Analytical solutions for bending, buckling, and vibration analyses of exponential functionally graded higher order beams

• DOI: 10.1007/s42107-018-0046-z
• Publication Date: 2018-05-10T06:17:11Z
• Authors: Atteshamuddin S. ...; Yuwaraj M. Ghugal
• Keywords: 0203 mechanical engineering; 02 engineering and technology; 0210 nano-technology

A simple modified exponential shear deformation theory (ESDT) is developed and applied for the bending, buckling, and free vibration analyses of functionally graded beams with different boundary conditions. The properties of functionally graded material are assumed to vary through the thickness direction according to power law (P-FGM) and exponential law (E-FGM). The present theory is different from existing theories, because in the present theory, the transverse displacement consists of bending and shear components to understand the contribution of transverse displacement due to bending and due to shear separately. The developed theory accounts for higher order variation of transverse shear stress through the thickness of the beam, and satisfies the traction-free conditions on the top and bottom surfaces of the beam. The theory appropriately represents the strain energy of shear deformation without using shear coefficient. Equations of motion and associated boundary conditions are derived from Hamilton’s principle. Closed-form solutions for various boundary conditions are obtained, and the numerical results are compared with those available in the literature. The present study contributes some new results on the P-FGM and E-FGM beams for the reference of future research in this area.