Date of Award


Level of Access

Campus-Only Thesis

Degree Name

Master of Science (MS)


Mechanical Engineering


Senthil S. Vel

Second Committee Member

Donald A. Grant

Third Committee Member

Richard Sayles, Jr.

Additional Committee Members

William G. Davids


Functionally graded materials are comprised of two or more material ingredients whose relative volume fractions and microstructure are engineered to have a continuous spatial variation. finctionally graded materials permit tailoring of the material volume fractions to extract maximum benefit from their inhomogeneity. Such materials offer great potential for components which operate under severe thermal or mechanical loadings, such as spacecraft heat shields, plasma facings for fusion reactors, crucial jet fighter structures and engine components. However, the performance of a functionally graded component is not just a function of the properties and mass of its material constituents alone, but is directly related to the ability of the designer to utilize the materials in the most optimal fashion. Therefore, we propose a methodology for the two-dimensional simulation and optimization of material distribution of functionally graded materials undergoing thermomechanical processes or free vibration.

We first present the two-dimensional quasi-static heat conduction and thermoelasticity problems and analyze them using a meshless method, namely the element-free Galerkin method. The element-free Galerkin code is validated by comparing the results with known exact solutions, one for a homogeneous beam subjected to a distributed load and the other for a thermally loaded, simply supported functionally graded plate. Subsequently, we show the steady-state vibration problem and the corresponding element-free Galerkin formulation. The meshless code is compared to the exact solution for the free vibration of a simply supported, functionally graded plate and good agreement is obtained between the two.

The spatial distribution of constituent volume fraction, which is to be optimized for various loading and boundary conditions, is obtained by piecewise bicubic interp* lation of volume fractions defined at a finite number of grid points. The effective material properties at a point in the domain are estimated from the local volume fractions of the material constituents using the Mori-Tanaka, self-consistent and Hashin- Shtrikman lower estimate homogenization schemes. The volume fraction distribution is optimized using real-coded genetic algorithms for both single and multi-objective problems.

Lastly, the proposed methodology is applied to several example problems to illustrate its effectiveness in designing superior functionally graded components. The method is utilized to minimize the residual stress due to cooling from a high fabrication temperature of a functionally graded material as well as minimize the mass of a functionally graded material under imposed nonlinear temperature and effective stress constraints. The methodology is also demonstrated for the maximization and tuning of natural frequencies for functionally graded structures. Multi-objective optimization of volume fraction distribution is also performed for functionally graded material experiencing intense heat fluxes. The example problems demonstrate that the proposed methodology is robust and is well suited for designing functionally graded materials with superior thermomechanical and dynarnical response.