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The goal of this paper is to analyze and predict the central deflection,natural frequency, and critical buckling load of the multi-directionalfunctionally graded (FG) plate with variable thickness resting on an elasticWinkler foundation. First, the mathematical models of the static andeigenproblems are formulated in great detail. The FG material properties areassumed to vary smoothly and continuously throughout three directions of theplate according to a Mori-Tanaka micromechanics model distribution of volumefraction of constituents. Then, finite element analysis (FEA) with mixedinterpolation of tensorial components of 4-nodes (MITC4) is implemented inorder 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 areinvestigated 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 FGplates. The DNN model also shows that it is a powerful technique capable ofhandling an extensive database and different vital parameters in engineeringapplications.

Static, dynamic and stability analysis of multi-dimensional functional graded plate with variable thickness using deep neural network