Contents

### **Preface XI**


Chapter 9 **Optimization of Functionally Graded Material Structures: Some Case Studies 157** Karam Maalawi

Preface

The subject of optimum composite structures is a rapidly evolving field and intensive research and development has taken place in the last few decades. Therefore, this book aims to provide an up-to-date comprehensive overview of the current status in this field to the research com‐ munity. The contributing authors combine structural analysis, design and optimization basis of composites with descriptions of the implemented mathematical approaches. Within this framework, each author has dealt with the individual subject as he/she thought appropriate. Each chapter offers detailed information on the related subject of its research with the main objectives of the works carried out as well as providing a comprehensive list of references that should provide a rich platform of research to the field of optimum composite structures.

**Chapter 1** is an introductory chapter that provides a brief review of the optimum design of composite structures as well as the relevant optimization models and techniques that are commonly implemented. As a practical application, the optimization of a composite cylin‐

**Chapter 2** focuses on the optimization of composite structures with nonlinear material prop‐ erties. Mathematical models for flexural deformation of carbon fiber reinforced plastics and polymer matrices have been built. An application considering optimization of a multilayer composite pressure vessel is presented and discussed, where the objective function is meas‐ ured by weight minimization subject to deformation and strength constraints. It is shown that the use of simplified mathematical models based on the Kirchhoff-Love and Timoshen‐ ko shell theories can be appropriate for solving the associated optimization problems.

**Chapter 3** presents a model for lay-up optimization of a cantilevered composite slender, tubular beam with varied cross-section that is manufactured by winding glass fiber unidir‐ ectional tape. The multilayered composite material is assumed and modeled as a single phase anisotropic elastic homogeneous continuum. For each accepted lay-up scheme and unidirectional prepreg orientation of the symmetric balanced laminate formation, the elastic moduli were determined independently by two methods, namely; the finite element method and the classical lamination theory. The first stage is based on the analysis of the angular distribution of all engineering constants of laminates. This analysis allows the choice of a small set of "candidate" lay-ups, which are used at the modeling of the mechanical response of the beam structure at three different load scenarios. The higher level "candidates" were appointed for the final dynamic test, which includes applying full load to the selected struc‐ tures and allows for the possibility to make the expert decision about final choice of quasioptimal structure. The short discussion of the obtained results confirms the necessity of multi-objective optimization, considering many requirements and constraints that help in

drical shell has been analyzed and solved in detail.

making the final choice of the optimal lay-up parameters.
