Preface

Chapter 9 **Optimization of Functionally Graded Material Structures: Some**

**Case Studies 157** Karam Maalawi

**VI** Contents

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‐ drical shell has been analyzed and solved in detail.

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

As an important structural element in several aerospace applications, **Chapter 4** treats de‐ sign sensitivity of stiffened composite panels using finite element analysis (FEA) and analyt‐ ical solution models. Manufacturing and experimental measurements of a hat-stiffened composite structure is performed to validate the FEA and idealized analytical solutions. This is an attempt to initiate a structural architecture methodology to speed up the develop‐ ment and qualification of composite aircraft structures that will reduce design cost, increase the possibility of content reuse, and improve time-to-market. In particular, FEA results were compared with analytical solutions to develop a design methodology that will allow exten‐ sive reuse of parametric hat-stiffened panels in the design of composite structural compo‐ nents. This methodology is now widely utilized in developing a library of commonly used, built-in, composite structural elements in the design of modern aircrafts. The main goal of the authors is to provide the aviation industry with the most up-to-date databases for the application of advanced composite materials incorporated into parametric models to elimi‐ nate redundancies in the current process. The results include a correlated material database, an optimized model component library and a standardized way to design future complex composites structures, e.g. hat-stiffened composites panels, with reliable and predictable quality and material weight/cost.

the ultimate strength and serviceability requirements of Eurocode2 and current practices rules. The optimization process is developed through the use of the Generalized Reduced Gradient algorithm. Two example problems are considered in order to illustrate the applicability of the proposed design model and solution methodology. It is concluded that this approach is eco‐ nomically more effective compared to conventional design methods applied by structural en‐

Considering the next optimization of nano-composites, **Chapter 8** investigates the effect of interface on the performance of epoxy-nano clay nano-composites. The nano-clay (oMMT) filler and polymer matrix (epoxy) of the polymer nano-composites play a very important role in improving the electrical, thermal and mechanical properties. Detailed studies on the interfacial effects of filler-matrix on several properties are investigated. The chemical bond‐ ing established between epoxy and oMMT nano-filler has been investigated using Fourier Transform Infrared Spectroscopy (FTIR). The cross linking between the polymer and nanofiller was measured to determine the glassy state of the nano-composite called glass transi‐ tion temperature by using Differential Scanning Calorimeter (DSC). Further, the Positron Annihilation Spectroscopy (PALS) was utilized to determine free volume as outlined in a multi-core model. In this study, a brief explanation of nano-composite interface dynamics, free volume estimation and the effect of intermolecular interactions and hydrogen bonding are included. The effect of these results on electrical property such as dielectric strength

**Chapter 9** presents a variety of optimized *FGM* structures along with detailed structural analysis and design. The mathematical formulation is based on dimensionless quantities; therefore, the analysis is valid for different configurations and sizes. Such normalization has led to naturally scaled optimization models, which is favorable for most optimization tech‐ niques. Case studies include structural dynamic optimization of thin-walled beams in bend‐ ing motion, optimization of drive shafts against torsional buckling and whirling, and aeroelastic optimization of subsonic aircraft wings. Other stability problems concerning flu‐ id-structure interaction have also been addressed. Several design charts that are useful for

It is hoped that this book will prove of particular value to structural engineers and research‐ ers working in the field. It should also prove useful to postgraduates wishing to gain special knowledge on design optimization of composite structures. Finally, I am glad to have had the opportunity of acknowledging all the contributing authors and express my gratitude for the help and support of INTECH staff particularly the Author Service Manager **Ms. Marija‐**

**Karam Y. Maalawi**

Cairo, Egypt

Preface IX

National Research Centre

Professor of Aeronautics & Mechanics

direct determination of the optimal values of the design variables are introduced.

gineers and can be extended to deal with other sections without major alterations.

(DES) at room temperature has been thoroughly investigated.

**na Francetic**.

A new hybrid material made of fiber metal laminate (*FML*), which has been successfully ap‐ plied to commercial aircraft structures, is introduced in **Chapter 5**. A common type is made of Glass Reinforced Aluminum Laminate "GLARE", which combines thin aluminum sheets with unidirectional glass fiber reinforced epoxy layers. Such advanced composite material can offer weight savings of 10% compared with conventional aluminum and its alloys, to‐ gether with benefits that include high tensile strength, better fatigue and damage tolerance characteristics and high level of fiber safety. A large number of practical applications dem‐ onstrate that the material properties of FMLs and their additional interlinked advantages make them the ideal option for thin-walled fuselage shells of next single aisle aircrafts. In addition, two methods have been introduced to predict the corresponding static properties with respect to the different lay-up patterns. Recently, the FML manufacturers have contin‐ ued to make a substantial progress in production technology, which allows for enabling FMLs in high-volume production rates and increasing affordability for aerospace industry. In addition to the consideration of each constituent material's properties, a strong interfacial bonding between metal sheets and composite layers is one of the key factors for the im‐ provement in joint strength and long-term durability of FML structures. Therefore, a proper surface treatment on the metallic substrate is a prerequisite for achieving long-term service capability through more efficient processing in production. Another work on *FMLs* is pro‐ vided in **Chapter 6**. The main goal of the study is to assess the application of metal pins deposited by CMT (Cold Metal Transfer) PIN on metal surfaces used as layers of FMLPs, yet controlling the thickness and the number of prepreg layers. The methodological approach includes comparing small-sized FMLPs with different pin deposition patterns and spans to a reference (without pins) FMLP, in terms of energy dissipation during drop-weight testing, impact damage characterization and buckling test after impact. Iosipescu shear test, modal analysis and cosmetic characterization are also carried out.

**Chapter 7** presents a method for minimizing the cost and weight of reinforced ordinary and High Strength Concrete (HSC) T-beams at limit state according to Eurocode2 (EC-2). The first objective function includes the costs of concrete, steel and formwork, whereas the second ob‐ jective function represents the weight of the T-beam. All the constraint functions are set to meet the ultimate strength and serviceability requirements of Eurocode2 and current practices rules. The optimization process is developed through the use of the Generalized Reduced Gradient algorithm. Two example problems are considered in order to illustrate the applicability of the proposed design model and solution methodology. It is concluded that this approach is eco‐ nomically more effective compared to conventional design methods applied by structural en‐ gineers and can be extended to deal with other sections without major alterations.

As an important structural element in several aerospace applications, **Chapter 4** treats de‐ sign sensitivity of stiffened composite panels using finite element analysis (FEA) and analyt‐ ical solution models. Manufacturing and experimental measurements of a hat-stiffened composite structure is performed to validate the FEA and idealized analytical solutions. This is an attempt to initiate a structural architecture methodology to speed up the develop‐ ment and qualification of composite aircraft structures that will reduce design cost, increase the possibility of content reuse, and improve time-to-market. In particular, FEA results were compared with analytical solutions to develop a design methodology that will allow exten‐ sive reuse of parametric hat-stiffened panels in the design of composite structural compo‐ nents. This methodology is now widely utilized in developing a library of commonly used, built-in, composite structural elements in the design of modern aircrafts. The main goal of the authors is to provide the aviation industry with the most up-to-date databases for the application of advanced composite materials incorporated into parametric models to elimi‐ nate redundancies in the current process. The results include a correlated material database, an optimized model component library and a standardized way to design future complex composites structures, e.g. hat-stiffened composites panels, with reliable and predictable

A new hybrid material made of fiber metal laminate (*FML*), which has been successfully ap‐ plied to commercial aircraft structures, is introduced in **Chapter 5**. A common type is made of Glass Reinforced Aluminum Laminate "GLARE", which combines thin aluminum sheets with unidirectional glass fiber reinforced epoxy layers. Such advanced composite material can offer weight savings of 10% compared with conventional aluminum and its alloys, to‐ gether with benefits that include high tensile strength, better fatigue and damage tolerance characteristics and high level of fiber safety. A large number of practical applications dem‐ onstrate that the material properties of FMLs and their additional interlinked advantages make them the ideal option for thin-walled fuselage shells of next single aisle aircrafts. In addition, two methods have been introduced to predict the corresponding static properties with respect to the different lay-up patterns. Recently, the FML manufacturers have contin‐ ued to make a substantial progress in production technology, which allows for enabling FMLs in high-volume production rates and increasing affordability for aerospace industry. In addition to the consideration of each constituent material's properties, a strong interfacial bonding between metal sheets and composite layers is one of the key factors for the im‐ provement in joint strength and long-term durability of FML structures. Therefore, a proper surface treatment on the metallic substrate is a prerequisite for achieving long-term service capability through more efficient processing in production. Another work on *FMLs* is pro‐ vided in **Chapter 6**. The main goal of the study is to assess the application of metal pins deposited by CMT (Cold Metal Transfer) PIN on metal surfaces used as layers of FMLPs, yet controlling the thickness and the number of prepreg layers. The methodological approach includes comparing small-sized FMLPs with different pin deposition patterns and spans to a reference (without pins) FMLP, in terms of energy dissipation during drop-weight testing, impact damage characterization and buckling test after impact. Iosipescu shear test, modal

**Chapter 7** presents a method for minimizing the cost and weight of reinforced ordinary and High Strength Concrete (HSC) T-beams at limit state according to Eurocode2 (EC-2). The first objective function includes the costs of concrete, steel and formwork, whereas the second ob‐ jective function represents the weight of the T-beam. All the constraint functions are set to meet

quality and material weight/cost.

VIII Preface

analysis and cosmetic characterization are also carried out.

Considering the next optimization of nano-composites, **Chapter 8** investigates the effect of interface on the performance of epoxy-nano clay nano-composites. The nano-clay (oMMT) filler and polymer matrix (epoxy) of the polymer nano-composites play a very important role in improving the electrical, thermal and mechanical properties. Detailed studies on the interfacial effects of filler-matrix on several properties are investigated. The chemical bond‐ ing established between epoxy and oMMT nano-filler has been investigated using Fourier Transform Infrared Spectroscopy (FTIR). The cross linking between the polymer and nanofiller was measured to determine the glassy state of the nano-composite called glass transi‐ tion temperature by using Differential Scanning Calorimeter (DSC). Further, the Positron Annihilation Spectroscopy (PALS) was utilized to determine free volume as outlined in a multi-core model. In this study, a brief explanation of nano-composite interface dynamics, free volume estimation and the effect of intermolecular interactions and hydrogen bonding are included. The effect of these results on electrical property such as dielectric strength (DES) at room temperature has been thoroughly investigated.

**Chapter 9** presents a variety of optimized *FGM* structures along with detailed structural analysis and design. The mathematical formulation is based on dimensionless quantities; therefore, the analysis is valid for different configurations and sizes. Such normalization has led to naturally scaled optimization models, which is favorable for most optimization tech‐ niques. Case studies include structural dynamic optimization of thin-walled beams in bend‐ ing motion, optimization of drive shafts against torsional buckling and whirling, and aeroelastic optimization of subsonic aircraft wings. Other stability problems concerning flu‐ id-structure interaction have also been addressed. Several design charts that are useful for direct determination of the optimal values of the design variables are introduced.

It is hoped that this book will prove of particular value to structural engineers and research‐ ers working in the field. It should also prove useful to postgraduates wishing to gain special knowledge on design optimization of composite structures. Finally, I am glad to have had the opportunity of acknowledging all the contributing authors and express my gratitude for the help and support of INTECH staff particularly the Author Service Manager **Ms. Marija‐ na Francetic**.

> **Karam Y. Maalawi** Professor of Aeronautics & Mechanics National Research Centre Cairo, Egypt

**Chapter 1**

Provisional chapter

**Introductory Chapter: An Introduction to the**

DOI: 10.5772/intechopen.81165

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

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

Several research papers and text books exist in the field of optimal design of composite structures with a variety of valuable applications in civil, mechanical, ocean, and aerospace engineering. An important stage has now been reached at which an investigation of such

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

distribution, and reproduction in any medium, provided the original work is properly cited.

find practical optimal solutions satisfying a given set of design constraints.

Introductory Chapter: An Introduction to the

**Optimization of Composite Structures**

Optimization of Composite Structures

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81165

Karam Maalawi

Karam Maalawi

1. Introduction

structures.

2. The optimal design problem

#### **Introductory Chapter: An Introduction to the Optimization of Composite Structures** Introductory Chapter: An Introduction to the Optimization of Composite Structures

DOI: 10.5772/intechopen.81165

#### Karam Maalawi Karam Maalawi

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.81165
