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