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.
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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
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.
01 Jul 2019
References
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TL;DR: In this paper, a thin walled bar is treated as a special case of the membrane shell with the internal constraints (Vlasov's and Wagner's assumptions), and the geometry of the bar is described by means of coordinates of the discrete points located on the midsurface of a bar.
Abstract: Instability of thin walled bars of variable, open cross sections is analyzed. A thin walled bar is treated as a special case of the membrane shell with the internal constraints (Vlasov’s and Wagner’s assumptions). The geometry of the bar is described by means of coordinates of the discrete points located on the midsurface of the bar. Principal coordinate system is assumed for the cross section. Large deformations of the cross section are analyzed in total Lagrangian formulation. Prebuckling strains are assumed to be small and the Green-Lagrange linearized tensor is used in strain analysis. The general, nonlinear formula for the strain tensor element ge\N\d2\d2 is obtained for the thin walled bars of variable, open cross sections. Special cases derived from this formula are in agreement with already known solutions. Numerical results are obtained by the use of the finite element approach. Stiffness and geometric matrices are constructed for a thin walled, variable element. Typical shape functions are used and a bifurcation point of stability is determined with the help of the eigenproblem solution.
37 citations
TL;DR: In this article, a set of kinematic assumptions and constraints are used to develop a formulation for the analysis of thin-walled beams, of arbitrary open cross-section, subjected to arbitrarily large displacements in three-dimensional space.
32 citations
TL;DR: In this article, energy equations governing the flexural, torsional, and lateral instability of thin walled bars of open cross section are derived, and solutions of the governing energy equations are obtained, by the finite element method, which agree with closed form solutions based on the governing differential equations.
Abstract: Energy equations governing the flexural, torsional, and lateral instability of thin walled bars of open cross section are derived. Shear deformations due to nonuniform bending, and distortion of the cross section are not considered, but the influence of pre‐buckling displacements is included in the analysis. Solutions of the governing energy equations are obtained, by the finite element method, which agree with closed form solutions based on the governing differential equations.
31 citations
TL;DR: In this paper, the behavior of axially compressed thin-walled I columns after torsional buckling is discussed and the initial postbuckling equilibrium paths are determined by utilizing a perturbation approach.
27 citations
Dissertation•
13 Jul 2007
TL;DR: Tese de doutoramento em Engenharia Civil (Mecânica das Estruturas e dos Materiais) apresentada a Fac. de Ciencias e Tecnologia de Coimbra as mentioned in this paper
Abstract: Tese de doutoramento em Engenharia Civil (Mecânica das Estruturas e dos Materiais) apresentada a Fac. de Ciencias e Tecnologia de Coimbra
24 citations