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This paper presents a novel shear deformation theory for analyzing porous microbeams’ bending, buckling, and free vibration resting on a foundation. The proposed shear function incorporating three kinetic variables satisfies zero-traction boundary conditions on the top and bottom surfaces of the beams and does not require a shear correction factor. The modified couple stress theory accounts for the size-dependent effects, and the governing equations are derived from Lagrange’s equation using the proposed shear function. Legendre–Ritz functions are developed to analyze the porous microbeams’ buckling, free vibration, and bending behaviors. The effects of material length scale parameter, porosity, span-to-height ratio, boundary condition, and foundation parameter on the mechanical responses of beams are investigated. Numerical results demonstrate the accuracy and efficiency of the proposed theory and can serve as benchmarks for future analysis of porous microbeams on elastic foundations. [ABSTRACT FROM AUTHOR]

This article proposes static, free vibration, and buckling analysis of thin-walled functionally graded (FG) sandwich and composite channel-section beams. It is based on the first-order shear deformable beam theory, which can recover to classical one by ignoring the shear effect. Ritz's approximation functions are developed to solve the characteristic problems. Both results from classical and the first-order shear deformable theories are given in a unified fashion. Ritz solutions are applied for thin-walled FG sandwich channel-section beams for the first time. Numerical examples are presented in relation to many important effects such as span-to-height ratio, material parameter, lay-ups, fiber orientation and boundary conditions on the beams' deflections, natural frequencies, and critical buckling loads. New results presented in this study can be of interests to the scientific and engineering community in the future. [ABSTRACT FROM AUTHOR]

Abstract The paper proposes a Ritz-type solution for free vibration and buckling analysis thin-walled composite and functionally graded sandwich I-beams. The variation of material through the thickness of functionally graded beams follows the power-law distribution. The displacement field is based on the first-order shear deformation theory, which can reduce to non-shear deformable one. The governing equations of motion are derived from Lagrange's equations. Ritz method is used to obtain the natural frequencies and critical buckling loads of thin-walled beams for both non-shear deformable and shear deformable theory. Numerical results are compared to those from previous works and investigate the effects of fiber angle, material distribution, span-to-height's ratio, and shear deformation on the critical buckling loads and natural frequencies of thin-walled I-beams for various boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the Ritz-based solutions are developed for the bending, buckling and vibration behaviors of laminated composite beams with arbitrary lay-ups. A quasi-3D theory, which accounts for a higher-order variation of both the axial and transverse displacements, is used to capture the effects of both shear and normal deformations on the behaviors of composite beams. Numerical results for various boundary conditions are presented and compared with existing ones available in the literature. Besides, the effects of fiber angle, span-to-height ratio, material anisotropy and Poisson's ratio on the displacements, stresses, natural frequencies and buckling loads of the composite beams are investigated. [ABSTRACT FROM AUTHOR]

This paper proposes novel Ritz functions for the size-dependent analysis of micro laminated composite beams with arbitrary lay-ups. Displacement field is based on a higher-order deformation beam theory and size effect is captured by the modified couple stress theory. Lagrange’s equations are used to obtain the governing equations of motion. The present beam model, which can recover the classical one by neglecting the material length scale parameter, is used to predict the size-dependent responses of micro composite beams. The results indicate that the present study is efficient for bending, vibration and buckling problems of micro composite beams. Some new results are given to serve as benchmarks for future studies. [ABSTRACT FROM AUTHOR]

New hybrid shape functions for buckling and vibration analysis of laminated composite beams under thermal and mechanical loads are presented in this study. The displacement field of present work is based on a higher-order shear deformation beam theory. The governing equations of motion are derived from Lagrange’s equations. A Ritz solution is developed in which new hybrid shape functions based on a combination of admissible and exponential functions for various boundary conditions are proposed. Numerical results are presented to compare with those from earlier works, and to examine the influences of span-to-height ratio, boundary conditions, material anisotropy and temperature changes on the buckling load and natural frequency of laminated composite beams. [ABSTRACT FROM AUTHOR]

A new analytical solution based on a higher-order beam theory for static, buckling and vibration of laminated composite beams is proposed in this paper. The governing equations of motion are derived from Lagrange’s equations. An analytical solution based on trigonometric series, which satisfies various boundary conditions, is developed to solve the problem. Numerical results are obtained to compare with previous studies and to investigate the effects of length-to-depth ratio, fibre angles and material anisotropy on the deflections, stresses, natural frequencies and critical buckling loads of composite beams with various configurations. [ABSTRACT FROM AUTHOR]

This paper presents a simple two-variable shear deformation theory for bucking, bending, and vibration behaviours of functionally graded porous (FGP) beams. The displacement field of beams is developed from the separation of variables. Three typical porosity distribution types are considered. Mass density and elastic modulus of FGP beams are assumed to be graded in the beam's thickness. Governing equations are derived from Lagrange's principle. The exponential approximation functions are developed for various boundary conditions to predict frequency, buckling load, deflection, and stress of beams. The effects of boundary condition, span-to-height ratio, porous distribution pattern, porosity parameter, and shear deformation on the critical buckling load, frequency, deflection, and stress of beams are investigated in detail. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the moment modification factors of an I-girder with trapezoidal web corrugations under moment gradient and various end restraint conditions. The moment modification factors are obtained by using the finite element method with beam elements and new general formulas of cross-section properties as well as a new warping constant of the I-girder with trapezoidal web corrugations. The theoretical results of moment modification factors are successfully verified by comparing them with the results from the commercial finite element software using shell elements. A series of finite element analyses with different corrugation profiles and lengths are investigated. From the results, it is found that the present design of moment modification factor formulas cannot satisfactorily predict the buckling capacities of the I-girder with trapezoidal web corrugations under unequal end moments with various end restraint conditions. For the purpose of design, the closed-form expressions for the moment modification factors are proposed and successfully verified. [Copyright &y& Elsevier]

Abstract: Moment modification factors of the I-girder with trapezoidal web corrugations subjected to concentrated load, applied at different heights on the cross section and various end restraint conditions, are investigated. The moment modification factors are obtained by finite element buckling analyses. The new FEM program is developed by using beam elements and new general formulas of cross-section properties as well as a new warping constant of the I-girder with trapezoidal web corrugations. The theoretical results of moment modification factors are compared with commercial finite element software (ABAQUS) using shell elements. A series of finite element analyses with different corrugation profiles and lengths is performed. Through comparative numerical studies, the theoretical results are successfully verified. The moment modification factors from the SSRC Guide are compared with present FEM results. The new values of the variable C b , the moment modification factor, in the SSRC Guide are proposed as the variable C b,c to improve the accuracy of lateral–torsional buckling strength. [Copyright &y& Elsevier]

Abstract: While I-girders with trapezoidal web corrugations have been used in various structural applications and bridges, lateral torsion–flexure of I-girders with trapezoidal web corrugations still needs to be investigated, especially the general formulation for cross-section properties. This paper presents the results of theoretical and finite element analyses of the lateral-torsional buckling of an I-girder with trapezoidal web corrugations under uniform moment. By using the numerical equations and method, the location of shear center and warping constant are proposed. The elastic lateral-torsional buckling strength is then calculated via proposed cross-section properties. The results are compared with previous studies in the literature. A series of finite element analyses with different corrugation profiles and lengths are investigated and the results are compared with proposed formulas. Through comparative numerical studies, the proposed formulas are successfully verified. The effects of corrugation profiles on elastic lateral-torsional buckling strength are also investigated and discussed. [Copyright &y& Elsevier]

This paper proposes an improved first-order beam theory by separation of variables for bending and buckling analysis of thin-walled functionally graded (FG) sandwich I-beams resting on a two-parameter elastic foundation. By dividing the displacements into bending and shear parts, this model can produce the deflections for both two cases with and without shear effect. The mechanical properties of beams based on the power law distribution of volume fraction of ceramic or metal. Governing equations are established from Lagrange's equations. The new Ritz's approximation functions, which are combined between orthogonal polynomial and exponential functions, are proposed to solve problem. The deflections and critical buckling loads of thin-walled FG sandwich I-beams are presented and compared with those available literature to verify the present theory. The effects of material distribution, boundary conditions, length-to-height ratio, shear deformation and foundation parameters on the results are investigated in detail. [ABSTRACT FROM AUTHOR]

A general higher-order shear deformation theory for buckling and free vibration analysis of laminated thin-walled composite I-beams is proposed in this paper. It is based on a unified nonlinear variation of shear strains in the wall thickness and then theoretical formulation is derived in the general form which can recover the previous conventional theories such as classical and first-order thin-walled beam theory. Series-type solutions with hybrid shape functions are developed for different boundary conditions. Numerical examples are performed on laminated thin-walled composite I-beams with arbitrary lay-ups. Effects of transverse shear strains, fiber angles and slenderness ratio on the critical buckling loads and natural frequencies of the beams are reported. [ABSTRACT FROM AUTHOR]