Advances in Mechanics

ISBN-13: 9783031373121 / Angielski / Twarda / 2023

Opis

This book covers research from modern directions in solid mechanics, in particular, in the fields of mechanics of composite materials, fracture mechanics, strength of materials and structures, thermo-viscoelasticity and plasticity, mechanics of shell structures, contact mechanics, theory of wave propagation, dynamics of mechanical and hydromechanical systems.The book presents some new results in the main research directions in mechanics on which the institutions of the National Academy of Sciences of Ukraine are focused. In addition to these studies, the results of joint scientific projects of the academic institutions with universities and research institutions of Ukraine are presented.The work is dedicated to the 145th anniversary of Stepan Prokopovich Timoshenko, the world-famous scientist in the field of mechanics, the founder of the Institute of Mechanics of the National Academy of Sciences of Ukraine, one of the founders of the National Academy of Sciences of Ukraine and academic teacher with world-wide reputation with great influence on engineering education.

Spis treści

1 A Brief Review of the Development of Mechanics in the NationalAcademy of Sciences of Ukraine 

Holm Altenbach, Viacheslav Bogdanov, Anatolii Bulat, Aleksander Guz, and Vladimir Nazarenko

1.1 Introduction 

1.2 Department of Mechanics of the NAS of Ukraine

1.3 Institutes of the Department of Mechanics of NAS of Ukraine

1.3.1 S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine

1.3.2 Institute of Hydromechanics of the NAS of Ukraine 

1.3.3 Institute of Technical Mechanics of the NAS of Ukraine and State Space Agency of Ukraine 

1.3.4 G.S. Pisarenko Institute for Problems of Strength of the NAS of Ukraine 

1.3.5 M.S. Polyakov Institute of Geotechnical Mechanics of the NAS of Ukraine 

1.3.6 Institute of Transport Systems and Technologies of the NAS of Ukraine

References

2 Thermoviscoplasticity Equations of Isotropic Material with Stress Mode Dependence 

Maya Babeshko, Alexander Galishin, Vitalii Savchenko, and Mykola Tormakhov

2.1 Introduction 

2.2 Thermoviscoplastic Problem Formulation 

2.3 Constitutive Equations 

2.4 Numerical Results

2.5 Conclusions 

References 

3 Influence of Finite Initial Deformations on Velocities of Generalized Lamb Waves in an Incompressible Elastic Layer Interacting with a Layer of an Ideal Fluid 

Olexandr Bagno

3.1 Introduction 

3.2 Problem Statement. Basic Equations 

3.3 Problem-Solving Method 

3.4 Numerical Results and Their Analysis 

3.5 Influence of the Liquid Layer on the Wave Process 

3.6 Influence of Finite Initial Strains on the Wave Characteristics of Generalized Lamb Modes 

3.7 Conclusions 

References 

4 Fracture of Materials Loaded Along Cracks: Approach and Results 

Viacheslav Bogdanov, Aleksander Guz, and Vladimir Nazarenko

4.1 Introduction 

4.2 Approach to Studying the Problems

4.3 Formulation of the Problems

4.3.1 Initially Stressed Half-Space with a Near-Surface Circular Crack 

4.3.2 Pre-Stressed Body with Two Parallel Circular Cracks 

4.4 Fredholm Integral Equations 

4.4.1 Half-Space with a Near-Surface Circular Crack

4.4.2 Body with Two Parallel Circular Cracks 

4.5 Stress Intensity Factors 

4.5.1 Half-space with a Near-Surface Circular Crack 

4.5.2 Body with Two Parallel Circular Cracks

4.6 Numerical Results 

4.7 Conclusions 

References 

5 Evolution of Electron Structure of the Methane-Coal Sorption System Components and Properties 

Anatolii Bulat, Oleksandr Burchak, Volodymyr Trachevskyi, and Andrey Tokar

5.1 Introduction 

5.2 Research Methods and Objects 

5.3 Experimental Studies 

5.4 Theoretical Background of the Concept 

5.5 Conclusions 

References 

6 Stress-Strain State of a Two-Layered Half-Space With Initial Stresses Under the Influence of a Moving Load 

Yuriy Glukhov, Stepan Babich, and Victoria Kornienko

6.1 Introduction

6.2 Problem Statement 

6.3 Solution of the Problem in the Image Area

6.4 Numerical Study 

6.5 Results 

6.6 Conclusions

References 

7 Numerical Modelling of Fatigue Cracks Growth in Thin Isotropic Plates Considering the Damage Accumulation History 

Vladislav Golub and Alla Plashchynska

7.1 Introduction 

7.2 Problem Statement. Initial Equations

7.3 Simulation of the Fatigue Crack Growth Process 

7.3.1 Incubation Stage 

7.3.2 Fatigue crack growth stage 

7.3.3 Technique of Determining the Functions and Constants of the Model 

7.4 Calculation of the Kinetics of Fatigue Cracks Growth in Finite Plates 

7.4.1 Fully Reversed Uniaxial Tension-Compression

7.4.2 Asymmetric Sign-Variable Stress Cycle 

7.4.3 Repeated Zero-to-Tension Stress Cycle

7.4.4 Asymmetric Constant-Sign Stress Cycle 

7.5 Analysis of the Obtained Results 

7.6 Conclusion 

References

8 Solving Plates and Shells of Complex Shape Static Problems Using Coordinates Transformations 

Alexander Grigorenko, Mykola Kryukov, Wolfgang H. Müller, and Serhii Yaremchenko

8.1 Introduction 

8.2 Constitutive Equations 

8.2.1 Bending of Oblique and Trapezoidal Plates 

8.2.2 Quadrilateral Plates in Refined Formulation 

8.2.3 Oblique Cylindrical Shells in Classical Formulation 

8.2.4 Circular Oblique Cylinders in Refined Formulation 

8.2.5 Cylindrical Shells with Elliptic Cross-Section with Oblique cuts 

8.3 Technique for Solving the Boundary Value Problem 

8.4 Numerical results 

8.4.1 Oblique plate 

8.4.2 Trapezoidal Plate 

8.4.3 Quadrilateral Plate in Refined Formulation 

8.4.4 Beveled Cylindrical Shells in Classical and Refined Formulations 

8.4.5 Noncircular Beveled Shells 

8.5 Conclusions 

References 

9 Wave Scattering on Finite Wedge-Shaped Objects 

Viktor Grinchenko, Ihor Vovk, Vitalii Husak, and Volodymyr Matsypura

9.1 Introduction

9.2 Formulation and Construction of the Analytical Solution to a Scattering Problem of a Plane Wave on a Finite Wedge-Shaped Object 

9.2.1 Sharp Wedge 

9.2.2 Rounded Wedge 

9.3 Scattering Cross-Section 

9.4 Construction of the Numerical Algorithm and Verification of the Fulfillment of Boundary Conditions 

9.4.1 Sharp Wedge 

9.4.2 Rounded Wedge 

9.5 Calculation of the Scattering Cross-Section 

9.6 Conclusions 

References 

10 Heat and Stress State of Coated Bodies under Dry Friction Taking into Account Radiation Heat Exchange

Oleksandr Hachkevych, Rostyslav Terlets’kyi, and Orest Gumenchuk

10.1 Introduction 

10.2 Statement of the Problem on the Study of Thermal and Stress States

10.2.1 Problem Statements on the Study of Thermal State 

10.2.2 Generalized Conditions of Heat Transfer through a Thin Layer 

10.2.3 Formulation of Problems on the Study of the Stress State 

10.2.4 Approximate Expressions for Thermal Stresses 

10.3 Investigation of Temperature and Stress State at Dry Friction 

10.4 Conclusions

References 

11 Problems of Thermomechanics of Multilayered Electroconductive Bodies Under the Action of the Pulsed Electromagnetic Fields with Modulation of Amplitude 

Oleksandr Hachkevych, Roman Musii, and Nataliya Melnyk

11.1 Introduction 

11.2 The Calculated Physicomathematical Model 

11.3 Initial Relations of the Thermomechanics of LCB Under the Action of EMF 

11.4 Formulation of Initial-Boundary Problems of Thermomechanics of Multilayer Electroconductive Bodies of Canonical Form 

11.5 Methodology for Constructing Solutions of Formulated Initial-Boundary Problems

11.6 Solutions of Problems for Bimetallic Bodies of Canonical Form Under Electromagnetic Action in MPMS

11.7 Study of Thermomechanical Behavior and Properties of the Contact Joint of a Bimetallic Cylinder Under Electromagnetic Action in MPMS 

11.8 Conclusions 

References 

12 Substantiation of Reliability of Calculation of Strength of Rocket and Space Technology Structures Without Destructive Tests 

Anatoly Dzyuba and Volodymyr Sirenko

12.1 Introduction 

12.2 Statement of the Problem 

12.3 Analysis of Errors in Strength Calculation 

12.3.1 Errors of Numerical Operations 

12.3.2 Errors Caused by Deviations of Input Data 

12.3.3 Influence of Strength Criteria on the Result of Critical Loads Calculation 

12.3.4 Numerical Studies 

12.4 Methods of Forecasting the Destructive Load 

12.4.1 Estimation of the Error of the Strength Calculation Result From Deviations of Input Data 

12.4.2 Application of the Approach 

12.5 Conclusions

References 

13 Strength Assessment of Critical Elements of Nuclear Power Plant Equipment: State-of-the-Art Calculation Approaches 

Valery Kharchenko and Alexander Chirkov

13.1 Introduction 

13.2 Mathematical Models of Material Deformation Processes 

13.3 Validity of Governing Equations via Drucker’s Postulate 

13.4 Boundary Problem Statement 

13.5 Main Provisions of the Calculation Technique 

13.6 Calculations for Critical Elements of the WWER-1000 Nuclear Reactor Pressure Vessel 

13.6.1 Reactor Pressure Vessel 

13.6.2 Welded Joint of the Coolant Collector and the Steam Generator Vessel 

13.6.3 Baffle of the Reactor’s Active Zone 

13.7 Conclusions

References 

14 Mathematical Modeling of the Stress State for the Displacement and Rotation of the Rigid Penny-Shaped Inclusion Embedded in a Piezoelectric Space 

Vitaly Kirilyuk and Olga Levchuk

14.1 Introduction 

14.2 Formulation of the Problem 

14.3 Basic Equations and Relations 

14.4 Solution Method 

14.5 Conclusion 

Appendix A. The Transition From an Electroelastic Problem to the Elasticity Problem for a Transversely Isotropic Elastic Material (Particular Case) 

References 

15 State-of-the-art methods of material’s current state assessment and life-time prediction for NPP primary circuit equipment 

Ievgen Kondryakov

15.1 Introduction 

15.2 Methods of Radiation and Thermal Embrittlement Assessment of NPP Reactor Pressure Vessels Materials

15.3 Methods of Construction of Fracture Toughness–Temperature Dependences and RPV Lifetime Assessment 

15.4 Engineering Methods of the SIF Assessment 

15.5 Calculation of SIF of a Pre-Existing Crack 

15.6 Application of the Extended Finite Element Method 

15.7 Conclusions 

References

16 Non-stationary Thermoelastic Problem for a Multilayer Coating/Half Space Assembly at Radiative and Convective Loading 

Leonid Kravchuk, Kostiantin Buiskykh, and Mykola Kucher

16.1 Introduction 

16.2 Methods of Studying the Behavior and Properties of Carbon-Carbon Composite Materials 

16.3 Analytical and Experimental Methods for Assessing the Effect of Ablation Processes on the Characteristics of Composite Materials 

16.4 Bench Tests of Composite Structural Elements 

16.4.1 Experimental and Calculation Methods of Ablative Thermal Protection Research 

16.4.2 Methods of Simulation of Aerodynamic Heating Conditions of Reusable Spacecraft Structural Elements

16.5 Conclusions 

References 

17 Scattering of SH-Waves by an Elastic Fiber of Non-Canonical Shape with a Thin Interphase Layer 

Yaroslav Kunets, Roman Kushnir, and Valery Matus

17.1 Introduction 

17.2 Formulation of the Problem 

17.3 Asymptotic Model of Thin Interphase Inhomogeneity 

17.4 Null-Field Method in Scattering Problems with Effective Contact Conditions 

17.5 The Effect of a Thin Compliant Interphase Layer on SH-Wave Scattering Amplitudes 

17.6 Pulses of Echo Signals in a Matrix With Fiber and a Thin Compliant Interphase Layer 

17.7 Conclusion 

References 

18 3D Time-Harmonic Elastic Waves Scattering on Shell-Like Rigid Movable Inclusions 

Roman Kushnir, Iaroslav Pasternak, and Heorhiy Sulym

18.1 Introduction 

18.2 Problem Statement. Boundary Integral Equations 

18.3 A Mathematical Model of a Rigid Shell-Like Inclusion 

18.4 Boundary Element Solution of the Problem

18.4.1 General Issues of the Boundary Element Solution 

18.4.2 Evaluation of Kernels for Anisotropic Materials 

18.4.3 Evaluation of the Generalized Stress Intensity Factors 

18.5 Numerical Example 

18.6 Conclusions

References

19 Dynamics of an Asymmetrical Three-Layer Spherical Dome With an Inhomogeneous Filler Under a Concentrated Impact 

Peter Lugovoi and Serhii Orlenko

19.1 Introduction 

19.2 Formulation of the Problem – Basic Equations 

19.3 Numerical Results 

References 

20 Analytical and Numerical Solution of Static Problems of Non-Circular Cylindrical Shells 

Volodymyr Maksymyuk, Evgen Storozhuk, and Ivan Chernyshenko

20.1 Introduction 

20.2 Boundary Value Problem Statement, Basic Linear Relations and General Solution for a Long Non-Circular Cylindrical Shell 

20.3 Analytical (Exact) Solutions of Statics Problems for Non-Circular Cylindrical Shells 

20.3.1 Exact Solutions of Boundary Value Problems for a Closed Cylindrical Shell of Oval Cross-Section 

20.3.2 Exact Solutions of Statics Problems for an Open Cylindrical Shell of Oval Cross-Section 

20.3.3 Numerical Results and Their Analysis 

20.4 Analytical-Numerical Approach to Solving Boundary-Value Problems for Cylindrical Shells of Non-Circular Cross-Section Under the Action of Static Loads

20.4.1 Closed Long Cylindrical Shell of Non-Circular Cross-Section 

20.4.2 Open Long Cylindrical Shell With Non-Circular Cross-Section and Hinged Longitudinal Edges 

20.4.3 Effect of Changing the Thickness of an Elliptical Cylindrical Shell on Its SSS 

20.5 Physically Nonlinear Problems of the Statics of Thin Non-Circular Cylindrical Shells Made of Composite Material 

20.5.1 Statement of Physically Nonlinear Problems for Orthotropic Shells and Numerical Methods for Their Solution 

20.5.2 Features of Deformation of Non-Circular Cylindrical Shells. Linear Statement 

20.5.3 Physically Nonlinear Deformation of an Orthotropic Cylindrical Shell of Elliptical Cross Section 

20.6 Conclusions 

References

 

21 Nonlinear Hereditary Creep of Transversely Isotropic Composites of Random Structure 

Borys Maslov

21.1 Introduction 

21.2 Problem Statement 

21.3 Generalized Schapery Correspondence Principle for Hereditary Creep Problems 

21.4 A Local Problem of the Mechanics of Hereditary Creep Under a Complex Stress State 

21.5 Multicomponent Linear Hereditary Materials 

21.6 Nonlinear Solution of Second-Order Hereditary Creep 

21.7 The Function of Stored Strain Energy and Additional Energy 

21.8 Conclusion 

References

 

22 Boundary Integral Equation Method for 3D Elastodynamic Problems with Chain-Arranged Rigid Disc-Shaped Inclusions 

Viktor Mykhas’kiv and Igor Zhbadynskyi

22.1 Introduction 

22.2 Boundary Integral Equation in the Domain of Reference Inclusion 

22.3 Regularization and Discretization of Boundary Integral Equation 

22.4 Determination of Actual Dynamic Quantities 

22.5 Numerical Analysis 

22.6 Conclusions 

References 

23 Using the Wiener–Hopf Method in Solving the Problem of Elastic Equilibrium of a Bihomogeneous Body with Interfacial Cracks at the Corner Point of a V-Shaped Interface 

Volodimir Nazarenko and Alexander Kipnis

23.1 Introduction 

23.2 Statement of the Problem 

23.3 Wiener–Hopf Functional Equation 

23.4 Investigation of the Stress State in the Vicinity of the Corner Point and in the Vicinity of the Tip of the Interfacial Crack 

23.5 Conclusions 

References 

24 Solving Current Problems in the Dynamics of Space-Rocket Systems 

Oleg Pylypenko

24.1 Dynamics of Liquid-Propellant Rocket Propulsion Systems 

24.2 Longitudinal Stability of Liquid-Propellant Launch Vehicles 

24.3 High-Frequency Processes in the LPRE Combustion Chamber

24.4 Dynamics of Vibration Protection Systems 

24.5 Aerodynamic Improvement of Gas Turbine Engine Components 

24.6 Conclusions 

References 

25 Comparison of Evolution of Five Types of Elastic Waves (Harmonic,Gauss, Whittaker, MacDonald, Friedlander Initial Profiles) 

Jeremiah Rushchitsky and Vasyl Yurchuk

25.1 Introduction 

25.2 Two Basic Nonlinear Equations Describing the Elastic Wave Propagations in Materials 

25.2.1 The Nonlinear Equation Describing the Propagation of Elastic Plane Longitudinal Wave 

25.2.2 The Nonlinear Equation Describing the Propagation of Elastic Cylindrical Wave 

25.3 Two Approximate Methods of Solving the Basic Nonlinear Wave Equations 

25.3.1 Method of Successive Approximations (Method 1) 

25.3.2 Method of Restrictions on the Gradient of Displacement (Method 2) 

25.4 Harmonic Wave as the Classic One (The Symmetric Initial Profile) 

25.4.1 Method 1. First Two Approximations 

25.4.2 Method 1. First Three Approximations 

25.4.3 Method 2. First Two Approximations 

25.5 Wave with the Symmetric Initial Profile in the Form of Gauss

Function 

25.5.1 Gauss Profile (Method 1, First Two Approximations) 

25.5.2 Gauss Profile (Method 2, First Two Approximations) 

25.5.3 Gauss Profile (Method 2, First Three Approximations) 

25.6 Wave with the Asymmetric Initial Profile in the Form of Whittaker Function 

25.7 Wave with the Asymmetric Initial Profile in the Form of the MacDonald Function 

25.8 Wave with the Asymmetric Initial Profile in the Form of Friedlander Function 

25.9 Results of comparisons 

25.10 Final Conclusions 

References

 

26 Stress-Strain State of Sheet Elements at One- and Two-Layer Build-Up with Liquid Metal

Ihor Senchenkov, Ihor Ryabtsev, Olha Chervinko, and Nina Yakovenko

26.1 Introduction 

26.2 Object of Study 

26.3 Model of Microstructural Transformations 

26.4 Model of Growing Bodies

26.5 Flow Model 

26.6 Problem Statement 

26.7 Thermomechanical Characteristics of the Material 

26.8 Method of Numerical Simulation 

26.9 Results of Calculations of Deflections of Sheet Elements at Surfacing 

26.10 Results of Calculations of Stresses and Plastic Deformations 

26.11 Conclusions 

References 

27 Nonstationary Thermoelastic Problem for a Multilayer Coating/Half Space Assembly at Radiative and Convective Loading 

Victor Shevchuk

27.1 Introduction 

27.2 Statement of the Heat Conduction Problem

27.3 Solution of the Heat Conduction Problem With a Generalized Boundary Condition 

27.3.1 Scheme of the Quasilinearization Method 

27.3.2 Construction of an Approximate Solution of the Linearized Problem for the ����th Approximation 

27.3.3 Iterative Scheme for Determining Temperature in the Half-Space

27.4 Relations for Determining the Coating Temperature

27.5 Solution of the Problem of Thermoelasticity 

27.6 Numerical Results and Their Analysis

27.7 Conclusions 

References 

28 Model of Nonlinear Deformation of Layered-Fibrous Materials with Physically Nonlinear Components 

Elena Shikula and Viktor Vyshnivskyi

28.1 Introduction 

28.2 Nonlinear Equations for Determination of the Effective Deformative Properties and Stress-Strain State of the Composite 

28.3 Algorithm for Determination of the Effective Deformative Properties and Stress-Strain State of the Composite 

28.4 Influence of Component Nonlinearity on the Deformation of the Composite 

28.5 Conclusions 

References 

29 Contact Problems for Cylindrical Stamps and Elastic Bodies with Initial (Residual) Stresses 

Natalia Yarets’ka

29.1 Introduction 

29.2 Main Relations 

29.3 Spatial Contact Problem for Prestressed Cylindrical Punch and Elastic Layer With Initial (Residual) Stresses 

29.3.1 Problem Statement and Boundary Conditions 

29.3.2 Method of Solution

29.3.3 Numerical Results 

29.4 Pressure of Two Prestressed Half-Spaces on Elastic Cylindrical Punch With Initial (Residual) Stresses

29.4.1 Problem Statement and Boundary Conditions 

29.4.2 Method of Solution 

29.4.3 Numerical Results 

29.5 Contact Problem for a Rigid Ring Punch With Half Space With Initial (Residual) Stresses 

29.5.1 Problem Statement and Boundary Conditions 

29.5.2 Method of Solution 

29.5.3 Numerical Results 

29.6 Pressure of Elastic Ring Punch With Initial Stresses on Prestressed Half-Space 

29.6.1 Problem Statement and Boundary Conditions 

29.6.2 Method of Solution 

29.6.3 Numerical Results

29.7 Conclusion

References 

30 Express Diagnostics of Materialstrength Properties Under Shock Wave Destruction 

Yaroslav Zhuk, Mykola Melnichenko, Volodymyr Andruschenko, and Mykhailo Vodotovka

30.1 Introduction 

30.2 Problem Statement and Experimental Technique 

30.3 Experimental Results 

30.3.1 Investigation of Ceramic Plate Strength Properties 

30.3.2 Strength Properties of Artificial Stone 

30.3.3 Investigation of Composite Material Strength Properties 

30.4 Conclusions 

References