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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]

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]

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]