A Novel nth-Order Shear Deformation Theory for the Bending and Free Vibration Analysis of Bi-functionally Graded Sandwich Plates

The main objective of this study is to establish a novel n th-order shear deformation theory for the bending and free vibration analysis of bi-functionally graded sandwich plates. The proposed theory consists of only four unknown displacement functions with undetermined differential terms. In the proposed theory, the transverse displacement does not have to separate into bending and shear parts, so the present theory is simpler and more efficient. Hamilton’s principle is adopted to established equations of motion, which are solved via Navier’s solution. The present results are compared with the available solutions to verify accuracy and efficiency. Then the proposed theory is applied to investigate the bending and free vibration of bi-functionally graded sandwich plates with one homogeneous core and two face-sheet layers of two different functionally graded materials with many parametric studies. Numerical results shows that the static bending and free vibration behaviors of sandwich plates significantly depends on both variation of materials in two face sheets. In addition, the behaviors of the sandwich plate with ceramic and metallic cores are opposite, and this should be considered when designing such structures. The proposed theory can be used as a good tool for analysis of many kinds of structure from nano-scale to macro-scale structures.