An asymptotically exact first-order shear deformation theory for functionally graded plates

TL;DR

This paper develops a highly accurate first-order shear deformation theory for functionally graded plates using the variational-asymptotic method, validated through wave propagation analysis and comparison with 3-D elasticity.

Contribution

It introduces an asymptotically exact shear deformation theory for functionally graded plates, improving accuracy over existing models.

Findings

The theory accurately predicts wave dispersion up to order h^2/l^2.

Analytical solutions align well with 3-D elasticity results.

The approach enhances modeling precision for functionally graded plates.

Abstract

An asymptotically exact first-order shear deformation theory for functionally graded elastic plates is derived using the variational-asymptotic method. As an application, an analytical solution to the problem of wave propagation in a sandwich plate is found in accordance with this refined theory. Comparison between the dispersion curves obtained by 2-D plate theory and 3-D elasticity theory reveals that the former is accurate up to the order of h^2/l^2, where h is the plate thickness and l the wavelength.