Softening and toughening size-dependent axisymmetric elastic buckling and free
vibration of functionally graded porous (FGP) Kirchhoff microplates with two
different porous distribution patterns are investigated through strain-driven
(D) and
stress-driven (D)
two-phase local/nonlocal integral polar models (TPNIPM), respectively. The
Hamilton’s principle is used to derive the differential governing equation and
boundary conditions. A few nominal variables are introduced to simplify the
differential governing equation and boundary conditions, and equivalent differential
constitutive relations and constitutive constraints are expressed in united
nominal forms. The general differential quadrature method is applied to
discretize differential governing equation and constitutive relations as well as
boundary conditions and constitutive constraints. L’Hospital’s rule is applied to
deal with the boundary conditions and constitutive constraints at center
for circular microplate. A general eigenvalue problem is obtained in matrix
form, from which one can determine buckling loads and vibration frequency
for different boundary conditions. The effects of nonlocal parameters, FGP
distribution patterns, geometrical dimensions and buckling/vibration order on
the buckling load and vibration frequency are investigated numerically for
different boundary conditions, and consistent size-effects are obtained for
D- and
D-TPNIPMs
TPNIPMs, respectively.
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