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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 this paper, stability analysis of thin-walled functionally graded (FG) sandwich box beams under combined bending and axial forces was carried out. Based on higher order theory that includes sectional distortion and warping, a nonlinear displacement field of closed cross-section is adopted. The energy principle is applied in the context of elastic behavior of materials. Simple power-law is used to adjust the material properties in the thickness direction of each wall of FGM box beam. Ritz's method is adopted to obtain the nonlinear coupled equilibrium equations, and then the critical loads are obtained by means of the corresponding tangent stiffness matrix. A Finite Element simulation performed with the code ABAQUS software is used to verify the efficiency and accuracy of the present approach in lateral torsional buckling predictions. The effects of the power-law index and skin–core-skin thickness ratios on the critical loads of FG sandwich box beams are presented through several case studies. Moreover, the numerical solutions show that the previous effects play a significant role in the stability analysis of FG sandwich box beams. [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]

The objective of this research is to investigate nonlinear elastic foundation effects on the damping characteristics and forced vibrations of sandwich beam, in which a viscoelastic layer is positioned between two identical elastic layers. The analytical formulation takes into account both normal and shear deformations in the core by employing the interlaminar continuous shear stress Zig–Zag Theories (IC-ZZT). The coupling of geometric nonlinearity results in a nonlinear frequency–amplitude equation, which is influenced by several complex coefficients. The paper's first section focuses on determining the linear and nonlinear damping parameters for laminated composite beams. In the second part, a nonlinear forced vibration analysis is conducted, considering both small and large vibration amplitudes. Results show that the nonlinear elastic foundation coefficients have a significant effect on the damping and nonlinear vibration response of sandwich beams. [ABSTRACT FROM AUTHOR]

In the present investigation, nonlinear forced vibration analyses of porous functionally graded material viscoelastic sandwich beams are studied. The analytical formulation takes into account normal and shear strains in the core layer by employing the higher-order Zig-Zag theories. The sandwich structure consists of FGM faces that exhibit porosities, while the core layer is composed of viscoelastic material. The proposed model is developed in the frequency domain, by incorporating the material properties of the viscoelastic material through complex numbers. The introducing of the geometric nonlinearity effect results in a sixth-order frequency-amplitude equation, affected by numerous intricate coefficients. This equation was resolved using the balanced harmonic method in conjunction with a one-mode Galerkin's method to predict damping and frequency response curves. These latters are presented and discussed for several geometrical and mechanical sandwich beams configuration. The parametric study is specifically aimed at delineating the influence of the FGM parameters of the face sheets, particularly, the power-law index and the porosity parameter on the response curves and the variation of the nonlinear loss factor with the amplitude of vibration. [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]

Purpose: This paper focuses on the analysis of non-linear forced vibrations of a sandwich beam with a viscoelastic core layer. The analytical formulation considers normal, transverse, and shear deformations in the core layer by utilizing the refined higher-order zig-zag theory (HZZT). Method: The Ritz's method coupled to the modal transformation was employed to derive the nonlinear differential equations of motion. In order to investigate superharmonic resonance cases, the perturbation technique was applied to the equation of motion, and analytical frequency-amplitude relationships were obtained using the multiple scale method. This model is commonly applied to describe materials exhibiting both elastic and viscous characteristics. Results: The frequency response curves, which depict superharmonic resonance behaviour were analyzed and commented upon by varying the material characteristics of the viscoelastic core layer and the geometric parameters of the sandwich beams. Particular attention was given to assessing the influence of the transverse stress on the response curves. [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]

In this paper, the nonlinear buckling analysis of rectangular hollow sections (RHS) beams considering distortional and the shear flexibility deformation effects is investigated. The kinematic model is based on the incorporation of non-classical terms, related to shear flexibility, according to Timoshenko model and distortion and warping. This analysis is carried out by proposing a new 3D finite element, formulated in the context of large torsion, incorporating flexural torsion, and distortion coupling effects. A 3D RHS beam element with two nodes and eleven degrees of freedom per node is proposed to perform the nonlinear buckling analysis. For this aim, the arc-length method is employed as a solution strategy to solve the nonlinear equilibrium equations, established as a function of the trigonometric functions of the twist angle. Many examples are proposed to check the validity of the proposed 3D finite element and the numerical procedure, either in pre-and post-buckling states. The present numerical results are compared to those of the commercial software ABAQUS using the brick finite elements. The incidences of the compressive load and the incorporated lateral stiffeners in the RHS beams in pre- and post-buckling behaviour are studied. [ABSTRACT FROM AUTHOR]

Summary: In the present paper, a constitutive viscoelastic model for periodic masonry structures is proposed. Using a dynamic homogenization approach of the continuous and discrete‐based model leads to the determination of the anisotropic material properties by assigning the fictitious stress and strains of the homogeneous cell masonry unit. These properties are defined as complex moduli, which consist of real parts representing elastic stiffness and imaginary ones referring to energy dissipations. The advantage of the proposed model is that the damping properties associated to different modes of vibrations can be easily evaluated. Numerical and parametric investigations are conducted that reveal the capabilities of the model to an accurate prediction of the dynamic properties of the masonry walls mainly under both in‐plane and out‐of‐plane vibrations. [ABSTRACT FROM AUTHOR]

This paper treats the distortional and shear deformation effects on the elastic lateral torsional buckling of thin-walled box beam elements, under combined bending and axial forces. For the purpose, a nonlinear kinematic model based on higher order theory is used applicable to both short and long thin-walled box beams. Because in the kinematic model of the higher order theory integrates additional flexibility terms related to shear, distortion and warping effects, it accurately predicts the lateral torsional buckling of the straight box beams. Ritz's method is adopted as solution strategy in order to obtain the nonlinear governing equilibrium equations, then the buckling loads are computed by solving the eigenvalue problem basing on the singularity of the tangential stiffness matrix. Owing to flexural–torsional and distortional couplings, new matrices are obtained in both geometric and initial stress parts of the tangent stiffness matrix. The proposed method with the new stiffness terms, is efficient and accurate in lateral torsional buckling predictions, when compared with the commercial FEM code ABAQUS results. Based on the existing European guidelines EC3, an extensive numerical investigation is performed to demonstrate the effects of both shear and distortional deformations on the moment carrying capacity. The convenience of the model is outlined and the limit of models developed without shear and distortion deformation effects on lateral buckling loads evaluation is discussed. [ABSTRACT FROM AUTHOR]

External bonding of FRP plates or sheets has emerged as a popular method for strengthening reinforced concrete structures. Debonding along the FRP-concrete interface can lead to premature failure of the structures. Shear and normal stresses (in the thickness direction) at interfaces (referred to as interfacial shear and transverse normal stresses hereafter) have played a significant role in understanding this premature debonding failure of such hybrid structures. Extensive experimental and analytical analyses have been undertaken to investigate this problem. Large discrepancies have been found from various studies. This paper reports a closed-form formulation for interfacial stresses in plated beams. The analysis is based on the deformation compatibility approach developed by Tounsi and Benyoucef [8] where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The composite plate with variable fiber spacing bonded to reinforced concrete beam is considered in the present study. In addition, an unrealistic restriction of the same curvatures in the RC beam and FRP panel commonly used in most of the existing studies is released in the present theoretical formulation. Compared with previously published analytical results, this one improves the accuracy of predicting the transverse normal stresses and the solution remains a closed form. [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]

An analytical method is presented for the three-dimensional frequency analysis of buildings braced by shear walls and thin-walled open-section structures. Owing to the asymmetry of the structure, the centre of gravity and the centre of flexural rigidity of the floor plan do not coincide, and hence the flexural vibration in two mutually perpendicular directions and the warping torsional vibrations are all coupled. Based on the continuum approach and D'Alembert's principle, the governing differential equation of free vibration and its corresponding eigenvalue problem for asymmetric shear walls and thin-walled open-section structures are derived. Based on the theory of differential equations, an analytical method of solution is proposed to solve the eigenvalue problem and a general solution is derived for determining the natural frequencies of the structures. Results obtained from the proposed method for the example structure show good agreement with those of finite element analysis. It is also shown that the proposed analysis is efficient and accurate enough to be used both at the concept design stage and for final analysis. [ABSTRACT FROM AUTHOR]