Advanced Problems in Mechanics : Proceedings of the XLVII International Summer School-Conference “Advanced Problems in Mechanics”, June 24-29, 2019, St. Petersburg, Russia

This book focuses on original theories and approaches in the field of mechanics. It reports on both theoretical and applied research, with a special emphasis on problems and solutions at the interfaces of mechanics and other research areas. The respective chapters highlight cutting-edge works fostering development in fields such as micro- and nanomechanics, material science, physics of solid states, molecular physics, astrophysics, and many others. Special attention has been given to outstanding research conducted by young scientists from all over the world. Based on the 47th edition of the international conference “Advanced Problems in Mechanics”, held on June 24–29, 2019, in St. Petersburg, Russia, and organized by Peter the Great St. Petersburg Polytechnic University and Institute for Problems in Mechanical Engineering of Russian Academy of Sciences under the patronage of Russian Academy of Sciences, the book provides researchers and graduate students with an extensive overview of the latest research and a source of inspiration for future developments in various fields of mechanics. Contents 6 Influence of the Sperm Velocity on Fertilization Capacity in the Oscillatory Model of Mouse Zona Pellucida 9 Abstract 9 1 Introduction 10 1.1 Importance of Sperm Velocity for Fertilization Success 10 1.2 Bio-Mechanical Models of Sperm-Oocyte Interaction 11 1.3 The Oscillatory Model of Fertilization – Basic Concept 12 1.4 Sperm Arrangement on ZP Surface and ZP Oscillations 13 1.5 Oscillatory Net Model of Mouse Zona Pellucida 14 2 Methods 16 3 Results 20 4 Discussion and Conclusions 23 4.1 The Limitations of the Model 25 Acknowledgements 26 References 26 Parameter Determination of Metamaterials in Generalized Mechanics as a Result of Computational Homogenization 30 1 Introduction 30 2 Computational Approach 32 3 Application 34 4 Discussion and Conclusion 35 References 35 A Model of Hydraulic Fractured Horizontal Well for Debit Computation of Slanged Gas and Oil 40 1 Hydraulic Fracturing 40 2 Well Model Without Fracturing 41 3 Well Model with Hydraulic Fracturing 42 4 The ``Infinite Permeability'' Model 45 5 Conclusions 46 A Appendix 46 A.1 Appendix 1 46 A.2 Appendix 2 47 A.3 Appendix 3 48 A.4 Appendix 4 48 References 48 Double Aging of Heat-Treated Aluminum Alloy of (7075) and (6061) to Increase the Hardness Number 50 Abstract 50 1 Introduction 50 2 Methodology 51 3 Heat Treatment of Aluminum Alloys 52 4 Experimental Data 53 5 Experimental Procedure 55 6 Experimental Results 56 7 Discussion of Results 57 8 Re-aging at 1985 °C 57 9 Conclusions 57 References 59 The Definition of Damage Parameter Changes from the Experimental High-Temperature Creep Curves 61 Abstract 61 1 Introduction 61 2 The Kachanov-Rabotnov Theory 62 3 The Theory for Compressible Medium 63 4 Deformation Creep Curves Description 63 5 Continuity Parameter Changes 64 6 Long-Term Strength Criterions 65 7 Conclusions 66 Acknowledgements 66 References 66 Evaluation Criteria for the Wear Resistance of High-Chromium Steels 68 Abstract 68 1 Introduction 68 2 Materials and Experiments 69 3 Results 69 4 Conclusions 73 References 73 Moving Web and Dynamic Problem of Aerothermoelastic Vibrations and Instability 74 1 Basic Relations 74 2 Dynamic Stability Analysis 75 3 Conclusions 78 References 79 New Ansatzes for Solution of Nonlinear Nonautonomous Klein-Fock-Gordon Equation 80 1 Introduction 80 2 Ansatzes and Methods of Their Construction 81 3 Special Solutions 86 4 Conclusion 88 References 88 Development of the Legs Fixation Mechanism for Lokomat Therapy Training Device 89 Abstract 89 1 Disadvantages of the Locomotor Therapy System 89 2 Modification of the Knee Support 91 3 Topological Optimization 93 3.1 General Idea 93 3.2 Topological Optimization of Locomotor Therapy System Parts 93 4 Weld Joints Calculations 97 5 Manufacturing 97 6 Futher Use 98 References 100 Modeling of the Superelastic Behavior of CuAlNi - Single Crystals Accounting Anisotropy of Elastic Properties 101 1 Introduction 101 2 Model 102 3 Simulation 105 4 Conclusions 106 References 107 Experimental Investigations of 3D-Deformations in Additively Manufactured Pantographic Structures 109 1 Introduction 109 2 Materials and Methods 111 2.1 Manufacturing 111 2.2 Experimental Setup 113 3 Results 115 3.1 Extension 115 3.2 Shearing 115 3.3 Torsion 117 4 Conclusion and Outlook 119 References 120 Fatigue Reliability of Structures: Methodology of Assessment and Problems 123 1 Introduction 123 2 Description of the Approach 124 3 Results and Discussion 126 4 Conclusions 130 References 130 Inhomogeneous Distribution of Thermal Characteristics in Harmonic Crystal 132 1 Introduction 132 2 Dynamic Relations for the Model 133 3 Kinetic Energy in a Small Time Interval 135 4 General Presentation for Average Kinetic Energy 139 5 Reduction of the Obtained Equations 143 References 145 Dynamics of the Microresonator in the Regime of Supercritical Compression 147 1 Introduction 147 2 The Scheme and Principle of Operation of the Microresonator 148 3 Equations of Motion 149 4 Research of Equilibrium Positions 150 5 Analysis of Free Oscillations 154 6 Self-oscillating Regime 156 7 The Influence of System Parameters on the Stability of Self-oscillation Frequency 157 8 Conclusions 159 References 159 Design and Simulation of an Acoustic Metamaterial Plate Incorporating Tunable Shape Memory Cantilever Absorbers 160 1 Introduction 160 2 Design of the SMM Absorber and Metamaterial Plate 161 3 Theoretical Formulation 162 4 Results and Discussion 165 4.1 A Rectangular Plate in Simply-Supported Boundary Condition 165 4.2 A Rectangular Plate in Cantilevered Boundary Condition 166 5 Conclusion 169 References 169 A New Class of Optimization Problems Related to Structural Control by Contact Interaction 171 1 Introduction 171 2 Control of Beam Deflection at Loading Point Q 173 2.1 Example: Beam I for the Discrete Punch Action 176 2.2 Example: Beam II for the Continuous Punch Action 177 3 Control of Beam Deflection and Slope by the Action of Two Concentrated Loads 179 4 Control of Displacement and Slope in a Beam with a Transverse Tool at Point Q 182 5 Conclusions 185 References 186 On Crack Propagation in a Two-Component Thermally Reinforced Pipe 187 Abstract 187 1 Introduction 187 2 Experimental Results 188 3 Calculation Model 188 3.1 Fracture Criterion 188 3.2 Stress Field in an Intact Pipe 189 3.3 Stress Field Near the Crack Tips 189 4 Deflection Versus Penetration 190 4.1 Deflection/ Penetration Criterion 190 4.2 Calculation Results 190 5 Conclusion 191 References 192 Rock Fracture During Oil Well Perforation 193 Abstract 193 1 Introduction 193 2 Modelling of Changes in the Stress State of an Oil Field 194 3 Jet Perforation 198 4 Conclusions 199 Acknowledgements 200 References 200 Cavity Flow of Nematic Liquid Crystals – A Parameter Study 201 1 Introduction 201 2 Governing Equations 202 3 Problem Statement and Simplified Field Equations 204 4 Results 206 4.1 Parameter Study 207 5 Conclusion and Outlook 211 References 212 HEDE Model vs Inner Pressure Model in Calculating the Strength of Hydrogenated Metals 214 Abstract 214 1 Introduction 214 2 HEDE Model Review 215 3 FE Simulations 216 3.1 FE Solution 216 3.2 The Results of FE Simulation 217 4 Conclusion 220 Acknowledgments 220 References 220 The Influence of Balcony Greening of High-Rise Buildings on Urban Wind and Thermal Environment: A Case of an Ideal City 221 Abstract 221 1 Introduction 221 2 Study Design and Verification 222 2.1 Basic Model and Environmental Setting 222 2.2 Designing the Study Variables 223 3 CFD Simulation Results and Analysis 225 4 Conclusions 229 Acknowledgements 229 References 229 Contour Convergence Regularities for Openings in Coal 230 Abstract 230 1 Introduction 231 2 The Use of Viscoplasticity Theory 232 3 Conclusions 240 References 240 On Finite Element Analysis in Generalized Mechanics 241 1 Introduction 241 2 Strain Gradient Elasticity 243 3 Analytical Solution 244 3.1 Shear Test, Prescribed Displacement 246 3.2 Shear Test Steered by Traction 248 4 Discussion and Conclusion 250 References 250 Model of the Effect of Low Natural Concentrations of Hydrogen on Cylindrical Steel Samples 254 Abstract 254 1 Introduction 254 2 Tension Model of Sample with Hydrogen 256 3 Results and Discussion 259 4 Conclusion 261 Acknowledgments 262 References 262 Calculation of the Activation Energies of Hydrogen in Titanium Manufactured with 3D Printing Technology by Means of a Multichannel Diffusion Model 264 Abstract 264 1 Introduction 264 2 Method Description 265 2.1 Measurements 265 2.2 Methods of Evaluation of the Activation Energies 267 3 Results 269 4 Conclusion 270 Acknowledgements 270 References 270 Author Index 272 Front Matter ....Pages i-vii Influence of the Sperm Velocity on Fertilization Capacity in the Oscillatory Model of Mouse Zona Pellucida (Andjelka Hedrih, Ana Mitrovic-Jovanovic, Mihailo Lazarevic)....Pages 1-21 Parameter Determination of Metamaterials in Generalized Mechanics as a Result of Computational Homogenization (Bilen Emek Abali, Hua Yang)....Pages 22-31 A Model of Hydraulic Fractured Horizontal Well for Debit Computation of Slanged Gas and Oil (Igor Abramov, Maksim Simonov)....Pages 32-41 Double Aging of Heat-Treated Aluminum Alloy of (7075) and (6061) to Increase the Hardness Number (Suleiman E. Al-Lubani, Ahmad I. Ateyat)....Pages 42-52 The Definition of Damage Parameter Changes from the Experimental High-Temperature Creep Curves (A. R. Arutyunyan, R. A. Arutyunyan, R. R. Saitova)....Pages 53-59 Evaluation Criteria for the Wear Resistance of High-Chromium Steels (S. A. Atroshenko)....Pages 60-65 Moving Web and Dynamic Problem of Aerothermoelastic Vibrations and Instability (Nikolay Banichuk, Svetlana Ivanova, Juha Jeronen)....Pages 66-71 New Ansatzes for Solution of Nonlinear Nonautonomous Klein-Fock-Gordon Equation (A. N. Bulygin, Yu. V. Pavlov)....Pages 72-80 Development of the Legs Fixation Mechanism for Lokomat Therapy Training Device (Andrei Dolgirev, Natalia Maltseva)....Pages 81-92 Modeling of the Superelastic Behavior of CuAlNi - Single Crystals Accounting Anisotropy of Elastic Properties (Tatiana Y. Chernysheva, Margarita E. Evard, Aleksandr E. Volkov, Fedor S. Belyaev)....Pages 93-100 Experimental Investigations of 3D-Deformations in Additively Manufactured Pantographic Structures (Gregor Ganzosch, Emilio Barchiesi, Rafal Drobnicki, Aron Pfaff, Wolfgang H. Müller)....Pages 101-114 Fatigue Reliability of Structures: Methodology of Assessment and Problems (Ruslan V. Guchinsky, Sergei V. Petinov)....Pages 115-123 Inhomogeneous Distribution of Thermal Characteristics in Harmonic Crystal (Mikhail A. Guzev, Vladimir M. Sadovskii, Chengzhi Qi)....Pages 124-138 Dynamics of the Microresonator in the Regime of Supercritical Compression (Vasilisa Igumnova, Lev Shtukin, Alexey Lukin, Ivan Popov)....Pages 139-151 Design and Simulation of an Acoustic Metamaterial Plate Incorporating Tunable Shape Memory Cantilever Absorbers (Hua-Liang Hu, Yi-Ting Wu, Ji-Wei Peng, Chun-Ying Lee)....Pages 152-162 A New Class of Optimization Problems Related to Structural Control by Contact Interaction (István Páczelt, Zenon Mróz)....Pages 163-178 On Crack Propagation in a Two-Component Thermally Reinforced Pipe (Alexander Maksimov, Yulia Pronina)....Pages 179-184 Rock Fracture During Oil Well Perforation (Evgenii Riabokon, Mikhail Turbakov, Evgenii Kozhevnikov, Vladimir Poplygin, Marian Wiercigroch)....Pages 185-192 Cavity Flow of Nematic Liquid Crystals – A Parameter Study (Wilhelm Rickert, Wolfgang H. Müller)....Pages 193-205 HEDE Model vs Inner Pressure Model in Calculating the Strength of Hydrogenated Metals (Julia Sedova, Vladimir Polyansky, Ivan Popov)....Pages 206-212 The Influence of Balcony Greening of High-Rise Buildings on Urban Wind and Thermal Environment: A Case of an Ideal City (Ying-Ming Su, Chiao-Jou Hsieh)....Pages 213-221 Contour Convergence Regularities for Openings in Coal (Vitaly A. Trofimov, Yury A. Filippov)....Pages 222-232 On Finite Element Analysis in Generalized Mechanics (Hua Yang, Bilen Emek Abali, Wolfgang H. Müller)....Pages 233-245 Model of the Effect of Low Natural Concentrations of Hydrogen on Cylindrical Steel Samples (Aleksandr Zegzhda, Vladimir Polyansky)....Pages 246-255 Calculation of the Activation Energies of Hydrogen in Titanium Manufactured with 3D Printing Technology by Means of a Multichannel Diffusion Model (P. A. Zumberov, Yu. A. Yakovlev, V. A. Polyanskiy)....Pages 256-263 Back Matter ....Pages 265-266