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Journal ArticleDOI

Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation

23 Mar 2018-Journal of Applied Mechanics and Technical Physics (Pleiades Publishing)-Vol. 59, Iss: 1, pp 176-184
TL;DR: In this article, the postbuckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler-Pasternak foundation is studied.
Abstract: The problem of the post-buckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler–Pasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.
Citations
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Journal ArticleDOI
TL;DR: In this article , a generalized base model is selected that contains two independent bed coefficients: stiffness for tensile (compressive) and shear deformations, and the model assumed dependence on the transverse midline beam and its gradient displacement.
Abstract: The paper considers dynamic behavior of a track structure, which is a beam performing bending vibrations and lying on the elastic foundation. In this case, a generalized base model is selected that contains two independent bed coefficients: stiffness for tensile (compressive) and shear deformations. Such a model takes into account the soil distributive ability, i.e., its property to settle not only under the loaded area and the foundation, but also in its vicinity. In addition,to describe the foundation stiffness nonlinear properties, the model assumed dependence on the transverse midline beam and its gradient displacement. Results analysis of the wave processes in the beam showed that, since bending waves had strong dispersion, solution to the problem in the presence of weak nonlinearity was close to solution of a linear problem, and it could be represented as a set of quasi-harmonics. Using the Lighthill criterion, conditions modulation instability manifestation (self-modulation) of the quasi-harmonic waves, which led to their spatial localization and division into separate wave packets, were studied. Analytical expressions were found that described the wave packets shapes. Dependences connecting the amplitude and the wave packet width with the elastic foundation rigidity were analyzed
Journal ArticleDOI
TL;DR: In this paper , the exact stress distribution of simply supported beams of any thickness is determined by performing a Fourier sine series expansion upon the bottom and top surfaces of the beam.
Abstract: Orthotropic materials and components are widely used in various engineering fields, such as aerospace, energy, infrastructure, and water conservancy projects. The orthotropic components such as slabs and beams cannot be investigated accurately by using traditional beam theory because it is unable to take more elastic constants into account. The precise stress distribution of orthotropic simply supported beams of any thickness is determined in this article. Meanwhile, all undetermined coefficients of the stress function are derived by performing a Fourier sine series expansion upon the bottom and top surfaces of the beam. It shows that the resolution corresponds well with the numerical analysis findings from the finite element method. It indicates rapid convergence and can obtain high-precision and high stress analysis results, which has a good application prospect in engineering.
References
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Journal ArticleDOI
TL;DR: In this article, the authors present a state-of-the-art report on the use of Generalized Beam Theory (GBT) to assess the buckling behavior of plane and space thin-walled steel frames.
Abstract: This paper presents a state-of-the-art report on the use of Generalised Beam Theory (GBT) to assess the buckling behaviour of plane and space thin-walled steel frames After a very brief overview of the main concepts and procedures involved in performing a GBT buckling analysis, one addresses the development and numerical implementation of a GBT-based beam finite element formulation that is able (i) to unveil local, distortional and global buckling modes, (ii) to handle arbitrary loadings (namely those causing non-uniform member internal force and moment diagrams) and (iii) to incorporate the presence of several frame joint configurations and arbitrary end and/or intermediate support conditions (including those associated with the modelling of bracing systems) In particular, one describes the procedures employed to establish the frame linear and geometric stiffness matrices – special attention is paid to the constraint conditions adopted to ensure the local displacement compatibility at the frame joints The paper closes with the presentation and discussion of a number of numerical results that make it possible to illustrate the application and show the potential of the GBT-based approach to perform frame buckling analyses – they concern both plane and space frames In order to validate and assess the numerical efficiency and accuracy of the GBT analyses and results (critical buckling loads and mode shapes), the frames are also rigorously analysed in the commercial code A nsys – both the members and joints are discretised by means of fine shell finite element meshes

99 citations

Journal ArticleDOI
TL;DR: In this article, a direct 1D model able to describe the mechanical behaviour of thin-walled beams is used to analyse the initial postbuckling of some sample frames, which allows to take into account the boundary conditions on warping in a very simple way.
Abstract: A direct 1D model able to describe the mechanical behaviour of thin-walled beams is used to analyse the initial postbuckling of some sample frames. The model allows to take into account the boundary conditions on warping in a very simple way and proves to be a very efficient tool for the analysis of thin-walled frames. Making use of the FEM based COMSOL multiphysics software, numerical results for a number of L frames are obtained and shown.

51 citations

Journal ArticleDOI
TL;DR: In this article, a direct one-dimensional beam model suitable for describing the buckling of thin-walled structures is presented. But the model is not suitable for the case of a two-bar Roorda frame.
Abstract: We present two applications of a direct one-dimensional beam model suitable for describing the buckling of thin-walled structures. The first application considers the buckling of a compressed beam with an intermediate stiffener under various warping constraints. The second describes the buckling of a two-bar frame, known as a Roorda frame, loaded by a dead force at the joint. Various warping constraints at the bar ends are considered and the relevant buckling modes and loads are numerically evaluated. Numerical results are presented for both cases; some of these appear to be new.

46 citations

Journal ArticleDOI
TL;DR: In this paper, a non-linear thin-walled beam theory for elastic beams of open section is presented, which takes into account geometric nonlinearities and longitudinal deformations caused by large cross-sectional rotation of the beam.

42 citations

Journal ArticleDOI
01 Jan 1979
TL;DR: The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated in this article by means of the general nonlinear theory of elastic stability, and it is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one.
Abstract: The postbuckling behavior of simply supported columns with thin-walled open cross section is investigated by means of the general nonlinear theory of elastic stability. Fourth-order terms in the series expansion of the total potential energy are disregarded. It is shown that interaction between linearly independent simultaneous buckling modes is responsible for neutral equilibrium at bifurcation if the column cross section has two axes of symmetry, and unstable if it has only one. If the buckling modes are not simultaneous, the equilibrium is neutral in both cases. Finally, the equilibrium at bifurcation is usually unstable if the cross section has no axis of symmetry.

38 citations