Effect of transverse shear deformation on static and dynamic responses of classes of thick functionally graded panels

There is an increasing demand for high performance materials that are used in high temperature applications. Functionally graded materials (FGM), which are used to manufacture plates with certain required stiffness and strength variation, are commonly made of metal and ceramic constituents. Classical plate theory (CLP), First order shear deformation theory (FSDT), and third order shear deformation theory (TSDT) are used to investigate bending and vibrations of functionally graded material with material model utilizing power law variation of properties across the thickness (P-FGM). In this work the TSDT is utilized to investigate both bending and vibrations of another class of FGM with sigmoid function variation of properties (S-FGM). First, the displacement distribution within the thick plate volume is presented. Then, the general equation of motion of the plate is derived. The final matrix equation is derived using a Navier-type expansion of the unknown displacements. The model is verified by comparisons of the calculated non-dimensional maximum displacement and natural frequencies with available published results. Upon validating the model, it is used to investigate the shear deformation effects on bending displacements and critical frequencies of vibrations at different values of plate geometric ratios and material variation properties. Finally, the effect of shear deformation is further investigated by comparison of results of both S-FGM and P-FGM with earlier results using CPT. Results show that the stiffening effect due to the incorporation of shear deformation is less pronounced in the S-FGM than in the more commonly used P-FGM panels. They also show the range of plate geometrical ratios for which this effect is more significant.