The aim of the thesis is to investigate the methods for finding the effective material properties of honeycomb structures and functionally graded materials in a 2-D domain. The thesis describes different modeling techniques of the two materials in boundary element method (BEM) and finite element method (FEM). It is assumed that the materials involved in manufacturing these composites are isotropic and subjected to loads only in their elastic region.
In the case of honeycomb structures, the size of the model is reduced by exploiting repeatability. A representative volume element (RVE) is developed in order to find the first component of reduced stiffness matrix. This is a function of in-plane Young's modulus in the x-direction and is used to evaluate the effective properties in the case of honeycomb structures. This value is used as the benchmark to compare all results.
Functionally graded materials with both circular and star-shaped inclusions have been modeled in order to find their effective properties. Effective Young's modulus and effective thermal conductivity are evaluated using the BEM. It is observed from the results that the circular inclusions made the FGM stronger than the star-shaped inclusions while the star-shaped inclusion FGM had a higher thermal conductivity.
In the case of functionally graded materials, BEM is found to be a better method for finding out the effective properties whereas FEM is found to be more efficient in the case of honeycomb structures. Analytical estimates to both the problem have also been discussed and have proved to be quite inaccurate in case of honeycomb structures.