Preface xi
Noël CHALLAMEL, Julius KAPLUNOV and Izuru TAKEWAKI
Chapter 1 Static Deformations of Fiber-Reinforced Composite Laminates by the Least-Squares Method 1
Devin BURNS and Romesh C BATRA
1.1 Introduction 2
1.2 Formulation of the problem 3
1.3 Results and discussion 7
1.3.1 Verification of the numerical algorithm 7
1.3.2 Simply supported sandwich plate 9
1.3.3 Laminate with arbitrary boundary conditions 10
1.4 Remarks 14
1.5 Conclusion 15
1.6 Acknowledgments 15
1.7 References 15
Chapter 2 Stability of Laterally Compressed Elastic Chains 17
Andrii IAKOVLIEV, Srinandan DASMAHAPATRA and Atul BHASKAR
2.1 Introduction 17
2.2 Compression of stacked elastic sheets 20
2.3 Stability of an elastically coupled cyclic chain 23
2.4 Elastic stability of two coupled rods with disorder 28
2.5 Spatial localization of lateral buckling in a disordered chain of elastically coupled rigid rods 31
2.6 Conclusion 39
2.7 References 40
Chapter 3 Analysis of a Beck's Column over Fractional-Order Restraints via Extended Routh-Hurwitz Theorem 43
Emanuela BOLOGNA, Mario DI PAOLA, Massimiliano ZINGALES
3.1 Introduction 43
3.2 Material hereditariness 44
3.2.1 Linear hereditariness: fractional-order models 48
3.3 Dynamic equilibrium of an elastic cantilever over a fractional-order foundation 51
3.4 Stability analysis of Beck's column over fractional-order hereditary foundation 54
3.4.1 The characteristic polynomial 55
3.4.2 State-space representation of the dynamic equilibrium equation 57
3.4.3 Stability analysis of fractional-order Beck's column via the extended Routh-Hurwitz criterion 60
3.5 Numerical application 63
3.6 Conclusion 65
3.7 References 65
Chapter 4 Localization in the Static Response of Higher-Order Lattices with Long-Range Interactions 67
Noël CHALLAMEL and Vincent PICANDET
4.1 Introduction 68
4.2 Two-neighbor interaction - general formulation - homogeneous solution 70
4.3 Two-neighbor interaction - localization in a weakened problem 76
4.4 Conclusion 86
4.5 References 86
Chapter 5 New Analytic Solutions for Elastic Buckling of Isotropic Plates 91
Joseph TENENBAUM, Aharon DEUTSCH and Moshe EISENBERGER
5.1 Introduction 91
5.2 Equilibrium equation 93
5.3 Solution 94
5.4 Boundary condition 96
5.5 Numerical results 98
5.6 Conclusion 105
5.7 Appendix A: Deflection, slopes, bending moments and shears 109
5.8 Appendix B: Function transformation 116
5.9 References 119
Chapter 6 Buckling and Post-Buckling of Parabolic Arches with Local Damage 121
U¿urcan ERO¿LU, Giuseppe RUTA, Achille PAOLONE and Ekrem TÜFEKCI
6.1 Introduction 121
6.2 A one-dimensional model for arches 122
6.2.1 Finite kinematics and balance, linear elastic law 124
6.2.2 Non-trivial fundamental equilibrium path 126
6.2.3 Bifurcated path 127
6.2.4 Special benchmark examples 128
6.3 Parabolic arches 130
6.4 Crack models for one-dimensional elements 133
6.5 An application 135
6.5.1 A comparison 138
6.6 Final remarks 138
6.7 Acknowledgments 139
6.8 References 139
Chapter 7 Inelastic Microbuckling of Composites by Wave-Buckling Analogy 145
Rivka GILAT and Jacob ABOUDI
7.1 Introduction 145
7.2 Buckling-wave propagation analogy 146
7.3 Microbuckling in elastic orthotropic composites 148
7.4 Inelastic microbuckling 150
7.5 Results and discussion 152
7.6 References 156
Chapter 8 Quasi-Bifurcation of Discrete Systems with Unstable Post-Critical Behavior under Impulsive Loads 159
Mariano P AMEIJEIRAS and Luis A GODOY
8.1 Introduction 160
8.2 Case study of a two DOF system with unstable static behavior 161
8.3 Exploring the static and dynamic behavior of the two DOF system 164
8.4 The dynamic stability criterion due to Lee 167
8.5 New stability bounds following Lee's approach 170
8.6 Conclusion 174
8.7 Acknowledgments 175
8.8 References 175
Chapter 9 Singularly Perturbed Problems of Drill String Buckling in Deep Curvilinear Borehole Channels 177
Valery I GULYAYEV and Natalya V SHLYUN
9.1 Introduction 177
9.2 Singular perturbation theory: elements and history 179
9.3 Posing the problem of a drill string buckling in the curvilinear borehole 184
9.4 Modeling the drill string buckling in lowering operation 195
9.5 References 199
Chapter 10 Shape-optimized Cantilevered Columns under a Rocket-based Follower Force 201
Yoshihiko SUGIYAMA, Mikael A LANGTHJEM and Kazuo KATAYAMA
10.1 Background 201
10.2 Aims 204
10.3 Numerical analysis 206
10.3.1 Stability analysis 206
10.3.2 Optimum design 209
10.4 Experiment 213
10.4.1 General description 213
10.4.2 Rocket motor 214
10.4.3 Columns 216
10.4.4 Free vibration test 219
10.5 Flutter test 220
10.6 Concluding remarks 223
10.7 Acknowledgments 224
10.8 Appendix 224
10.9 References 225
Chapter 11 Hencky Bar-Chain Model for Buckling Analysis and Optimal Design of Trapezoidal Arches 229
Chien Ming WANG, Wen Hao PAN and Hanzhe ZHANG
11.1 Introduction 230
11.2 Buckling analysis of trapezoidal arches based on the HBM 231
11.2.1 Description of the HBM 232
11.2.2 HBM stiffness matrix formulation 234
11.2.3 Governing equation considering compatibility conditions 235
11.2.4 Verification of the HBM 236
11.3 Optimal design of symmetric trapezoidal arches 239
11.3.1 Problem definition 239
11.3.2 Optimization procedure 240
11.3.3 Optimal solutions 240
11.3.4 Sensitivity analysis of optimal solutions 243
11.3.5 Comparison with the buckling load of optimal fully stressed trapezoidal arches 245
11.4 Concluding remarks 245
11.5 References 246
List of Authors 249
Index 251
Summaries of Volumes 2 and 3 255
