Solid Mechanics, Theory of Elasticity and Creep

Preface
Monographs of N. Kh. Harutyunyan
Contents
Contributors
1 On One Non-classical 3D Problem for a Layered Package of Isotropic Plate and the Problem of Earthquakes Prediction
1.1 Introduction
1.2 Solution of 3D Quasistatic Problems
1.3 Investigation of Fast Dynamic Processes
1.4 Conclusions
References
2 Diffraction of Plane Waves in an Elastic Half-Plane Enhanced Along Its Boundary by a Semi-infinite Stringer
2.1 Introduction
2.2 Statement of the Problem
2.3 Influence Function
2.4 Solution of the Contact Problem
2.5 Determination of the Radiated Wave Field
2.6 Numerical Analysis
2.7 Conclusion
References
3 Analysis of Equivalence Conditions of Model of an Inhomogeneous Elastic Half-Space and Model of an Inhomogeneous Elastic Layer on the Elastic Foundation
3.1 Introduction
3.2 Statement of the Contact Problem on the Shear of the Surface of an Inhomogeneous Half-Space
3.3 Models of an Inhomogeneous Half-Space
3.4 Integral Equations of Contact Problems and Solution Methods
3.5 Numerical Analysis
3.6 Conclusion
References
4 Docking of Inhomogeneous Surfaces of Piezoelectric Layers in a Composite Waveguide as a Harvesters of Wave Energy
4.1 Introduction
4.2 Modeling of a Two-Layer Piezoelectric Waveguide, Taking into Account the Roughness of the Surfaces of the Constituent Layers
4.3 Formulation of a Mathematical Boundary Value Problem in a Three-Layer Sandwich with a Thin Inhomogeneous Filling
4.4 Solution of the Mathematical Boundary Problem
4.5 Conclusion
References
5 About One Approach in Prevention of the Emerging Dangerous Phenomena Caused by the Existence of Defect in Continuous Media
5.1 Introduction
5.2 Formulation of the Problem
5.3 Eigenfunction Method in the Plane Problem of Vertical Vibrations for a Plate with a New Type Crack
5.4 Numerical Implementation Results
5.5 Conclusion
References
6 Stress–Strain State of a Magnetoelastic Ferromagnetic Plane with a Crack Under the Action of a Magnetic Field
6.1 Introduction
6.2 Statement of the Problem
6.3 Solution of the Problem in the Case of a Constant Transverse Magnetic Field
6.4 Solution of the Problem
6.5 Coefficients of Intensity of Magnetoelastic Stresses and Induced Magnetic Field
6.6 Occurrence of Concentrations of Magnetoelastic Stresses Due to Longitudinal Shear Due to the Orientation of the External Magnetic Field
References
7 The Effect of Longitudinal Oscillations Resonance on Stability and Domains of Attraction in the Generalized Kapitsa Problem
7.1 Introduction
7.2 Model of a Compressed Pendulum. Complete Nonlinear System of Equations
7.3 Averaged Motion Equation of the Pendulum
7.4 Stability Conditions for the Upper Equilibrium Position
7.5 Oscillation Stability Zone
7.6 Conclusion
References
8 Band Gaps of Metastructure with Periodically Attached Piezoelectric Patches and Internal Hinges
8.1 Introduction
8.2 Band Gaps of a Beam with Periodically Attached Piezoelectric Patches
8.3 Band Gaps of a Beam with Periodically Attached Piezoelectric Patches and Internal Hinges
8.4 Analysis and Conclusions
References
9 Periodic Contact Problem for a Two-level System of Punches and a Viscoelastic Half-space
9.1 Introduction
9.2 Statement of the Contact Problem
9.3 Contact Problem Solution for the First Level Punches
9.3.1 Derivation of the Main Equations for Calculation of the First Level Contact Characteristics
9.3.2 Determination of the Instant of Time When the Second Level of Punches Comes into Contact with the Half-space
9.3.3 Analysis of the Indentation of the First Level Punches into the Half-space
9.4 Two-level Contact of the System of Punches and the Half-space
9.4.1 Asymptotic Analysis of the Contact Characteristics
9.4.2 Solution of the Viscoelastic Two-level Periodic Problem
9.4.3 Analysis of the Dependence of the Real Contact Area on Time
9.5 Conclusions
References
10 On an Axisymmetric Contact Problem for a Piecewise-Homogeneous Space with Disk-Shaped Crack
10.1 Introduction
10.2 Statement of the Problem and Derivation of Governing Equations
10.3 Solution of the Governing Singular Integral Equation
10.4 Numerical Analysis
10.5 Conclusion
References
11 High-Temperature Creep of Cast Irons
11.1 Introduction to Cast Iron
11.2 Microstructure of Cast Iron
11.3 Chemical Composition of Cast Iron
11.4 Mechanical Properties of Cast Iron
11.5 High-Temperature Applications of Cast Irons
11.6 Introduction to Creep
11.7 Creep Models
11.7.1 Empirical Models
11.7.2 Mechanism-Based Models
11.7.3 Continuum-Mechanics and Micromechanical Models
11.8 Creep in Cast Irons
11.9 Experimental Results for CGI Creep
References
12 About the Energy Dissipation Coefficient of Thin-Walled Glass-Plastic Pipes with the Initial Reinforcement Asymmetry with Respect to Axis Subjected to Pulsating Internal Hydrostatic Pressure
12.1 Introduction
12.2 Research Methodology
12.3 Results and Discussions
12.4 Conclusions
References
13 Contact Problem for Coated Viscoelastic Tube and Rigid Inserts with Complex Profiles
13.1 Introduction
13.2 Problem Formulation and Mathematical Model
13.3 Getting an Analytical Solution
13.4 Conclusions
References
14 Inelastic Behavior of High-Temperature Steel Under Cyclic Loading Conditions
14.1 Introduction
14.2 Two-Time-Scale Technique
14.3 Material Model
14.3.1 Elastic Behavior
14.3.2 Inelastic Behavior
14.3.3 Application of the Two-Time-Scale Approach
14.4 Simulation of the Material Behavior
14.4.1 Cyclic Loading Condition
14.4.2 Results of the Finite Element Simulation
14.5 Conclusion
References
15 One Case of a Lubrication Problem for a Line Contact of Elastic Solids with Soft Double Coatings
15.1 Introduction
15.2 Main Simplified Relationships Used in the Problem Formulation
15.3 Some Results for the Lubrication Problem
15.4 Closure
References
16 On the Exact Solution of the First Boundary Value Problem for a Plane with a Circular Hole in the Formulation of the Nonlinear Power-Law Theory of Steady Creep Under Antiplane Deformation
16.1 Introduction
16.2 Representation of Stresses and Strain Rates in Terms of the Harmonic Function of Pseudostresses
16.3 Formulation of the Problem and Derivation of the Basic Equations
16.4 Solving Nonlinear Singular Integral Equation
16.5 Conclusion
References
17 On the Generalised Boundary Conditions in Harutyunyan's Model of Growing Solids
17.1 Introduction
17.2 Governing Equations of Harutyunyan's Model of Surface Growing Solids
17.3 Differential Constraints on Propagating Growing Surface
17.4 Pseudoscalar Geometry of Propagating Growing Surface
17.5 Differential Constraints on Propagating Growing Pseudoscalar Surface
17.6 Conclusions
References
18 Concerning Identification of Two Thermomechanical Characteristics of Functionally Graded Pipe
18.1 Intro
18.2 Inverse Thermoelasticity Problem Statement
18.3 Solution of the Direct Thermoelasticity Problem
18.4 Iterative Scheme for Solving the Inverse Thermoelasticity Problem
18.5 Results of Two Thermomechanical Characteristics Reconstruction
18.6 Conclusion
References
19 Regularities of Technological Residual Stress Fields Formation in Cylindrical Products Manufactured by Additive Methods
19.1 Introduction
19.2 Basic Relations for the Problem Under Consideration
19.3 Calculating Residual Stresses After Stopping Rotation
19.4 Conclusions
References
20 Two-Point Rotations in Geometry of Finite Deformations
20.1 Requisite Notions and Equations
20.2 Pairs of Reciprocal Deformation and Strain Tensors
20.3 Unconventional Orthogonality of the Two-point Rotation Tensor
20.4 Conventionally Orthogonal Finite Rotation Tensors. Finite Rotation Pseudovectors
20.5 Final Remarks and Conclusions
References
21 Quadrature Formulas for Integrals with a Weak Singularity in the Kernel and a Weight Function of Jacobi Polynomials with Complex Exponents
21.1 Introduction
21.2 Quadrature Formula for an Integral with a Logarithmic Singularity
21.3 Numerical Analysis
21.4 Quadrature Formula for an Integral with a Signum Function
21.5 Quadrature Formulas for Particular Values of the Exponents α and β
21.6 Conclusion
References
22 Bending and Contact Problem for a Graphene Sheet Within the Framework of the Model of Bending Deformation of Elastic Thin Plates Based on Cosserat Theory
22.1 Introduction
22.2 Basic System of Equations, Boundary Conditions and Variational Lagrange Principle of Bending Deformation of an Elastic Plate Based on Cosserat Theory
22.3 Bending of a Hinged Supported Rectangular Plate Under the Action of a Distributed Normal Load
22.4 Elastic Constants of the Plane Stress State and Bending Deformation of Plates for the Graphene Material
22.5 An Example of Calculating the Bending of a Graphene Sheet
22.6 Cylindrical Bending of a Plate (Graphene Sheet) with a Rigid Stamp
22.7 Conclusion
References
23 Non-axisymmetric Vibration of Tuned Thin Functionally Graded Planar Structures
23.1 Introduction
23.2 Equations of Motion
23.3 Implicit Boundary Conditions
23.4 Exact Solutions to the Boundary Value Problems
23.5 Explicit Boundary Conditions
23.6 Numerical Results
23.7 Conclusions and Discussions
References
24 Adhesive Contact Problems of the Theory of Viscoelasticity
24.1 Introduction
24.2 Formulation of the Problems and Reduction to the Integral Equations
24.3 The Asymptotic Investigation
24.4 An Approximate Solution of SIDE (3)
24.5 Discussion and Numerical Results
References
25 An Efficient Treatment of Sound Diffraction by Arbitrary Obstacles with Angles
25.1 Introduction
25.2 Formulation of the Problem
25.3 An Example of a Specific Geometry
25.4 Qualitative Algebraic Properties of the Basic Matrix
25.5 Two Methods to Improve the Structure of the Basic Matrix
25.6 Conclusions
References
26 Exact Solution of the Axisymmetric Problem for Poroelastic Finite Cylinder
26.1 Introduction
26.2 Statement of the Problem
26.3 Exact Solution of a One-Dimensional Problem in the Transform Domain and Its Analytical Inversion
26.4 Results and Discussion
26.5 Conclusions
Appendix A
References