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

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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 This book presents a collection of articles reporting the current challenges in solid and fracture mechanics. The book is devoted to the 90th birthday of academician Nikita F. Morozov―a well-known specialist in the field of solid and fracture mechanics.