Nöel Challamel is Professor at the University of Southern Brittany, France. He is the co-author of several books and over a hundred journal papers in the field of mechanics and civil engineering and is on the editorial board of numerous international journals. He is also Editor and Head of the Solid Mechanics and Mechanical Engineering series published by ISTE-Wiley.Julius Kaplunov is Professor at Keele University, UK. He is the co-author of over a hundred publications in mechanics, including three books. He is a member of the European Academy of Sciences and sits on the editorial boards of more than ten journals.Izuru Takewaki is Professor of building structures at Kyoto University, Japan, and is the 56th President of the Architectural Institute of Japan. He is the Field Chief Editor of Frontiers in Built Environment and has published over 200 international journal papers.

• Preface xiNoël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKIChapter 1 Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method 1Devin BURNS and Romesh C BATRA1.1 Introduction 21.2 Formulation of the problem 31.3 Results and discussion 71.3.1 Verification of the numerical algorithm 71.3.2 Simply supported sandwich plate 91.3.3 Laminate with arbitrary boundary conditions 101.4 Remarks 141.5 Conclusion 151.6 Acknowledgments 151.7 References 15Chapter 2 Stability of Laterally Compressed Elastic Chains 17Andrii IAKOVLIEV, Srinandan DASMAHAPATRA and Atul BHASKAR2.1 Introduction 172.2 Compression of stacked elastic sheets 202.3 Stability of an elastically coupled cyclic chain 232.4 Elastic stability of two coupled rods with disorder 282.5 Spatial localization of lateral buckling in a disordered chain of elastically coupled rigid rods 312.6 Conclusion 392.7 References 40Chapter 3 Analysis of a Beck’s Column over Fractional-Order Restraints via Extended Routh–Hurwitz Theorem 43Emanuela BOLOGNA, Mario DI PAOLA, Massimiliano ZINGALES3.1 Introduction 433.2 Material hereditariness 443.2.1 Linear hereditariness: fractional-order models 483.3 Dynamic equilibrium of an elastic cantilever over a fractional-order foundation 513.4 Stability analysis of Beck’s column over fractional-order hereditary foundation 543.4.1 The characteristic polynomial 553.4.2 State-space representation of the dynamic equilibrium equation 573.4.3 Stability analysis of fractional-order Beck’s column via the extended Routh–Hurwitz criterion 603.5 Numerical application 633.6 Conclusion 653.7 References 65Chapter 4 Localization in the Static Response of Higher-Order Lattices with Long-Range Interactions 67Noël CHALLAMEL and Vincent PICANDET4.1 Introduction 684.2 Two-neighbor interaction – general formulation – homogeneous solution 704.3 Two-neighbor interaction – localization in a weakened problem 764.4 Conclusion 864.5 References 86Chapter 5 New Analytic Solutions for Elastic Buckling of Isotropic Plates 91Joseph TENENBAUM, Aharon DEUTSCH and Moshe EISENBERGER5.1 Introduction 915.2 Equilibrium equation 935.3 Solution 945.4 Boundary condition 965.5 Numerical results 985.6 Conclusion 1055.7 Appendix A: Deflection, slopes, bending moments and shears 1095.8 Appendix B: Function transformation 1165.9 References 119Chapter 6 Buckling and Post-Buckling of Parabolic Arches with Local Damage 121Uğurcan EROĞLU, Giuseppe RUTA, Achille PAOLONE and Ekrem TÜFEKCI6.1 Introduction 1216.2 A one-dimensional model for arches 1226.2.1 Finite kinematics and balance, linear elastic law 1246.2.2 Non-trivial fundamental equilibrium path 1266.2.3 Bifurcated path 1276.2.4 Special benchmark examples 1286.3 Parabolic arches 1306.4 Crack models for one-dimensional elements 1336.5 An application 1356.5.1 A comparison 1386.6 Final remarks 1386.7 Acknowledgments 1396.8 References 139Chapter 7 Inelastic Microbuckling of Composites by Wave-Buckling Analogy 145Rivka GILAT and Jacob ABOUDI7.1 Introduction 1457.2 Buckling-wave propagation analogy 1467.3 Microbuckling in elastic orthotropic composites 1487.4 Inelastic microbuckling 1507.5 Results and discussion 1527.6 References 156Chapter 8 Quasi-Bifurcation of Discrete Systems with Unstable Post-Critical Behavior under Impulsive Loads 159Mariano P AMEIJEIRAS and Luis A GODOY8.1 Introduction 1608.2 Case study of a two DOF system with unstable static behavior 1618.3 Exploring the static and dynamic behavior of the two DOF system 1648.4 The dynamic stability criterion due to Lee 1678.5 New stability bounds following Lee’s approach 1708.6 Conclusion 1748.7 Acknowledgments 1758.8 References 175Chapter 9 Singularly Perturbed Problems of Drill String Buckling in Deep Curvilinear Borehole Channels 177Valery I GULYAYEV and Natalya V SHLYUN9.1 Introduction 1779.2 Singular perturbation theory: elements and history 1799.3 Posing the problem of a drill string buckling in the curvilinear borehole 1849.4 Modeling the drill string buckling in lowering operation 1959.5 References 199Chapter 10 Shape-optimized Cantilevered Columns under a Rocket-based Follower Force 201Yoshihiko SUGIYAMA, Mikael A LANGTHJEM and Kazuo KATAYAMA10.1 Background 20110.2 Aims 20410.3 Numerical analysis 20610.3.1 Stability analysis 20610.3.2 Optimum design 20910.4 Experiment 21310.4.1 General description 21310.4.2 Rocket motor 21410.4.3 Columns 21610.4.4 Free vibration test 21910.5 Flutter test 22010.6 Concluding remarks 22310.7 Acknowledgments 22410.8 Appendix 22410.9 References 225Chapter 11 Hencky Bar-Chain Model for Buckling Analysis and Optimal Design of Trapezoidal Arches 229Chien Ming WANG, Wen Hao PAN and Hanzhe ZHANG11.1 Introduction 23011.2 Buckling analysis of trapezoidal arches based on the HBM 23111.2.1 Description of the HBM 23211.2.2 HBM stiffness matrix formulation 23411.2.3 Governing equation considering compatibility conditions 23511.2.4 Verification of the HBM 23611.3 Optimal design of symmetric trapezoidal arches 23911.3.1 Problem definition 23911.3.2 Optimization procedure 24011.3.3 Optimal solutions 24011.3.4 Sensitivity analysis of optimal solutions 24311.3.5 Comparison with the buckling load of optimal fully stressed trapezoidal arches 24511.4 Concluding remarks 24511.5 References 246List of Authors 249Index 251Summaries of Volumes 2 and 3 255

Nöel Challamel is Professor at the University of Southern Brittany, France. He is the co-author of several books and over a hundred journal papers in the field of mechanics and civil engineering and is on the editorial board of numerous international journals. He is also Editor and Head of the Solid Mechanics and Mechanical Engineering series published by ISTE-Wiley.Julius Kaplunov is Professor at Keele University, UK. He is the co-author of over a hundred publications in mechanics, including three books. He is a member of the European Academy of Sciences and sits on the editorial boards of more than ten journals.Izuru Takewaki is Professor of building structures at Kyoto University, Japan, and is the 56th President of the Architectural Institute of Japan. He is the Field Chief Editor of Frontiers in Built Environment and has published over 200 international journal papers.

• Preface xiNoël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKIChapter 1 Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method 1Devin BURNS and Romesh C BATRA1.1 Introduction 21.2 Formulation of the problem 31.3 Results and discussion 71.3.1 Verification of the numerical algorithm 71.3.2 Simply supported sandwich plate 91.3.3 Laminate with arbitrary boundary conditions 101.4 Remarks 141.5 Conclusion 151.6 Acknowledgments 151.7 References 15Chapter 2 Stability of Laterally Compressed Elastic Chains 17Andrii IAKOVLIEV, Srinandan DASMAHAPATRA and Atul BHASKAR2.1 Introduction 172.2 Compression of stacked elastic sheets 202.3 Stability of an elastically coupled cyclic chain 232.4 Elastic stability of two coupled rods with disorder 282.5 Spatial localization of lateral buckling in a disordered chain of elastically coupled rigid rods 312.6 Conclusion 392.7 References 40Chapter 3 Analysis of a Beck’s Column over Fractional-Order Restraints via Extended Routh–Hurwitz Theorem 43Emanuela BOLOGNA, Mario DI PAOLA, Massimiliano ZINGALES3.1 Introduction 433.2 Material hereditariness 443.2.1 Linear hereditariness: fractional-order models 483.3 Dynamic equilibrium of an elastic cantilever over a fractional-order foundation 513.4 Stability analysis of Beck’s column over fractional-order hereditary foundation 543.4.1 The characteristic polynomial 553.4.2 State-space representation of the dynamic equilibrium equation 573.4.3 Stability analysis of fractional-order Beck’s column via the extended Routh–Hurwitz criterion 603.5 Numerical application 633.6 Conclusion 653.7 References 65Chapter 4 Localization in the Static Response of Higher-Order Lattices with Long-Range Interactions 67Noël CHALLAMEL and Vincent PICANDET4.1 Introduction 684.2 Two-neighbor interaction – general formulation – homogeneous solution 704.3 Two-neighbor interaction – localization in a weakened problem 764.4 Conclusion 864.5 References 86Chapter 5 New Analytic Solutions for Elastic Buckling of Isotropic Plates 91Joseph TENENBAUM, Aharon DEUTSCH and Moshe EISENBERGER5.1 Introduction 915.2 Equilibrium equation 935.3 Solution 945.4 Boundary condition 965.5 Numerical results 985.6 Conclusion 1055.7 Appendix A: Deflection, slopes, bending moments and shears 1095.8 Appendix B: Function transformation 1165.9 References 119Chapter 6 Buckling and Post-Buckling of Parabolic Arches with Local Damage 121Uğurcan EROĞLU, Giuseppe RUTA, Achille PAOLONE and Ekrem TÜFEKCI6.1 Introduction 1216.2 A one-dimensional model for arches 1226.2.1 Finite kinematics and balance, linear elastic law 1246.2.2 Non-trivial fundamental equilibrium path 1266.2.3 Bifurcated path 1276.2.4 Special benchmark examples 1286.3 Parabolic arches 1306.4 Crack models for one-dimensional elements 1336.5 An application 1356.5.1 A comparison 1386.6 Final remarks 1386.7 Acknowledgments 1396.8 References 139Chapter 7 Inelastic Microbuckling of Composites by Wave-Buckling Analogy 145Rivka GILAT and Jacob ABOUDI7.1 Introduction 1457.2 Buckling-wave propagation analogy 1467.3 Microbuckling in elastic orthotropic composites 1487.4 Inelastic microbuckling 1507.5 Results and discussion 1527.6 References 156Chapter 8 Quasi-Bifurcation of Discrete Systems with Unstable Post-Critical Behavior under Impulsive Loads 159Mariano P AMEIJEIRAS and Luis A GODOY8.1 Introduction 1608.2 Case study of a two DOF system with unstable static behavior 1618.3 Exploring the static and dynamic behavior of the two DOF system 1648.4 The dynamic stability criterion due to Lee 1678.5 New stability bounds following Lee’s approach 1708.6 Conclusion 1748.7 Acknowledgments 1758.8 References 175Chapter 9 Singularly Perturbed Problems of Drill String Buckling in Deep Curvilinear Borehole Channels 177Valery I GULYAYEV and Natalya V SHLYUN9.1 Introduction 1779.2 Singular perturbation theory: elements and history 1799.3 Posing the problem of a drill string buckling in the curvilinear borehole 1849.4 Modeling the drill string buckling in lowering operation 1959.5 References 199Chapter 10 Shape-optimized Cantilevered Columns under a Rocket-based Follower Force 201Yoshihiko SUGIYAMA, Mikael A LANGTHJEM and Kazuo KATAYAMA10.1 Background 20110.2 Aims 20410.3 Numerical analysis 20610.3.1 Stability analysis 20610.3.2 Optimum design 20910.4 Experiment 21310.4.1 General description 21310.4.2 Rocket motor 21410.4.3 Columns 21610.4.4 Free vibration test 21910.5 Flutter test 22010.6 Concluding remarks 22310.7 Acknowledgments 22410.8 Appendix 22410.9 References 225Chapter 11 Hencky Bar-Chain Model for Buckling Analysis and Optimal Design of Trapezoidal Arches 229Chien Ming WANG, Wen Hao PAN and Hanzhe ZHANG11.1 Introduction 23011.2 Buckling analysis of trapezoidal arches based on the HBM 23111.2.1 Description of the HBM 23211.2.2 HBM stiffness matrix formulation 23411.2.3 Governing equation considering compatibility conditions 23511.2.4 Verification of the HBM 23611.3 Optimal design of symmetric trapezoidal arches 23911.3.1 Problem definition 23911.3.2 Optimization procedure 24011.3.3 Optimal solutions 24011.3.4 Sensitivity analysis of optimal solutions 24311.3.5 Comparison with the buckling load of optimal fully stressed trapezoidal arches 24511.4 Concluding remarks 24511.5 References 246List of Authors 249Index 251Summaries of Volumes 2 and 3 255

Nöel Challamel is Professor at the University of Southern Brittany, France. He is the co-author of several books and over a hundred journal papers in the field of mechanics and civil engineering and is on the editorial board of numerous international journals. He is also Editor and Head of the Solid Mechanics and Mechanical Engineering series published by ISTE-Wiley.Julius Kaplunov is Professor at Keele University, UK. He is the co-author of over a hundred publications in mechanics, including three books. He is a member of the European Academy of Sciences and sits on the editorial boards of more than ten journals.Izuru Takewaki is Professor of building structures at Kyoto University, Japan, and is the 56th President of the Architectural Institute of Japan. He is the Field Chief Editor of Frontiers in Built Environment and has published over 200 international journal papers.

• Preface xiNoël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKIChapter 1 Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method 1Devin BURNS and Romesh C BATRA1.1 Introduction 21.2 Formulation of the problem 31.3 Results and discussion 71.3.1 Verification of the numerical algorithm 71.3.2 Simply supported sandwich plate 91.3.3 Laminate with arbitrary boundary conditions 101.4 Remarks 141.5 Conclusion 151.6 Acknowledgments 151.7 References 15Chapter 2 Stability of Laterally Compressed Elastic Chains 17Andrii IAKOVLIEV, Srinandan DASMAHAPATRA and Atul BHASKAR2.1 Introduction 172.2 Compression of stacked elastic sheets 202.3 Stability of an elastically coupled cyclic chain 232.4 Elastic stability of two coupled rods with disorder 282.5 Spatial localization of lateral buckling in a disordered chain of elastically coupled rigid rods 312.6 Conclusion 392.7 References 40Chapter 3 Analysis of a Beck’s Column over Fractional-Order Restraints via Extended Routh–Hurwitz Theorem 43Emanuela BOLOGNA, Mario DI PAOLA, Massimiliano ZINGALES3.1 Introduction 433.2 Material hereditariness 443.2.1 Linear hereditariness: fractional-order models 483.3 Dynamic equilibrium of an elastic cantilever over a fractional-order foundation 513.4 Stability analysis of Beck’s column over fractional-order hereditary foundation 543.4.1 The characteristic polynomial 553.4.2 State-space representation of the dynamic equilibrium equation 573.4.3 Stability analysis of fractional-order Beck’s column via the extended Routh–Hurwitz criterion 603.5 Numerical application 633.6 Conclusion 653.7 References 65Chapter 4 Localization in the Static Response of Higher-Order Lattices with Long-Range Interactions 67Noël CHALLAMEL and Vincent PICANDET4.1 Introduction 684.2 Two-neighbor interaction – general formulation – homogeneous solution 704.3 Two-neighbor interaction – localization in a weakened problem 764.4 Conclusion 864.5 References 86Chapter 5 New Analytic Solutions for Elastic Buckling of Isotropic Plates 91Joseph TENENBAUM, Aharon DEUTSCH and Moshe EISENBERGER5.1 Introduction 915.2 Equilibrium equation 935.3 Solution 945.4 Boundary condition 965.5 Numerical results 985.6 Conclusion 1055.7 Appendix A: Deflection, slopes, bending moments and shears 1095.8 Appendix B: Function transformation 1165.9 References 119Chapter 6 Buckling and Post-Buckling of Parabolic Arches with Local Damage 121Uğurcan EROĞLU, Giuseppe RUTA, Achille PAOLONE and Ekrem TÜFEKCI6.1 Introduction 1216.2 A one-dimensional model for arches 1226.2.1 Finite kinematics and balance, linear elastic law 1246.2.2 Non-trivial fundamental equilibrium path 1266.2.3 Bifurcated path 1276.2.4 Special benchmark examples 1286.3 Parabolic arches 1306.4 Crack models for one-dimensional elements 1336.5 An application 1356.5.1 A comparison 1386.6 Final remarks 1386.7 Acknowledgments 1396.8 References 139Chapter 7 Inelastic Microbuckling of Composites by Wave-Buckling Analogy 145Rivka GILAT and Jacob ABOUDI7.1 Introduction 1457.2 Buckling-wave propagation analogy 1467.3 Microbuckling in elastic orthotropic composites 1487.4 Inelastic microbuckling 1507.5 Results and discussion 1527.6 References 156Chapter 8 Quasi-Bifurcation of Discrete Systems with Unstable Post-Critical Behavior under Impulsive Loads 159Mariano P AMEIJEIRAS and Luis A GODOY8.1 Introduction 1608.2 Case study of a two DOF system with unstable static behavior 1618.3 Exploring the static and dynamic behavior of the two DOF system 1648.4 The dynamic stability criterion due to Lee 1678.5 New stability bounds following Lee’s approach 1708.6 Conclusion 1748.7 Acknowledgments 1758.8 References 175Chapter 9 Singularly Perturbed Problems of Drill String Buckling in Deep Curvilinear Borehole Channels 177Valery I GULYAYEV and Natalya V SHLYUN9.1 Introduction 1779.2 Singular perturbation theory: elements and history 1799.3 Posing the problem of a drill string buckling in the curvilinear borehole 1849.4 Modeling the drill string buckling in lowering operation 1959.5 References 199Chapter 10 Shape-optimized Cantilevered Columns under a Rocket-based Follower Force 201Yoshihiko SUGIYAMA, Mikael A LANGTHJEM and Kazuo KATAYAMA10.1 Background 20110.2 Aims 20410.3 Numerical analysis 20610.3.1 Stability analysis 20610.3.2 Optimum design 20910.4 Experiment 21310.4.1 General description 21310.4.2 Rocket motor 21410.4.3 Columns 21610.4.4 Free vibration test 21910.5 Flutter test 22010.6 Concluding remarks 22310.7 Acknowledgments 22410.8 Appendix 22410.9 References 225Chapter 11 Hencky Bar-Chain Model for Buckling Analysis and Optimal Design of Trapezoidal Arches 229Chien Ming WANG, Wen Hao PAN and Hanzhe ZHANG11.1 Introduction 23011.2 Buckling analysis of trapezoidal arches based on the HBM 23111.2.1 Description of the HBM 23211.2.2 HBM stiffness matrix formulation 23411.2.3 Governing equation considering compatibility conditions 23511.2.4 Verification of the HBM 23611.3 Optimal design of symmetric trapezoidal arches 23911.3.1 Problem definition 23911.3.2 Optimization procedure 24011.3.3 Optimal solutions 24011.3.4 Sensitivity analysis of optimal solutions 24311.3.5 Comparison with the buckling load of optimal fully stressed trapezoidal arches 24511.4 Concluding remarks 24511.5 References 246List of Authors 249Index 251Summaries of Volumes 2 and 3 255