Analysis, Design and Optimization of

Rapidly varying material and geometrical characteristics of composite materials and structures do not allow the direct study of their mechanical behavior even with the use of modern computers. This book is devoted to the mechanical design and optimization problems of composite structures, based on the previously developed asymptotic homogenization models and on the newly elaborated rigorous mathematical methods. It describes how to construct mathematically rigorous mechanical models to determine strength, stiffness, and weight minimization requirements, all important factors of design and optimization.

Alexander L. Kalamkarov is the author of Analysis, Design and Optimization of Composite Structures, 2nd Edition, published by Wiley.

Alexander G. Kolpakov is the author of Analysis, Design and Optimization of Composite Structures, 2nd Edition, published by Wiley.

Preface

ix

PART I. ANALYSIS OF COMPOSITE MATERIALS AND STRUCTURAL MEMBERS OF A PERIODIC STRUCTURE

1

(212)

1 Asymptotic Methods in the Mechanics of Composites

3

(42)

1.1. Asymptotic methods in mechanics of deformable solids having small geometric parameters

3

(11)

1.2. The homogenization method in the theory of elasticity of composite materials with a periodic structure

14

(9)

1.3. Modification of the homogenization method for periodically inhomogeneous thin plates

23

(5)

1.4. Modification of the homogenization method for thin beams and rods with a periodic structure

28

(6)

1.5. The homogenization method as applied to plates with a system of periodically distributed contacts

34

(5)

1.6. The homogenization method as applied to beams with a system of periodically distributed contacts

39

(2)

1.7. Memory effects in thin-walled solids

41

(4)

2 Analysis of the Effective Properties of Highly Porous Composite Materials and Structures

45

(38)

2.1. Homogenization in the elasticity and thermoelasticity of highly porous composites

46

(7)

2.2. Effective properties of elastic frameworks

53

(15)

2.3. Effective thermoelastic properties of frameworks

68

(7)

2.4. Effective elastic properties of prestressed frameworks

75

(4)

2.5. Highly porous plates and beams

79

(4)

3 Homogenization Models for Thin-Walled Composite Structural Members

83

(38)

3.1. Elasticity problem for thin-walled composite structural members

83

(12)

3.2. Equations for the homogenized shell

95

(9)

3.3. Thermal conductivity of thin-walled composite structural members

104

(6)

3.4. Equations of thermal conduction for a homogenized shell

110

(4)

3.5. Thermoelasticity of thin-walled composite structural members

114

(7)

4 Effective Properties of Thin-Walled Composite Structural Members

121

(48)

4.1. Laminated plates and shells

121

(4)

4.2. Local elasticity problems in the case fo orthotropic constituent materials

125

(7)

4.3. General properties of the effective stiffnesses of ribbed shells and plates

132

(1)

4.4. Local heat conduction and thermoelasticity problems

133

(2)

4.5. Effective stiffnesses of ribbed and wafer shells of orthotropic materials

135

(11)

4.6. Effective thermoelastic and heat conduction properties of wafer and ribbed shells of orthotropic materials

146

(3)

4.7. Effective stiffnesses of honeycomb-like shells

149

(2)

4.8. Effective stiffnesses of network shells

151

(10)

4.9. Effective thermoelastic properties of network shells

161

(4)

4.10. Effective constitutive relations of network shells

165

(4)

5 Strength Criteria for Composite Materials

169

(44)

5.1. Effective strength criteria

169

(5)

5.2. Strength of laminated composites

174

(15)

5.3. Strength of fibre-reinforced composites

189

(13)

5.4. Strength of high-modulus angle-ply composite shells subject to tension and bending

202

(8)

5.5. Strength of a wafer-like plate subject to tension and bending

210

(3)

PART II. DESIGN OF COMPOSITE MATERIALS AND STRUCTURAL MEMBERS

213

(114)

6 Design of Laminated Composites with Given Effective Characteristics

215

(48)

6.1. The problem of designing one-dimensional composites with a given set of effective properties

215

(14)

6.2. The discrete design problem

229

(7)

6.3. A numerical method for solving the design problem

236

(6)

6.4. Design of laminated structures with a prescribed distribution of effective properties

242

(3)

6.5. Design of composites of one-dimensional structure with given stiffness and strength characteristics

245

(7)

6.6. Design of laminated composites using a given set of constituent materials

252

(11)

7 Design of High-Stiffness, Fibre-Reinforced Composites

263

(24)

7.1. Design of fibre-reinforced composites with a given set of effective stiffnesses

263

(8)

7.2. Design of high-stiffness, fibre-reinforced composites with given deformation and strength properties

271

(5)

7.3. Design of high-stiffness, fibre-reinforced composites taking account of thermoelastic deformations

276

(4)

7.4. Examples of a numerical solution for design problems of fibre-reinforced composites

280

(7)

8 Design of Composite Structural Members with Given Effective Characteristics

287

(20)

8.1. Design of laminated plates with specified effective stiffnesses

287

(10)

8.2. Design of laminated plates with specified strength and stiffness characteristics

297

(4)

8.3. Design of wafer and honeycomb-like plates with specified effective characteristics

301

(6)

9 Smart Composite Structures

307

(20)

9.1. Smart structures and the optimal control theory

307

(1)

9.2. Formulation of governing equations and optimization problems

308

(3)

9.3. Optimal design of residual strains

311

(6)

9.4. Optimal design of material properties

317

(6)

9.5. Optimization of the geometry of a smart composite structure

323

(4)

Appendix A Homogenization of materials with one-dimensional inhomogeneity

327

(4)

Appendix B On the correctness of problems on convex combinations

331

(2)

Appendex C Homogenization of some systems of ordinary differential equations

333

(2)

Appendix D Computational software package DESIGNER

335

(14)

D.1. Main menu of the program DESIGNER.EXE

336

(1)

D.2. Program _FCAL.EXE for analysis of fibre-reinforced plates

337

(1)

D.3. Program _FDES.EXE for the design of fibre-reinforced plates

338

(3)

D.4. Program _HCAL.EXE for analysis of plates with a honeycomb-like filler

341

(1)

D.5. Program _HDES.EXE for the design of honeycomb-like plates

342

(3)

D.6. Program _WCAL.EXE for analysis of ribbed and wafer plates

345

(1)

D.7. Program _WDES.EXE for the design of ribbed and wafer plates

346

(3)

References

349

(4)

Index

353

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Analysis, Design and Optimization of Composite Structures

Summary

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Table of Contents

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Analysis, Design and Optimization of Composite Structures

Summary

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Table of Contents

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