Gdoutos Recent Advances in Mechanics

Selected Papers from the Symposium on Recent Advances in Mechanics, Academy of Athens, Athens, Greece, 17-19 September, 2009, organised by the Pericles S. Theocaris Foundation in Honour of P. S. Theocaris, on the Tenth Anniversary of his Death
1. Auflage 2011
ISBN: 978-94-007-0557-9
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)

E-Book, Englisch, 459 Seiten

This book contains 24 papers presented at the symposium on 'Recent Advances in Mechanics' dedicated to the late Professor - Academician Pericles S. Theocaris in commemoration of  the tenth anniversary of his death. The papers are written by world renowned and recognized experts in their fields and serve as a reference and guide for future research. The topics covered in the book can be divided into three major themes: Mathematical methods in applied mechanics (nine papers), experimental mechanics (nine papers) and fracture mechanics (six papers).Topics covered include: Application of reciprocity relations to laser-based ultrasonics, boundary value problems of the theory of elasticity, optimal design in contact mechanics, scaling of strength and lifetime distributions of quasibrittle structures, directional distortional hardening in plasticity, vibration of systems, instability phenomena in damped systems, variational methods for static and dynamic elasticity problems, an accelerated Newmark scheme for solving the equations of motion in the time domain, photoelastic tomography, electronic speckle pattern interferometry, composites exposed to fire, sampling moiré, microelecromechanical systems, experimental mechanics in nano-scale, advanced cement based nanocomposites, piezonuclear transmutations in brittle rocks under mechanical loading, stress triaxiality at crack tips studied by caustics, reinforcement of a cracked elastic plate with defects, some actual problems of fracture mechanics, cyclic plasticity with applications to extremely low cycle fatigue of structural steel, and fracture of a highly filled polymer composite.

Autoren/Hrsg.

Gdoutos, E.E.

Inhaltsverzeichnis

1;Title;1
2;Preface;7
3;Biography;13
4;Contents;20
5;Contributors;23
6;Part I Mathematical Methods in Applied Mechanics;27
6.1;Application of Reciprocity Relations to Laser-Based Ultrasonics;28
6.1.1;Introduction;28
6.1.2;Thermo-anisotropic Elasticity;28
6.1.3;Reciprocity Theorem;29
6.1.4;Transverse Isotropy with Depth Dependent Properties;30
6.1.5;Heating of the Boundary;30
6.1.6;Surface Waves due to Laser Irradiation;32
6.1.7;References;33
6.2;An Asymptotic Method of Boundary-Value Problems Solution of Elasticity Theory for Thin Bodies;34
6.2.1;Introduction;34
6.2.2;The Asymptotic Solution of the First Boundary Value Problem of Elasticity Theory for the Orthotropic Thermoelastic Strip: The Connection with the Classical Theories of Beams and Bars;35
6.2.3;Conjugation of the Inner Problem and the Boundary Layer Solutions: Proof of Validity of Saint-Venant Principle;41
6.2.4;The Solution of the Second and Mixed Space Boundary-Value Problem for Thin Bodies;44
6.2.5;Solutions of Plane and Space Dynamic Problems;47
6.2.6;Conclusions;51
6.2.7;References;51
6.3;Reliable Optimal Design in Contact Mechanics;52
6.3.1;Introduction;52
6.3.2;Formulation of the Problem;54
6.3.3;Finding of the Optimal Pressure Distribution;55
6.3.4;Determination of the Optimal Punch Shape;58
6.3.5;Conclusions;66
6.3.6;References;67
6.4;Scaling of Strength and Lifetime Distributions of Quasibrittle Structures;68
6.4.1;Introduction;68
6.4.2;Failure Statistics of Nano-structure;70
6.4.3;Multi-scale Transition of Strength Statistics;70
6.4.4;Lifetime Distribution of One RVE;78
6.4.5;FiniteWeakest Link Model and Optimum Fits of Histograms;78
6.4.6;Size Effect on Mean Structural Strength and Lifetime;80
6.4.7;Conclusion;81
6.4.8;References;82
6.5;Directional Distortional Hardening in Plasticity within Thermodynamics;85
6.5.1;Introduction;85
6.5.2;Mathematical Formulation of Models;88
6.5.3;Model Performance;90
6.5.3.1;Ratchetting;93
6.5.4;Conclusion;101
6.5.5;References;101
6.6;Forced Vibrations of the System: Structure – Viscoelastic Layer;103
6.6.1;Introduction;103
6.6.2;Investigation and Analysis of the FFM Vibrations;103
6.6.3;Conclusion;112
6.6.4;References;113
6.7;Extreme Instability Phenomena in Autonomous Weakly Damped Systems: Hopf Bifurcations, Double Pure Imaginary Eigenvalues, Load Discontinuity;114
6.7.1;Introduction;114
6.7.2;Basic Equations;116
6.7.3;Conservative Systems;117
6.7.3.1;Conditions for Dynamic Bifurcation;118
6.7.3.2;Approximate Technique: |C|<-e^{2} for e.0;121
6.7.4;.on-conservative Systems;123
6.7.4.1;Li\'{e}nard-Chipart Stability Criterion;123
6.7.4.2;Symmetrization of Asymmetric Matrices;124
6.7.5;Numerical Results;126
6.7.5.1;Conservative System (.=1);127
6.7.5.2;Non Conservative Systems (..1);143
6.7.6;Conclusions;150
6.7.7;References;152
6.8;Variational Approach to Static and Dynamic Elasticity Problems;154
6.8.1;Introduction;154
6.8.2;Statement of the Problems;155
6.8.2.1;Dynamical Formulation;155
6.8.2.2;Formulation for the Static Problem;157
6.8.3;The Method of Integrodifferential Relations;159
6.8.3.1;MIDR for Static Problems;159
6.8.3.2;MIDR for Dynamical Problems;164
6.8.4;Relations of the Dynamical Variational Principles;166
6.8.5;Dynamical Variational Principle in Displacements and Stresses;169
6.8.6;Numerical Algorithm and Error Analysis;170
6.8.7;3D Beam Lateral Motions;172
6.8.8;Numerical Results;175
6.8.9;Conclusions;179
6.8.10;References;180
6.9;An Accelerated Newmark Scheme for Integrating the Equation of Motion of Nonlinear Systems Comprising Restoring Elements Governed by Fractional Derivatives;182
6.9.1;Introduction;182
6.9.2;Fractional Derivative Estimation;184
6.9.3;Dual Mesh of the Time Domain;185
6.9.4;Accelerated Algorithm;186
6.9.5;Numerical Example;191
6.9.6;Numerical Results for Earthquake Excitation;194
6.9.7;Concluding Remarks;199
6.9.8;References;199
7;Part II Experimental Mechanics;201
7.1;Photoelastic Tomography as Hybrid Mechanics;202
7.1.1;Classical Tomography;202
7.1.2;Photoelastic Tomography;203
7.1.2.1;Linear Approximation in Integrated Photoelasticity;203
7.1.2.2;The Method of Decomposition;205
7.1.3;Algorithms of Hybrid Mechanics;206
7.1.3.1;Stresses due to External Loads;206
7.1.3.2;The Case of Residual Stresses in Glass;207
7.1.4;Conclusions;210
7.1.5;References;210
7.2;Using an Electronic Speckle Interferometry for Measurement of a Stress-Deformation State of Elastic Bodies and Structures;212
7.2.1;Introduction;212
7.2.2;Combined Methods of the ESPI and Blind-Hole Drilling;213
7.2.2.1;Calculating Models in the Blind-Hole Method;213
7.2.2.2;Experimental Studies of the Residual Stresses;217
7.2.3;Other Applications of Use ESPI;221
7.2.4;References;227
7.3;Structural Integrity and Residual Strength of Composites Exposed to Fire;228
7.3.1;Introduction;228
7.3.2;Temperature, Char Distribution and Thermal Buckling Analysis;229
7.3.3;Numerical Results;237
7.3.4;Experiments;242
7.3.5;References;247
7.4;Theory and Application of Sampling Moir\'{e} Method;248
7.4.1;Introduction;248
7.4.2;Theory of Moiré Method;249
7.4.3;Phase Analysis of Grating or Fringe Pattern;252
7.4.4;Measurement Method of Displacement and Strain by Phase Analysis of Moir\'{e} Fringe;254
7.4.5;Sampling Moire Method (Scanning Moire Method);255
7.4.5.1;Background of Sampling Moir\'{e} Method;255
7.4.5.2;Process of Sampling Moiré Method Using 1-D Grating;256
7.4.5.3;Process of 2-D Displacement Analysis by Sampling Moiré Method Using 2-D Cross Grating;257
7.4.6;Deflection Measurement by Sampling Moiré Method;258
7.4.6.1;Experimental Setup and Grating Tape;259
7.4.6.2;Experimental Results of Deflection Measurement;261
7.4.7;Shape and Displacement Measurement by Sampling Moir\'{e} Method;263
7.4.7.1;Process of Measurement;263
7.4.7.2;Calibration with Two Reference Planes;265
7.4.7.3;Shape and Strain Distribution Measurement;265
7.4.7.4;Experimental Results of Shape and Strain Distributions of Rotating Object;265
7.4.8;Conclusions;267
7.4.9;References;267
7.5;Recent Advances in Microelectromechanical Systems and Their Applications for Future Challenges;270
7.5.1;Introduction;271
7.5.2;Representative MEMS Samples;273
7.5.3;ACES Methodology;276
7.5.3.1;Analytical Solution;277
7.5.3.2;Computational Solution;277
7.5.3.3;Optoelectronic Methodology;277
7.5.4;Representative Results;282
7.5.4.1;Motions of HRS Microengine;282
7.5.4.2;Deformations of a Microgyroscope;284
7.5.4.3;Deformations of a Pressure Sensor;286
7.5.4.4;Deformations of a Cantilever Microcontact;288
7.5.5;Conclusions and Future Work;290
7.5.6;References;292
7.6;Experimental Mechanics in Nano-engineering;295
7.6.1;Introduction and Theoretical Background;296
7.6.1.1;Properties of Evanescent Waves;296
7.6.1.2;Super-Resolution;297
7.6.2;Applications to Nanometrology;300
7.6.2.1;Observation of Nano-crystals and Nano-spheres;301
7.6.2.2;Generation of Multi-k Vector Fields;302
7.6.2.3;Formation of Holograms at the Nano-scale;305
7.6.2.4;Analysis of the Polystyrene Nano-spheres;309
7.6.3;Application of Surface Plasmon Resonance to Surface Roughness Topography;311
7.6.3.1;Generation of a Wide Spectrum of Frequencies due to Interaction between Evanescent Waves and Rough Surfaces;312
7.6.3.2;Application of the Model to the Analysis of Surface Topography;314
7.6.3.3;High Accuracy Measurements of Surface Topography;316
7.6.4;Determination of Contact Strains;324
7.6.4.1;Determination of the Contact Strains of a Small Cylinder;325
7.6.5;Summary and Conclusions;329
7.6.6;References;330
7.7;Advanced Cement Based Nanocomposites;333
7.7.1;Introduction;333
7.7.2;Applications of Nanotechnology in Cement Based Materials;336
7.7.2.1;Dispersion;336
7.7.2.2;Effect of CNTs/CNFs Type and Concentration;340
7.7.2.3;Nanomechanical Properties;342
7.7.2.4;Autogenous Shrinkage;345
7.7.3;A New Generation of Cement Based Materials-Conclusions;346
7.7.4;References;346
7.8;Application of Digital Speckle Pattern Interferometry (DSPI) in Determination of Elastic Modulus Using Plate Vibration;348
7.8.1;Introduction;348
7.8.2;Principle;349
7.8.2.1;Determination of Elastic Modulus Using the Concept of Plate Vibration;349
7.8.3;Theoretical Background of Time-Averaged Specklegrams;351
7.8.3.1;Interferogram Formation;351
7.8.3.2;Subtraction Fringe Formation;353
7.8.4;Experiments and Results;354
7.8.5;Conclusion;358
7.8.6;References;359
7.9;The Development and Applications of Amplitude Fluctuation Electronic Speckle Pattern Interferometry Method;361
7.9.1;Introduction;361
7.9.2;Principle of Time-Averaged ESPI Method;364
7.9.2.1;The Traditional TA ESPI Method;364
7.9.2.2;The AF ESPI Method;365
7.9.3;Experiments and Discussions;367
7.9.4;Engineering Applications of the AF ESPI Method;374
7.9.5;Conclusions;374
7.9.6;References;375
8;Part III Fracture Mechanics;377
8.1;Piezonuclear Transmutations in Brittle Rocks under Mechanical Loading: Microchemical Analysis and Geological Confirmations;378
8.1.1;Introduction;378
8.1.2;Neutron Emission Detection Techniques;380
8.1.2.1;\^{3}He Proportional Counter;380
8.1.2.2;Neutron Bubble Detectors;380
8.1.3;Preliminary Tests on Prismatic Specimens in Carrara Marble and Green Luserna Granite;381
8.1.4;Experimental Set-Up;382
8.1.4.1;Compression Tests under Monotonic Displacement Control;382
8.1.4.2;Compression Test under Cyclic Loading;384
8.1.4.3;Ultrasonic Test;384
8.1.5;Experimental Results;385
8.1.5.1;Compression Tests under Monotonic Displacement Control;385
8.1.5.2;Compression Test under Cyclic Loading;387
8.1.5.3;Ultrasonic Test;388
8.1.6;Compositional and Microchemical Evidence of Piezonuclear Fission Reactions in the Rock Specimens;389
8.1.6.1;EDS Results for Phengite;391
8.1.6.2;EDS Results for Biotite;392
8.1.7;Piezonuclear Reactions: From the Laboratory to the Earth Scale;393
8.1.8;Heterogeneity in the Composition of the Earth’s Crust: Fe and Al Reservoir Locations;394
8.1.9;Geochemical Evidence of Piezonuclear Reactions in the Evolution of the Earth’s Crust;395
8.1.10;Conclusions;397
8.1.11;References;397
8.2;Stress Triaxiality at Crack Tips Studied by Caustics;400
8.2.1;Introduction;400
8.2.2;Stress-Optical Equations;401
8.2.2.1;Plane Stress;401
8.2.2.2;Plane Strain;403
8.2.3;The Optical Method of Caustics;404
8.2.4;Experimental;407
8.2.5;Limits of Applicability of the Method of Caustics;409
8.2.6;Conclusions;411
8.2.7;References;412
8.3;Reinforcement of a Cracked Infinite Elastic Plate with Defects;414
8.3.1;Introduction;414
8.3.2;Reinforcement of a Cracked Plate with Stringers;415
8.3.3;Reinforcement of a Plate with a Patch;418
8.3.4;Linear Crack of Finite Size, the Lips of Which Are Connected with Elastic Springs;420
8.3.5;Linear Crack of Finite Size, with Transverse Loading, the Lips of Which Are Connected with Thin Inclusions;424
8.3.6;Reinforcement of the Crack Lips with Stringers and Elastic Springs;425
8.3.7;Conclusions;427
8.3.8;References;427
8.4;Some Actual Problems of Fracture Mechanics of Materials and Structures;429
8.4.1;Introduction;429
8.4.2;Classical and Non-classical Approaches;430
8.4.3;Griffith–Irwin Concept;431
8.4.4;Linear Fracture Mechanics;432
8.4.5;Non-linear Fracture Mechanics;435
8.4.6;Fatigue Crack Nucleation and Growth (Fatigue of Materials);438
8.4.7;Interaction between Environments and Deformed Metal;443
8.4.8;References;448
8.5;Cyclic Plasticity with an Application to Extremly Low Cycle Fatigue of Structural Steel;452
8.5.1;Introduction;452
8.5.2;The Preisach Model of Hysteresis;453
8.5.3;The Preisach Model for Cyclic Behaviour of Ductile Materials;455
8.5.3.1;A Three-Element Unit;455
8.5.3.2;Ilustrative Example;457
8.5.4;Extremly Low Cycle Fatigue;459
8.5.5;Application and Testing of DC90 Dampers;459
8.5.6;Conclusions;460
8.5.7;References;461
8.6;The Fracture Toughness of a Highly Filled Polymer Composite;462
8.6.1;Introduction;462
8.6.2;Materials and Experiments;463
8.6.3;Experimental Results;463
8.6.4;Toughness Model;466
8.6.5;Analysis of Results;469
8.6.6;Discussion;471
8.6.7;Conclusions;473
8.6.8;References;474
9;Author Index;475