Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories

A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate

Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory

http://nrl.northumbria.ac.uk/13388/1/Thai_Vo_MS2274.pdf

Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (ez ≠ 0) is also included in the present theory Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors The neutral surface position for such beams in which the material properties vary in the thickness direction is determined Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses

Mechab Ismail

Papers

A theoretical analysis of flexional bending of Al/Al2O3 S-FGM thick beams