Advances in Mechanics of Solids: In Memory of Professor E. M. Haseganu

by Guran, Ardeshir; Smirnov, Andrei L.; Steigmann, David J.

ISBN13: 9789812568670

ISBN10: 9812568670

Format: Hardcover

Pub. Date: 2006-09-30

Publisher(s): World Scientific Pub Co Inc

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"The contributions in this volume are written by well-known specialists in the fields of mechanics, materials modeling and analysis. They comprehensively address the core issues and present the latest developments in these and related areas. In particular, the book demonstrates the breadth of current research activity in continuum mechanics. A variety of theoretical, computational, and experimental approaches are reported, covering finite elasticity, vibration and stability, and mechanical modeling. The coverage reflects the extent and impact of the research pursued by Professor Haseganu and her international colleagues."--BOOK JACKET.

Preface	p. vii
Vibrations and Stability of Thin Structures	p. 1
Eliza Haseganu's Analysis of Wrinkling in Pressurized Membranes	p. 3
Introduction	p. 3
Relaxed Membrane Theory	p. 5
Numerical Scheme	p. 7
Examples	p. 12
References	p. 16
Buckling, Vibrations and Optimal Design of Ring-Stiffened Thin Cylindrical Shells	p. 17
Introduction	p. 17
Equations of Cylindrical Shells	p. 19
Approximate Equations	p. 20
Ring-stiffened Shell	p. 22
First Approximation	p. 23
Shell Stiffened with a Ring	p. 25
Optimal Rings Arrangement	p. 28
Homogenization	p. 31
Irregular Arrangement	p. 35
Effective Stiffness	p. 37
Optimal Design of Vibrting Stiffened Shells	p. 39
Optimal Design of Buckling Shells	p. 43
Conclusion	p. 46
References	p. 46
Asymptotic Analysis of Thin Shell Bukling	p. 49
Introduction	p. 49
Bifurcation Equations	p. 50
Orthotropic Ellipsoid Under External Pressure	p. 53
Orthotropic Elliptical Shell Under Internal Pressure	p. 58
Buckling of Cylindrical Shells	p. 59
Buckling of Orthotropic Cylindrical Shell Under Hydrostatic Pressure	p. 61
Buckling of Axially Compressed Orthotropic Cylindrical Shell	p. 63
Buckling of an Orthotropic Cylindrical Shell Under Torsion	p. 65
Effect of Anisotropy on the Critical Loading	p. 65
References	p. 67
Thin-Wall Structures Made of Materials with Variable Elastic Moduli	p. 69
Introduction	p. 69
Relations Between the Curvature of the Beam Neutral Line and the Bending Moment	p. 71
Stiffness of a Beam Made of Variable Modulus Material	p. 74
Fiber-reinforced Shell	p. 76
Strains and Stresses in a Shell Made of Composite Material	p. 76
The Threshold Constant [epsilon subscript 0]	p. 78
Elasticity Relations for a Shell Made of a Composite Material	p. 78
Cylindrical Shell Under Internal Pressure	p. 80
References	p. 83
Asymptotic Integration of Free Vibration Equations of Cylindrical Shells by Symbolic Computation	p. 85
Introduction	p. 85
Problem Formulation	p. 86
Formal Asymptotic Solutions of the Equations of Cylindrical Shells	p. 89
Axisymmetric Vibrations	p. 90
Boundary Value Problem	p. 95
Nonaxisymmetric Vibrations	p. 98
Symbolic Computation	p. 102
References	p. 104
Vibrations and Stability in Continuum Mechanics	p. 105
The Mechanics of Pre-Stressed and Pre-Polarized Piezoelectric Crystals	p. 107
Introduction	p. 107
Background	p. 109
General Theory of Piezoelectricity with Initial Fields	p. 112
Small deformation and electric fields superposed on large static fields	p. 112
Special case of homogeneous initial state and non-polarizable environment	p. 117
Special Case of Antiplane Deformation	p. 120
Stability Considerations	p. 123
Static and dynamic local stability	p. 123
Local stability against antitplane perturbations	p. 131
Transverse Electro-Acoustic Waves	p. 132
References	p. 136
On the Stability of Transient Viscous Flow in an Annulus	p. 139
Introduction	p. 139
Mathematical Formulation of the Problem	p. 141
Numerical Results	p. 146
Conclusion	p. 148
References	p. 149
Biomechanics	p. 151
Mechancial Models of the Development of Glaucoma	p. 153
Introduction	p. 153
Deformations of LC. Linear Theory	p. 156
Axisymmetric deformation of the LC	p. 159
Nonaxisymmetric deformation of the LC	p. 162
Deformation of the oval LC	p. 168
Shear of the Layers	p. 170
Buckling of the LC	p. 174
Conclusion	p. 177
References	p. 178
A Micromechanical Model for Predicting Microcracking Induced Material Degradation in Human Cortical Bone Tissue	p. 179
Introduction	p. 180
Experimental Materials and Methods	p. 181
Prediction of Material Property Degradation by a Micromechanical Damage Model	p. 187
Experimental Results	p. 190
Results of the Micromechanical Damage Model	p. 192
Comparison of Experimental Results to the Micromechanical Damage Model	p. 194
Discussion	p. 196
References	p. 199
Experimental and Computational Mechanics of Solids	p. 201
An Evolution of Solid Elements for Thermal-Mechanical Finite Element Analysis	p. 203
Introduction	p. 203
8- to 26-Node Linear Hexahedron	p. 204
A Nonconforming 8- to 26-Node Hexahedron	p. 207
Nonconforming Elements in Thermal-Mechanical Analysis	p. 210
8- to 16-Node Solid Shell	p. 212
Solid Shell Elements in Thermal-Mechanical Analysis	p. 220
Contributions	p. 224
References	p. 225
Nomenclature	p. 227
Quantization Effects in Shallow Powder Bed Vibrations	p. 229
Introduction	p. 229
Review and Discussion of Prior Works	p. 232
Notation	p. 233
Literature survey	p. 235
Discussion	p. 239
Periodic Response with Soft Landing	p. 242
Low Velocity Impact Model	p. 246
Quantization Effects	p. 249
Digital experiments	p. 249
Classical elastic impact model	p. 250
Low velocity impact model	p. 251
Quantum influence	p. 253
Existence and uniqueness of quantized states	p. 254
Stability of quantized states	p. 255
Conclusion	p. 256
References	p. 257
About the Authors	p. 259
Index	p. 277
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Advances in Mechanics of Solids: In Memory of Professor E. M. Haseganu

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