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The aim of the present study is to develop an efficient and accurate analytical model for the lateral torsional buckling (LTB) prediction of RHS beams. To this end, a coherent nonlinear geometric theory is formulated assuming large torsion angles. This theory is based on a new kinematic model that incorporates the distortion deformations in addition to the bending and torsion ones. Ritz's method is employed to discretize the governing equilibrium equations basing on trigonometric shape functions, and then the eigenvalue problem is defined according to the fundamental state. The Buckling loads are obtained by imposing the singularity condition of the tangential stiffness matrix. The numerical investigation is carried out to prove the accuracy of the proposed model in LTB load evaluation, when compared with the nonlinear shell finite element simulation using Abaqus software. The numerical results reveal that the classical linear models associated with moderate torsion angles, such as those provided by Generalized Beam Theory (GBT) and the classical eigenvalue shell finite element method, tend to underestimate the correct value of LTB loads of simply supported RHS beams. In accordance with linear and non‐linear models, the numerical study is focused on the impact of load height, intensity of introduced compressive load and section ratio b/h in the LTB loads prediction. [ABSTRACT FROM AUTHOR]

We develop a new analytical and numerical approach, based on existing models, to describe the onset of lateral–torsional buckling (LTB) for simply supported thin-walled steel members. The profiles have uniform I cross-sections with variable lengths of the flanges, to describe also H cross-sections, they are prestressed by external tendons, and they are subjected to fire and various loadings. Our approach manages to update the value of the prestressing force, accounting for thermal and loads; the critical multipliers result from an eigenvalue problem obtained applying Galërkin's approach to a system of nonlinear equilibrium equations. Our results are compared to buckling, steady state, and transient state analyses of a Finite Element Method (FEM) simulation, in which an original expression for an equivalent thermal expansion coefficient for the beam–tendon system that accounts for both mechanical and thermal strains is introduced. Our aim is to find estimates for the critical conditions with no geometric imperfections and accounting for the decay of material properties due to fire, thus providing limit values useful for conservative design. This approach can surpass others in the literature and in the existing technical norms. [ABSTRACT FROM AUTHOR]

In the present article, an analytical model is proposed to assess the nonlinear damping and frequency curves of the three layered sandwich beams, constituted with FGM faces and viscoelastic core layers. The proposed analytical model is formulated in the context of forced vibration analysis. The kinematical model developed for the purpose is based on the higher order zig-zag theories coupled with the higher order shear deformation theory (HSDT), employing shear functions, formulated by Timoshenko, Reddy, and Touratier. The frequency response curves and the nonlinear loss factors are provided by resourcing to analytical solution, derived from the harmonic balance technique coupled with the one mode of Galerkin's method. The elastic moduli of the viscoelastic material are described with complex numbers in the frequency domain. The material proprieties of the FGM beams vary gradually along the thickness direction, transiting from metal to ceramic materials. The effect of the geometrical and material parameters of the FGM and viscoelastic composite layers on the damping and frequency response curves of the sandwich beams are studied according to the first and higher-order shear deformation theories. Basing on the proposed analytical model, numerical results are presented to study the effect of the FGM parameters and the fiber orientation angle of the composite core on the nonlinear damping evolution with the vibration amplitude and the frequency curves. [ABSTRACT FROM AUTHOR]

This work deals with the damping and vibration characteristics evaluation of sandwich beams based on higher-order shear deformation theories (HSDT's). The studied sandwich beams are composed of composite materials at faces and homogeneous, isotropic viscoelastic material in the core layer. This latter (viscoelastic material) is described by complex Young's modulus in the frequency domain. Indeed, the real part represents the stiffness, and the imaginary one describes the damping property. Nonlinear damping parameters and frequency curves are obtained using the nonlinear equation of frequency amplitude governed by multiple complex coefficients. In conjunction with a one-mode Galerkin's procedure, the harmonic balance method is employed to obtain the nonlinear loss factor and the response frequency curves. The nonlinear frequency value and, in turn, the system loss factor ratio are obtained for various amplitudes to examine the impacts of the ply angle of fiber-reinforced composite faces, the viscoelastic shear modulus, the shear deformation model, for considering different geometric and material parameters. In the framework of this study, one attempt is to describe a better way to achieve satisfactory passive vibration control of the laminated beams. [ABSTRACT FROM AUTHOR]

In this study, the finite element approach for linear vibration analysis of FGM beams under various thermal loads is investigated. The formulation is developed by using CPT, FSDT and HSDT kinematical models, in conjunction with the Hamilton's principle to obtain the governing equations of motion. Following, one-dimensional finite element that integrating shear and thermal stress is formulated for free vibration analysis. Based on the obtained results, a conceptual analysis is conducted to assess the effects of shear deformation, aspect ratio and thermal effect on fundamental frequencies of FGM beams, under various boundary conditions. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical investigation in free vibration of a functionally graded beam (FGB) which has a variable cross-section. It is assumed that material properties vary along the beam thickness only according to exponential distributions (it is simply called E-FGB). The governing equation is reduced to an ordinary differential equation in spatial coordinate for a family of cross-section geometries with exponentially varying width. Analytical solutions of the natural frequencies are obtained for E-FG beams with clamped-free, hinged-hinged, and clamped-clamped end supports. Results show that the non-uniformity in the cross-section and the inhomogeneity in material properties influence the natural frequencies. It is also shown that, all other parameters remaining the same, the natural frequencies of E-FG beams are always proportional to those of homogeneous isotropic beams. Therefore, one can predict the behaviour of E-FG beams knowing that of similar homogeneous beams. [ABSTRACT FROM PUBLISHER]

This work aims to examine the stability of rectangular hollow section (RHS) beams with functionally graded (FG) thin walls that are subjected to thermo-mechanical loads and different boundary conditions. A nonlinear analytical model for predicting thermal buckling that introduces distortional deformation and takes porosity into account is presented. Using Ritz’s method, coupled nonlinear equilibrium equations are established and then the tangential matrix is formed to obtain critical values. Material properties vary continuously and progressively across the thickness according to a power law of the porous volume fraction and are assumed to be unrelated to the temperature. A finite element (FE) simulation using the FE ABAQUS software is employed to verify the applicability of the current model in predicting lateral torsional buckling (LTB) resistance. Several numerical examples are used to illustrate the impacts of temperature, porosity, power-law index, and axial loads on the instabilities of FG box beams. [ABSTRACT FROM AUTHOR]