Advances in mechanics of solids: in memory of Prof. E.M. Haseganu

Ardeshir Guran, Andrei L. Smirnov, David J. Steigmann9789812568670, 9812568670

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.

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Table of contents :
CONTENTS……Page 10
Preface……Page 8
I. Vibrations and Stability of Thin Structures……Page 16
1.1 Introduction……Page 18
1.2 Relaxed Membrane Theory……Page 20
1.3 Numerical Scheme……Page 22
1.4 Examples……Page 27
References……Page 31
2.1 Introduction……Page 32
2.2 Equations of Cylindrical Shells……Page 34
2.3 Approximate Equations……Page 35
2.4 Ring-stiffened Shell……Page 37
2.5 First Approximation……Page 38
2.6 Shell Stiffened with a Ring……Page 40
2.7 Optimal Rings Arrangement……Page 43
2.8 Homogenization……Page 46
2.9 Irregular Arrangement……Page 50
2.10 Effective Stiffness……Page 52
2.11 Optimal Design of Vibrating Stiffened Shells……Page 54
2.12 Optimal Design of Buckling Shells……Page 58
References……Page 61
3.1 Introduction……Page 64
3.2 Bifurcation Equations……Page 65
3.3 Orthotropic Ellipsoid Under External Pressure……Page 68
3.4 Orthotropic Elliptical Shell Under Internal Pressure……Page 73
3.5 Buckling of Cylindrical Shells……Page 74
3.6 Buckling of Orthotropic Cylindrical Shell Under Hydrostatic Pressure……Page 76
3.7 Buckling of Axially Compressed Orthotropic Cylindrical Shell……Page 78
3.9 Effect of Anisotropy on the Critical Loading……Page 80
References……Page 82
4.1 Introduction……Page 84
4.2 Relations Between the Curvature of the Beam Neutral Line and the Bending Moment……Page 86
4.3 Stiffness of a Beam Made of Variable Modulus Material……Page 89
4.5 Strains and Stresses in a Shell Made of Composite Material……Page 91
4.7 Elasticity Relations for a Shell Made of a Composite Material……Page 93
4.8 Cylindrical Shell Under Internal Pressure……Page 95
References……Page 98
5.1 Introduction……Page 100
5.2 Problem Formulation……Page 101
5.3 Formal Asymptotic Solutions of the Equations of Cylindrical Shells……Page 104
5.4 Axisymmetric Vibrations……Page 105
5.5 Boundary Value Problem……Page 110
5.6 Nonaxisymmetric Vibrations……Page 113
5.7 Symbolic Computation……Page 117
References……Page 119
II. Vibrations and Stability in Continuum Mechanics……Page 120
6.1 Introduction……Page 122
6.2 Background……Page 124
6.3 General Theory of Piezoelectricity with Initial Fields……Page 127
6.4 Special Case of Antiplane Deformation……Page 135
6.5 Stability Considerations……Page 138
6.6 Transverse Electro-Acoustic Waves……Page 147
References……Page 151
7.1 Introduction……Page 154
7.2 Mathematical Formulation of the Problem……Page 156
7.3 Numerical Results……Page 161
7.4 Conclusion……Page 163
References……Page 164
III. Biomechanics……Page 166
8.1 Introduction……Page 168
8.2 Deformations of LC. Linear Theory……Page 171
8.3 Shear of the Layers……Page 185
8.4 Buckling of the LC……Page 189
8.5 Conclusion……Page 192
References……Page 193
9 A MICROMECHANICAL MODEL FOR PREDICTING MICROCRACKING INDUCED MATERIAL DEGRADATION IN HUMAN CORTICAL BONE TISSUE……Page 194
9.1 Introduction……Page 195
9.2 Experimental Materials and Methods……Page 196
9.3 Prediction of Material Property Degradation by a Micromechanical Damage Model……Page 202
9.4 Experimental Results……Page 205
9.5 Results of the Micromechanical Damage Model……Page 207
9.6 Comparison of Experimental Results to the Micromechanical Damage Model……Page 209
9.7 Discussion……Page 211
References……Page 214
IV. Experimental and Computational Mechanics of Solids……Page 216
10.1 Introduction……Page 218
10.2 8- to 26-Node Linear Hexahedron……Page 219
10.3 A Nonconforming 8- to 26-Node Hexahedron……Page 222
10.4 Nonconforming Elements in Thermal-Mechanical Analysis……Page 225
10.5 8- to 16-Node Solid Shell……Page 227
10.6 Solid Shell Elements in Thermal-Mechanical Analysis……Page 235
10.7 Contributions……Page 239
References……Page 240
Nomenclature……Page 242
11.1 Introduction……Page 244
11.2 Review and Discussion of Prior Works……Page 247
11.3 Periodic Response with Soft Landing……Page 257
11.4 Low Velocity Impact Model……Page 261
11.5 Quantization Effects……Page 264
11.6 Conclusion……Page 271
References……Page 272
About the Authors……Page 274
Index……Page 292