Flexural response of bidirectional FG-plates via hyperbolic integral higher order shear deformation theory

The current work aims to study the mechanical-elastic bending of bidirectional functionally graded materials using a combined integral theory (I-HSDT) with the transverse shear effect. The presented model contains undetermined integral in which reduce the numbers of the unknown’s variables and therefore reduce the calculation time while ensuring the accuracy of results. This combined-integral model satisfies the free surface conditions by using the exponential-hyperbolic warping function. Unlike the two-materials unidirectional FG plate. The studied bidirectional functionally graded plate is made of three constituents (Al₂O₃–ZrO₃–Al) with a different power law volume fraction. The variations of the volume fractions are continuously varied in two perpendicular direction (longitudinal and thickness direction). The analytical solution of the mechanical bending analysis is determined by the virtual work principle and resolved via Navier's approach functions. The validity and the exactness of the current combined integral theory are confirmed by the comparisons study with the others similar model found in the open literature. Also, various parametric studies are presented and discussed to illustrates the impact of the composition of 2D-FGM, thickness, width-to-length ratio on the flexural characteristics of the simply supported FG plate.