Simultaneous optimal tri-directional distribution of material and porosity in functionally graded plates under free vibration

Abstract

This paper for the first time attempts to find the simultaneously optimal three-dimensional distribution of porosity and material phases in functionally graded materials (FGMs) model that altogether maximize the natural frequency of porous FG plates. By using the same concept of non uniform rational B-splines (NURBS) based interpolation for the material distribution, the problem of finding the optimal porosity distribution is enabled. An upper bound of porosity is pointed out, which is necessary for considering the porosity design variables. Generalized shear deformation theory (GSDT) in the framework of isogeometric analysis (IGA) for free vibration analysis of the porous FG plates is verified with previous works. The findings are: in the optimal design of material only, the uniformly distributed pores have a neutral or detrimental effect on 4-side constrained plates but slightly increase the frequency for the cantilever plate; and with that same amount of porosity, the simultaneously optimal distributions of pores, similar to those in bio-materials or natural bones in the way that are most foam-like in the center or at the furthest from the boundaries, result in lighter yet of significantly elevated vibration frequency structures.