Theories and Analysis of Functionally Graded Beams

This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Karman nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.

Automated summary

This review paper presents the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The theories account for through-thickness material variation, strain gradient effects, and nonlinearity. Analytical solutions for bending, some of which are not commonly available, demonstrate the influence of material variation, boundary conditions, and loads.