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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]