Optimum material distribution of porous functionally graded plates using Carrera unified formulation based on isogeometric analysis

Abstract

The current literature deals with the multi-objective optimal material distribution of porous functionally graded plates subjected to free vibration in the framework of Carrera Unified Formulation (CUF) based on isogeometric analysis (IGA). The objective function is to maximize the natural frequencies and minimize the weight of the PFG plate, considering the material properties and porosity through the thickness of the plate. The governing equation of the PFG plate is obtained by using the principle of virtual displacement (PVD) based on the CUF. A non-uniform rational B-splines (NURBS)-based isogeometric finite element model associated with CUF is utilized for the plate free vibration analysis. The Legendre polynomials are used to approximate the thickness direction of plates. The rule of mixture is used to estimate the effective material properties. The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is employed as an optimizer. Design variables are the power and porosity indices. For verification, several structural design examples are compared with those available in the literature. Several numerical examples for optimizing the PFG plates, including maximization of the first natural frequency and minimization of mass, illustrate the effectiveness and reliability of the proposed method. The results show that the optimum values for the power and porosity indices depend on the objective function and boundary conditions. Furthermore, the clamped boundary condition leads to less mass than the simply-supported boundary condition for each desired first natural frequency.