  The goal of this paper is to analyze and predict the central deflection,
natural frequency, and critical buckling load of the multi-directional
functionally graded (FG) plate with variable thickness resting on an elastic
Winkler foundation. First, the mathematical models of the static and
eigenproblems are formulated in great detail. The FG material properties are
assumed to vary smoothly and continuously throughout three directions of the
plate according to a Mori-Tanaka micromechanics model distribution of volume
fraction of constituents. Then, finite element analysis (FEA) with mixed
interpolation of tensorial components of 4-nodes (MITC4) is implemented in
order to eliminate theoretically a shear locking phenomenon existing. Next,
influences of the variable thickness functions (uniform, non-uniform linear,
and non-uniform non-linear), material properties, length-to-thickness ratio,
boundary conditions, and elastic parameters on the plate response are
investigated and discussed in detail through several numerical examples.
Finally, a deep neural network (DNN) technique using batch normalization (BN)
is learned to predict the non-dimensional values of multi-directional FG
plates. The DNN model also shows that it is a powerful technique capable of
handling an extensive database and different vital parameters in engineering
applications.
