Bending Analysis of Cantilever Micro-Beams Based on Strain Gradient Elasticity Theory

Abstract:

The bending deformation problem of cantilever micro-beams is solved analytically on the basis of strain gradient elasticity theory. The governing equations and boundary conditions are obtained by using Hamiltons principle. The size effect on deflections of the cantilever micro-beams is analyzed. It is found that the deflections of the cantilever micro-beams predicted by the newly model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is assessed.

• Periodical: Advanced Materials Research (Volumes 694-697)
• Pages: 172-175
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.694-697.172
• Online since: May 2013
• Authors: Sheng Li Kong
• Keywords: Size Effect, Strain Gradient Theory, Variational Principle

References

[1] D.C.C. Lam, F. Yang and A.C.M. Chong: J. Mech. Phys. Solids. Vol. 51 (2003), p.1477

[2] A.W. McFarland, J.S. Colton: J. Micromech. Microeng. Vol. 15 (2005), p.1060

[3] K.Z. Huang: Constitutive Relations of Solids (Tsinghua University Press, China 1999)

[4] R.A. Toupin: Arch. Ration. Mech. An. Vol. 11 (1962), p.385

[5] N.A. Fleck, G.M. Muller and M.F. Ashby: Acta Metall. Mater. Vol. 42 (1994), p.475

[6] F. Yang, A.C.M. Chong and D.C.C. Lam: Int. J. Solid Struct. Vol. 39 (2002), p.2731

[7] C.L. Dym, I.H. Shames: Solid Mechanics: a Variational Approach (China Railway Publishing House, China 1984), (in Chinese)