1. Introduction

Structural applications of composite materials are increasing in several engineering areas where high stiffness and strength-to-weight ratios, long fatigue life, superior thermal properties, and corrosive resistance are most beneficial [1–4]. Common types include laminated composites [5], functionally graded material (FGM) structures, and nanocomposites as well as smart composite structures [6]. In fact composite structures are usually tailored, depending upon the specific objectives, by choosing the individual constituent materials and their volume fractions, fiber orientation angles, and laminas thickness and number, as well as the fabrication procedure. To attain the best results, adequate optimization models have to be implemented to find practical optimal solutions satisfying a given set of design constraints.

This introductory chapter provides a brief review on the optimum design of composite structures and the relevant optimization techniques that are capable of finding the needed optimal solutions. Several problems can be addressed, including the structural design for maximum stability, maximum natural frequencies, and minimum mass or maximum stiffness subject to limits on strength, deflections, and side constraints. The relevant design variables include geometrical dimensions and material properties as well. A numerical example is given at the end of this chapter to demonstrate a real and practical application of the optimum composite structures.
