Mathematical analysis

Neutral plane

Materials science

Displacement field

Shear (geology)

Simple shear

Composite material

Geometry

Physics

Finite element method

Plate theory

Isotropy

Bending

Bending of plates

Mathematics

Mechanics

Optics

Boundary value problem

Surface (topology)

Classical mechanics

Thermodynamics

Steel and Composite Structures, an International Journal

This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position