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Finite Element Analysis of Functionally Graded Nano-Scale Films

M. Shaat's picture

This paper is now in press at Finite Element Analysis and Design International Journal.

this paper, a size-dependent finite element model, for Mindlin plate theory
accounting for the position of the neutral plane for continuum incorporating
surface energy effect, is proposed to study the bending behavior of ultra-thin
functionally graded (FG) plates.
size-dependent mechanical response is very important while the plate thickness
reduces to micro/nano scales. The classical finite
element model is adopted to allow insertion of the surface energy into the
total energy of the plate.
Bulk stresses on the surfaces are required to
satisfy the surface balance conditions involving surface stresses. Therefore,
unlike the classical continuum plate models, the bulk transverse normal stress
is preserved here. Moreover, unlike most of previous
studies in the literature, the exact neutral plane position is pre-determined
and considered for FG plates.
A series of continuum governing
differential equations which include surface energy and neutral plane position
effects are derived. A comparison between the continuum analysis of FG
ultra-thin plates with and without incorporating surface energy effects is

M. Shaat

Best regards,
Mohammed Ibrahim Shaat (M.Shaat) 
Research Assistant
Mechanical Engineering Department, Zagazig University, Zagazig 44511, Egypt 
Tel: +20 0122 2232469

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