Science and Engineering of Composite Materials (Apr 2018)

Exact solution for bending analysis of functionally graded micro-plates based on strain gradient theory

  • Mohammadi Meisam,
  • Iranmanesh Afshin,
  • Naseralavi Seyed Sadegh,
  • Farahmand Hamed

DOI
https://doi.org/10.1515/secm-2015-0415
Journal volume & issue
Vol. 25, no. 3
pp. 439 – 451

Abstract

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In the present article, static analysis of thin functionally graded micro-plates, based on Kirchhoff plate theory, is investigated. Utilizing the strain gradient theory and principle of minimum total potential energy, governing equations of rectangular micro-plates, subjected to distributed load, are explored. In accordance with functionally graded distribution of material properties through the thickness, higher-order governing equations are coupled in terms of displacement fields. Introducing a novel methodology, governing equations are decoupled, with special privilege of solving analytically. These new equations are solved for micro-plates with Levy boundary conditions. It is shown that neutral plane in functionally graded micro-plate is moved from midplane to a new coordinate in thickness direction. It is shown that considering micro-structures effects affects the governing equations and boundary conditions. Finally, the effects of material properties, micro-structures, boundary conditions and dimensions are expounded on the static response of micro-plate. Results show that increasing the length scale parameter and FGM index increases the rigidity of micro-plate. In addition, it is concluded that using classical theories for study of micro-structures leads to inaccurate results.

Keywords