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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]

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]

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]