This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution

2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures

In this paper, we present a generic method/model for multi-objective design optimization of laminated composite components, based on Vector Evaluated Artificial Bee Colony (VEABC) algorithm VEABC is a parallel vector evaluated type, swarm intelligence multi-objective variant of the Artificial Bee Colony algorithm (ABC) In the current work a modified version of VEABC algorithm for discrete variables has been developed and implemented successfully for the multi-objective design optimization of composites The problem is formulated with multiple objectives of minimizing weight and the total cost of the composite component to achieve a specified strength The primary optimization variables are the number of layers, its stacking sequence (the orientation of the layers) and thickness of each layer The classical lamination theory is utilized to determine the stresses in the component and the design is evaluated based on three failure criteria: failure mechanism based failure criteria, maximum stress failure criteria and the tsai-wu failure criteria The optimization method is validated for a number of different loading configurations-uniaxial, biaxial and bending loads The design optimization has been carried for both variable stacking sequences, as well fixed standard stacking schemes and a comparative study of the different design configurations evolved has been presented Finally the performance is evaluated in comparison with other nature inspired techniques which includes Particle Swarm Optimization (PSO), Artificial Immune System (AIS) and Genetic Algorithm (GA) The performance of ABC is at par with that of PSO, AIS and GA for all the loading configurations

/pdf/artificial-bee-colony-abc-for-multi-objective-design-1tt1askavn.pdf

Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures

In recent years many articles concerned with the mechanics of functionally graded plates have been published. Usually new analysis methods are developed to handle the continuous variation in material properties through the thickness of the plate and extensive results are presented. This article shows that no special tools are required because functionally graded plates behave like homogeneous plates. This simple result is developed using the classical plate theory and is shown to hold true when higher order plate theories or the three dimensional elasticity theory is used. The variation in material properties through the thickness of the plate introduces a coupling between the inplane and bending deformations which complicates the analysis. Here we show that by a proper choice of the reference surface, this coupling can be eliminated so that the bending of the plate is governed by the same equation of motion as that of homogeneous plates.

Functionally graded plates behave like homogeneous plates

Multi-objective optimization of fiber reinforced composite laminates for strength, stiffness and minimal mass

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

Multi-objective optimization of functionally graded thick shells for thermal loading

In this paper, we present a methodology for the simulation and multi- objective optimization of material distribution of functionally graded materials (FGMs). The proposed approach focuses on metal/ceramic and metal/metal functionally graded materials, which oer great promise in high temperature and high heat flux applications. The spatial dis- tribution of the volume fraction is defined using piecewise cubic interpolation of volume fractions at a finite number of control points. The eective material properties are estimated from the local volume fractions of the material constituents us- ing the Mori-Tanaka and self-consistent homoge- nization schemes. Functionally graded rectangu- lar structures that are graded in two-dimensions are analyzed using the element-free Galerkin method to obtain the temperature and stress fields. An exact solutions to the heat conduc- tion and thermoelasticity problems has also been developed for functionally graded thick shells that are graded in the radial direction. The volume fraction distribution is optimized using an elitist, non-dominated sorting multi-objective genetic algorithm. Results for two model prob- lems demonstrate that the proposed methodol- ogy provides a useful design tool for tailoring the material composition of functionally graded components for multiple, often conflicting, ob- jectives.

Jacob L. Pelletier

Papers

Multi-objective optimization of fiber reinforced composite laminates for strength, stiffness and minimal mass

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

Multi-objective optimization of functionally graded thick shells for thermal loading

Multi-objective Design Optimization of Functionally Graded Materials