Application of boundary element method for analysis of FGMs thick plate
structures based on the physical neutral surface

In this article, a first-order shear deformation plate theory based on the neutral surface position is developed to analyze functionally graded plates using the boundary element method. The property of functionally graded materials (FGMs) varies gradually along the thickness, following a power-law. The governing equations and boundary conditions of the functionally graded plate based on the neutral surface are derived using the principle of virtual work. The proposed methodology is developed by applying the concept of the analog equation method (AEM). The original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. The fictitious sources are established by applying a technique based on the boundary element method and approximated using radial basis functions. The numerical results of the present method are highly reliable when compared to other analysis methods and plate theories. Both sinusoidal and uniformly distributed loadings are analyzed in this work. A parametric study is undertaken to explore the effect of neutral surfaces, power-law index, and boundary conditions on deflections and stresses.