics of the vehicle structure are mainly influenced by the shape of the pillar cross section. In this paper a vehicle structural optimization technique has been developed to investigate a lightweight vehicle structure subject to constraints on natural frequencies in a simple beam-and-shell model. In this technique, the optimization procedures involve two stages. In the first stage, the section procedures involve tow stages. In the first stage, the section properties of beam elements of the vehicle structure has been optimized to have minimum weight while satisfying the constraints of natural frequencies. And, in the second stage, the shape of the cross section of the elements of the structure has been determined.

• International Journal of Aeronautical and Space Sciences
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• v.16 no.2
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• pp.206-222
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• 2015

This work uses different finite element approaches to the free vibration analysis of reinforced shell structures, and a simplified model of a typical launcher with two boosters is used as an example. The results obtained using a refined one-dimensional (1D) beam model are compared to those obtained with commercial finite element software. The 1D models that are used in the present work are based on the Carrera Unified Formulation (CUF), which assumes a variable kinematic displacement field over the cross-sections of the beam. Two different sets of polynomials that correspond to Taylor (TE) or Lagrange (LE) expansions were used. The analyses focused on three reinforced structures: a stiffened panel, a reinforced cylinder and the complete structure of the launcher. The frequencies and natural modes obtained using one-dimensional models are compared to those obtained from classical finite element analysis. The classical FE models were built using a beam-shell or solid elements, and the results indicate that the refined beam models can in fact be used to investigate the behavior of very complex reinforced structures. These models can predict the shell-like modes that are typical of thin-walled structures that cannot be detected using classical beam models. The refined 1D models used in the present work provide results that are as accurate as those from solid FE models, but the 1D models have a much lower computational cost.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2007.12a
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• pp.25-26
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• 2007

Ship are typically thin-walled structures and consists of stiffened plate structure by purpose of required design load and weight reduction etc. Also, a hull structural characteristics are often used in structures with curvature at deck plating with camber, side shell plating at fore and aft parts and bilge circle parts, It have been believed that these structures can be modelled fundamentally by a part of cylinder. Structural component with curvature subjected to combined loading regimes and complex boundary conditions, which can potentially collapse due to buckling. Hence, for more rational and safe design of ship structures, it is crucial importance to better understand the interaction relationship of the buckling and ultimate strength for cylindrically curved plate under these load components. In this study, the ultimate strength characteristic of curved plate under combined load(lateral pressure load + axial compressive load) are investigated through using FEM series analysis with varying geometric panel properties.

• Composites Research
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• v.14 no.6
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• pp.9-15
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• 2001

In the present work, a linear static analysis is presented for thin-walled prismatic box-beams made of generally anisotropic materials. A mixed beam theory has been used to model and carry out the analysis. Several different constitutive assumptions for the shell-wall of the beam section are assessed into the beam formulation. Simple layup cases of box-beams representing bending-torsion or extension-torsion coupled configuration have been considered and tested to clearly show the effects of elastic couplings of the beam. A detailed finite element structural analysis using the MSC/NASTRAN has been carried out to validate the current analytical results. Numerical results show that appropriate assumptions for the constitutive relations are important and crucial for the accurate prediction of beam stiffness constants and also thor the beam behavior.

• Structural Engineering and Mechanics
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• v.43 no.4
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• pp.411-437
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• 2012

In this paper, we propose a continuum mechanics based 3-D beam finite element with cross-sectional discretization allowing for warping displacements. The beam element is directly derived from the assemblage of 3-D solid elements, and this approach results in inherently advanced modeling capabilities of the beam element. In the beam formulation, warping is fully coupled with bending, shearing, and stretching. Consequently, the proposed beam elements can consider free and constrained warping conditions, eccentricities, curved geometries, varying sections, as well as arbitrary cross-sections (including thin/thick-walled, open/closed, and single/multi-cell cross-sections). We then study the modeling and predictive capabilities of the beam elements in twisting beam problems according to geometries, boundary conditions, and cross-sectional meshes. The results are compared with reference solutions obtained by analytical methods and solid and shell finite element models. Excellent modeling capabilities and solution accuracy of the proposed beam element are observed.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.6 s.144
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• pp.631-636
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• 2005

One and three dimensional whipping response analyses of a naval surface combatant subjected to an underwater explosion bubble pulse were carried out to compare the efficiency and accuracy according to the modeling methods. In 1-D analysis, program UNDEXWHIP developed by KIMM was used, which is based on the thin-walled Timoshenko's beam theory and on the modal analysis method using wetted vibratory modes of the hull girder. In 3-D analysis, three finite element models were suggested using LS-DYNA/USA code, such as 3-D beam model considering geometric shape of wetted side shell, coarse and fine 3-D F.E. models. Through the comparison of results from the 1-D and 3-D analyses, it could be confirmed that 1-D analysis result is in good agreement with 3-D analysis ones, and that fine 3-D F.E. model, shock analysis one, is also used both in the shock response and whipping response analyses for the analyst effort and time savings.

• Steel and Composite Structures
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• v.30 no.5
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• pp.471-481
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• 2019

Beam-columns are structural members subjected to a combination of axial and bending forces. Lateral-torsional buckling is one of the main failure modes. Beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting as the values of the applied loads reach a limiting state. Lateral-torsional buckling failure occurs suddenly in beam-column elements with a much greater in-plane bending stiffness than torsional or lateral bending stiffness. This study intends to establish a unique convenient closed-form equation that it can be used for calculating critical elastic lateral-torsional buckling load of beam-column in the presence of a known axial load. The presented equation includes first order bending distribution, the position of the loads acting transversely on the beam-column and mono-symmetry property of the section. Effects of axial loads, slenderness and load positions on lateral torsional buckling behavior of beam-columns are investigated. The proposed solutions are compared to finite element simulations where thin-walled shell elements including warping are used. Good agreement between the analytical and the numerical solutions is demonstrated. It is found out that the lateral-torsional buckling load of beam-columns with mono-symmetric sections can be determined by the presented equation and can be safely used in design procedures.