Advances in Solid and Fracture Mechanics: A Liber Amicorum to Celebrate the Birthday of Nikita Morozov

Preface
Contents
List of Contributors
Chapter 1 On Forced Vibrations of Orthotropic Plates in the Presence of Internal Friction
1.1 Introduction
1.2 The Formulation of the Problem and Basic Equations
1.3 The Solution to the External Problem
1.4 On Mathematically Precise Solutions
1.5 Conclusions
References
Chapter 2 Asymmetric Buckling of Orthortropic Plates Under Normal Pressure
2.1 Introduction
2.2 Problem Formulation
2.3 Equations for Buckling
2.4 Numerical Results
2.5 Conclusion
References
Chapter 3 On Ladyzhenskaya’s Inequality and its Applications
3.1 Introduction
3.2 Preliminaries
3.2.1 Some Standard Inequalities
3.2.2 Functions of Compact Support
3.3 Ladyzhenskaya’s Inequality in Two Dimensions
3.4 Ladyzhenskaya’s Inequalities in Three Dimensions
3.4.1 First Result
3.4.2 Second Result
3.5 Further Possible Applications
3.6 Conclusions
References
Chapter 4 Mechanical Behaviour of Nonwovens: Continuous Approach with Parametric Finite-element Modelling
4.1 Introduction
4.2 Background
4.3 Parametric Finite-element Modelling Strategy
4.4 Multiscale Experimental Characterisation
4.4.1 Calendered Fabrics
4.4.2 Experimental Methods
4.5 Generation of Calendered-fabric Model
4.5.1 Computation of Local Mechanical Properties
4.5.2 Meshing
4.5.3 Failure Criterion
4.6 Results and Discussion
4.6.1 Developed Models and Validation
4.6.2 Effect of Load Direction
4.6.3 Effect of Fabric Size
4.6.4 Effect of Bond Pattern
4.7 Conclusions
References
Chapter 5 Free Vibrations of a Cylindrical Shell Closed with the Cap
5.1 Introduction
5.2 Numerical Results
5.3 Basic Equations
5.4 Asymptotic Solution for the Plate-like Vibrations
5.5 Asymptotic Solution for the Shell-like Vibrations
5.6 Vibrations of the Third (Beam-like) Type
5.7 Spectrum Optimization by Thickness Variation
5.8 Conclusions
References
Chapter 6 Indentation of an Absolutely Rigid Thin Inclusion into One of the Crack Faces in an Elastic Plane Under Slippage at the Ends
6.1 Introduction
6.2 Statement of the Problem and Derivation of the Governing System of Integral Equation
6.3 Numerical Analysis
6.4 Conclusion
References
Chapter 7 Biomechanics as a Basis for Clinical Decision Support Systems in the Surgery of the Spine-pelvic Complex
7.1 Introduction
7.2 Noninvasive Method of Obtaining Bone Tissues Mechanical Properties by Computer Tomography
7.2.1 Results of Experiments on Scanning Samples of the Femoral Heads Spongy Bone in a Computer Tomograph
7.2.2 Results of Uniaxial Compression Mechanical Experiments of Femoral Heads Spongy Bone Samples
7.3 Sagittal Balance and its Relation to Vertebral-pelvic Complex Biomechanics
7.4 Quantitative Criteria for Assessing the Success of Surgical Treatment
7.5 Geometric Criteria for Evaluating the Success of Spinal Surgery
7.6 Geometric Criteria for Assessing the Success of Hip Replacement
7.7 Biomechanical Criteria for Evaluating the Success of Treatment: Assessment of Mechanical Strength, Fixation Stability, Implant Life
7.8 Results of the Pilot Implementation of Biomechanical Modeling in the Process of Preoperative Planning
7.8.1 Development of the Accord Software Platform
7.8.2 Substantiation of the Effectiveness of Biomechanical Modeling in Preoperative Planning
7.8.3 The Concept of Clinical Decision Support Systems with Biomechanical Support
7.9 Conclusion
References
Chapter 8 Dispersion of the Bending Wave in a Fluid-loaded Elastic Layer
8.1 Introduction
8.2 Basic Equations
8.3 Dispersion Relations
8.4 Asymptotic Expansions
8.5 Concluding Remarks
References
Chapter 9 Mathematical Models of Local Ice Strength and Problems Elastic-plastic Bending of Hydraulic Structures Supports
9.1 Introduction
9.2 Complex System “Borehole Jack”
9.3 Methodology for Determination of the Local Ice Strength at Compression in Boreholes by a Borehole Jack
9.4 Anisotropy of Ice
9.5 Estimation of Ice Pressure on the Vertical Supports of Hydraulic Structures, Taking into Account the Local Ice Strength
9.6 Conclusions
References
Chapter 10 Stress Distribution at the Wavy Surface of a Solid Incorporating Surface Stresses and Surface Tension
10.1 Introduction
10.2 Problem Formulation
10.3 Boundary Equation for Complex Potentials
10.4 Boundary Perturbation Method
10.5 Numerical Results
10.6 Conclusions
References
Chapter 11 Analytical and Numerical Methods for Analysis of Stress Singularity in Three-Dimensional Problems of Elasticity Theory
11.1 Introduction
11.2 Analysis of Stress Singularity Based on the Constructed Analytical Eigensolutions for Semi-infinite Circular Conical Bodies
11.3 Numerical-analytical Method of Stress Singularity Analysis at the Vertices of Circular and Non-circular Conical Bodies
11.4 Finite Element Analysis of Stress Singularity in Three-dimensional Problems of Elasticity Theory
11.5 Conclusion
References
Chapter 12 On Estimating Prestress State in an Elastic Cylinder
12.1 Intro
12.2 Linearized Deformation Model for a Prestressed Body
12.3 Weak Problem Statement for Prestressed Cylinder
12.4 Sensitivity Analysis
12.5 Comparison of Analytical and FE Prestress Fields
12.5.1 Initial Inflation
12.5.2 Initial Axial Tension
12.5.3 Initial Torsion
12.6 Inverse Problem of Prestress Identification
12.6.1 Problem Statement
12.6.2 Problem Solution
12.6.3 Computational Experiments
12.7 Conclusion
References
Chapter 13 A Method of the JR-curve Determination Using Linear Normalization
13.1 Introduction
13.2 Statement of the Problem
13.3 Obtaining the Solution
13.4 Examples of Application of the Method and Analysis of Results
13.5 Conclusion
References
Chapter 14 Application of Galerkin’s Method to Buckling of Functionally Graded or Stepped Columns
14.1 Introduction
14.2 The Clamped-Free Column
14.3 Buckling of a Heavy Simply Supported-Sliding Column
14.4 Buckling of a Stepped Column Under Axial Load
14.4.1 Galerkin Solution: First Version
14.4.2 Galerkin Solution: Second Version
14.5 Buckling of a Heavy Stepped Column
14.5.1 Exact Solution
14.5.2 Galerkin Solution
14.6 Conclusion
References
Chapter 15 Inter-laminar Delamination in Composite Laminates: Role of Buckling in its Growth
15.1 Introduction
15.2 Mathematical Preliminaries
15.3 Numerical Results
15.4 Conclusions
References
Chapter 16 Suppression of Oscillations of a Loaded Flexible Robotic “Arm” as a Generalized Chebyshev Problem
16.1 Statement of the Problem and Motion Equations of the Mechanical System
16.2 Application of the Pontryagin Maximum Principle. Relation to the Nonholonomic Problem
16.3 Application of the Generalized Gauss Principle for Solving the Above Generalized Chebyshev Problem
16.4 Statement and Solution of the Extended (Generalized) Boundary-value Problem
16.5 Calculation Results
16.6 Conclusions
References
Chapter 17 Theory of Cosserat-type Elastic Shells with Distributed Dislocations and Disclinations
17.1 Introduction
17.2 Initial Relations of the Geometrically Linear Theory of the Cosserat-type Shells
17.3 Continuously Distributed Dislocations and Disclinations in an Elastic Shell
17.4 Boundary-value Problem of Equilibrium of a Shell with Distributed Dislocations and Disclinations
17.5 Variational Formulation of the Equilibrium Problem for an Elastic Shell with Distributed Dislocations and Disclinations
17.6 Static-geometry Analogy
17.7 Spherical Shell with Uniformly Distributed Dislocations and Disclinations
17.8 Conclusion
References