Is it always worthwhile to resolve the governing equations of plate theories for graded porosity along the thickness?

TL;DR

This paper evaluates the applicability of existing exact solutions for analyzing functionally graded porous plates with various porosity distributions, providing explicit formulations and insights into their mechanical behavior for design purposes.

Contribution

It introduces explicit formulas for stiffness and inertia coefficients for 12 porosity distributions, enabling the use of existing analytical solutions for FGP plates analysis.

Findings

Different porosity distributions significantly affect stiffness and vibration characteristics.

Explicit formulations facilitate the application of existing solutions to graded porous plates.

Guidelines for designers to evaluate porosity effects based on literature solutions.

Abstract

Functionally graded porous (FGP) plates have been introduced as modern structural members which open a new window to optimal and functional designs. Despite the need to study the effect of graded porosity on the mechanical behavior of FGP plates, it is necessary to consider the very extensive and valuable literature in this field, presenting remarkable closed-form solutions. Hence, this paper aims to answer where is possible to implement the available exact solutions for the analysis of FGP plates. As the special distinction of FGP plates, graded porosity, is reflected in their stiffnesses and moments of inertia coefficients, 12 different functionality of porosity distribution along the thickness are considered and a set of explicit formulation for evaluating these coefficients are presented to be substituted in already provided analytical solutions. Many examples including bending and free vibration of thin and thick FGP plates are exhibited and the influence of the type of porosity distribution is discussed in details. This work can be considered as a guideline for designers to evaluate the effect of graded porosity based on the cornerstone of the huge number of solutions in the precious literature of plate theories.