Progress in Continuum Mechanics (Advanced Structured Materials, 196)

✍ Scribed by Holm Altenbach (editor), Hans Irschik (editor), Alexey V. Porubov (editor)

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 504
• Category: Library

✦ Synopsis

This book gives an insight into the current developments in the field of continuum mechanics. Twenty-five researchers present new theoretical concepts, e.g., better inclusion of the microstructure in the models describing material behavior. At the same time, there are also more applications for the theories in engineering practice.

In addition to new theoretical approaches in continuum mechanics and applications, the book puts an emphasis on discussing multi-physics problems.

✦ Table of Contents

Preface
Contents
List of Contributors
Chapter 1 A Semi-Empirical Fluid Force Model for Vortex-Induced Vibration of an Elastic Structure
1.1 Introduction
1.2 A Fluid Force Model
1.2.1 Formulation of the Problem
1.2.2 Solution of the Structure Motion Equation
1.2.3 Effect of Variation of an Added Mass with the Reduced Velocity
1.3 An Example
1.4 Conclusion and Discussion
References
Chapter 2 Nonlinear Buckling and Equilibria of Layered Shallow Parabolic Arches with Interlayer Slip
2.1 Introduction
2.2 Basic Equations
2.3 Solution
2.4 Buckling and Post-Buckling Analysis
2.4.1 Primary Equilibrium Path
2.4.2 Limit Loads and Limit Points
2.4.3 Bifurcation Loads and Bifurcation Points
2.4.4 Post-Bifurcation Equilibrium Path
2.5 Application
2.5.1 Example Problem 1
2.5.2 Example Problem 2
2.5.3 Critical Loads
2.5.4 Parabolic Shallow Arch vs. Circular Shallow Arch
2.6 Summary and Conclusions
References
Chapter 3 On the General Strategies to Formulate Shell and Plate Theories
3.1 Introduction
3.2 Classification Principles
3.2.1 Classification of Structural Models
3.2.2 Classification of Theories for Two-Dimensional Structures
3.3 Direct Approach
3.3.1 General Cosserat Surface Theory
3.3.2 12-Parameter Theory
3.3.3 6-Parameter Theory
3.3.4 5-Parameter Theory
3.3.5 3-P arameter Theory
3.4 Conclusions
References
Chapter 4 Conceptual Generalizations of the Kapitsa Problem
4.1 Introduction
4.2 Mathieu Equation
4.3 Model of the Flexible Rod of the Kapitsa Pendulum
4.4 Asymptotic Expansion
4.5 Pade Approximation
4.6 Discussion of Results
4.6.1 Resonances of Longitudinal Vibrations
4.6.2 General Picture of Stability by Asymptotic Formulas
4.6.3 Comparison with the Exact Solution
4.6.4 Conclusions
4.7 Some Hypotheses Regarding the Possible Application of the Kapitsa Pendulum Effect in Modern and Advanced Technology
References
Chapter 5 Dynamic Properties of Periodic Structures with Symmetric Inclusions
5.1 Introduction
5.2 Oscillations of Symmetric n-gon Frames
5.3 Oscillations of Periodic Systems Containing Symmetric Subsystems
5.4 An Example of Calculation of a 3-Section System with Symmetric Subsystems
5.5 Structure of the Spectrum of Natural Frequencies of a Multisection Structure
5.6 Conclusions
Appendix A. Application of the Group Representation Theory for Mechanical Systems
A.1. Basic Concepts of the Representation Theory of Symmetry Groups
A.2. Matrix Symmetry Operators
References
Chapter 6 Mathematical Model for Myopia Correction with MyoRing Implants
6.1 Introduction
6.2 Problem Statement
6.3 Results and Discussion
6.4 Conclusion
References
Chapter 7 Numerical Modeling the Stresses in Incompressible and Rigid Bodies
7.1 Introduction
7.2 Numerical Modeling of the Flow of the Incompressible Micropolar Liquids
7.3 Numerical Modeling of the Deformation of a Rubber-Like Incompressible Solid Body
7.4 Numerical Modeling of Stresses in the Rigid Body
7.4.1 First Example
7.4.2 Second Example
Appendix A: 3D Iterative Alternative Direction Implicit Method
References
Chapter 8 Three-Dimensional Numerical Analysis of Natural Vibrations and Stability of Cylindrical Shells Interacting with Fluid
8.1 Introduction
8.2 Mathematical and Numerical Formulations
8.3 Single Cylindrical Shells
8.3.1 Circular Cylindrical Shells
8.3.2 Elliptical Cylindrical Shells
8.4 System of two Circular Cylindrical Shells
8.4.1 Coaxial Shells
8.4.2 Eccentric shells
8.5 Conclusion
References
Chapter 9 On the Problem of Modeling the Influence of Ice Cover and Surface Waves of a Liquid on the Dynamics of a Floating Body
9.1 Introduction
9.2 Statement of the Problem
9.3 Numerical Method
9.4 Results
9.5 Conclusion
References
Chapter 10 Nonlinear Stationary Waves in a Thin-Walled Bar Affected by Deplanation of Its Cross-Section in Torsion
10.1 Introduction
10.2 Differential Equation for Torsional Vibrations of a Bar Taking into Account the Nonlinearity and Deplanation of the Bar Cross Section
10.3 Wave Processes in a Thin-Walled Bar Taking into Account the Quadratic Nonlinearity
10.4 Wave Processes in a Thin-Walled Bar Taking into Account the Cubic Nonlinearity
10.5 Wave Processes in a Thin-Walled Bar with Simultaneous Consideration to the Quadratic and Cubic Nonlinearities
10.6 Conclusions
References
Chapter 11 Linear Reduced Elastic Isotropic Cosserat Medium Subjected to the External Follower Viscoelastic Torque as a Smart Acoustic Metamaterial
11.1 Introduction and Notation
11.2 Equations of the Reduced Elastic Linear Isotropic Cosserat Medium Subjected to a Viscoelastic Follower Body Torque. Spectral Problem
11.3 Isotropic Linear Elastic Reduced Cosserat Medium Subjected to an Elastic Follower Torque
11.4 Isotropic Elastic Reduced Cosserat Medium Subjected to a Viscous or Viscoelastic Follower Torque
11.4.1 Dispersion Relation for the Shear–Rotational Wave
11.4.2 Small Dissipation far from Characteristic Frequencies Ω = Ω1 and Ω = 1
11.4.3 Small Dissipation near the Lower Characteristic Frequency Ω1
11.4.4 Small Dissipation near the Upper Characteristic Frequency Ω = 1
11.5 Conclusions
References
Chapter 12 Nonlinear Vibrations of Bimodular Continua by Means of Isogeometric Analysis
12.1 Introduction
12.2 Mechanical Modeling
12.2.1 Kinematic Relations
12.2.2 Governing Equations of Elastic Bimodular Beams
12.3 Considered Geometries - Isosceles Triangle Cross-Section
12.4 Application of Isogeometric Analysis to the Bimodular Beam
12.4.1 B-Splines
12.4.2 Isogeometric Analysis of Bimodular Beam Vibration
12.5 Numerical Studies
12.6 Conclusions
References
Chapter 13 On the Equivalence Between Singular Waves Propagating in Force Loaded Viscoelastic Bodies and in Elastic Bodies Additionally Loaded by Eigenstrains
13.1 Introduction
13.2 Basic Relations
13.3 An Equivalence Problem and its Solution
13.4 1D ShockWave Propagating in a Semi-Infinite Half-Space or Rod
References
Chapter 14 Influence Tensors for the Analytical Mechanics of Anisotropic Eigenstressed Composites with Inclusions of Various Shapes and Orientations
14.1 Introduction
14.2 Fundamentals of Continuum Micromechanics and Composite Mechanics
14.2.1 Representative Volume Element, Average Rules, and Scale Transition Relations
14.2.2 Characteristics of Strain Concentration and Microeigenstress-to-Microstrain Influence Tensors
14.3 Derivation of Influence Tensors for Inclusions in Anisotropic Multishape Composites, from Eigenstressed Matrix-Inclusion Problems
14.4 Determination of Matrix Influence Tensor QMM
14.5 Check of Influence Tensor Expressions
14.5.1 Fulfillment of Influence Tensor Average Rule
14.5.2 Consistency of Influence Tensor Expressions with Levin’s Theorem
14.5.3 Consistency of Influence Tensor Expressions with Elastic Reciprocal Theorem
14.6 Benchmark Examples
14.6.1 Benchmark I: Multishape Composite with Isotropic Phase Properties
14.6.2 Benchmark II: Multishape Composite with Transversely Isotropic Matrix Phase
14.7 Conclusions
References
Chapter 15 Computation of Eigenstrains for Static Shape Control of Arbitrarily Shaped Sub-Domains of Force-Loaded Elastic Bodies
15.1 Introduction
15.2 Static Shape Control of Material Bodies - a Brief Introduction
15.2.1 Displacement Tracking
15.2.2 Numerical Example
15.3 Static Shape Control of Sub-Domains
15.3.1 Strain Tracking
15.3.2 Displacement Tracking
References
Chapter 16 Flexural Deformations and Vibrations of a Three-Layer Beam-Strip with a Stiff Core and Soft Skins
16.1 Introduction
16.2 Statement of the Problem
16.3 Asymptotic Integration of Boundary-Value Problem
16.3.1 Leading Approximation
16.3.2 First-Order Approximation
16.3.3 Governing Equation
16.4 Free Vibrations
16.5 Conclusions
References
Chapter 17 Maxwell’s Equations Through the Ages
17.1 Introduction and Scope of the Paper
17.2 Physical Principles of Electromagnetism
17.2.1 Conservation of Electromagnetic Flux
17.2.2 Conservation of Electric Charge
17.3 Early Forms of Maxwell’s Equations
17.3.1 Maxwell’s Treatise on Electromagnetism
17.3.2 Maxwell’s Disciples
17.4 World-Tensor Form of Maxwell’s Equations
17.4.1 A Naive Introduction of the World-Tensors of Electrodynamics and Maxwell’s Equation in Space-Time Formulation
17.4.2 Absolute Space-Time Notations
17.5 Conclusions and Outlook
References
Chapter 18 Multi-Objective Optimization of the Helix Shape of Cylindrical Milling Tools
18.1 Introduction
18.2 Milling Flute Cutting Force
18.3 An Analytical Cutting Force Model
18.3.1 The Integrated Force Components
18.3.2 Force Dependence on the Variable Helix Angle βp
18.4 Optimization
18.4.1 The Objective Functions
18.4.2 The Optimization Problem
18.5 Numerical Results
18.6 Conclusions
References
Chapter 19 Experimental and Numerical Studies on the Tensile Strength of Lap Joints of PEEK Plates and CF Fabric Prepregs Formed by Ultrasonic Welding
19.1 Introduction
19.2 Experimental Investigation of the Influence of the Prepreg ‘Design’ and its Properties on the Tensile Strength of the USW Lap Joints
19.2.1 Samples’ Fabrication
19.2.2 Tensile Tests of the USW Joints
19.3 A Parametric Study of the Tensile Deformation Behavior of the USW Joints Based on Numerical Simulation
19.3.1 The Problem Statement for the Parametric Studies on the Tensile Deformation Behavior of the USW Lap Joints
19.3.2 Criteria for the Damage Simulation
19.3.3 A Study of the Tensile Strength of the USW Joints in the 3D Formulation
19.3.4 The Effect of the Dimensions of the PEEK Adherends, Their Properties and the Loading Type on the Tensile Strength of the USW Lap Joints (2D Formulation)
19.4 Conclusions
References
Chapter 20 On two Approaches for Determination of the Effective Conductivity of a Polycrystalline Material by Homogenization Methods
20.1 Introduction
20.2 Problem Statement
20.3 Results
20.4 Conclusion
References
Chapter 21 The Functionally Invariant Solutions and Nonlinear Wave Equations
21.1 Introduction
21.2 Functionally Invariant Solutions
21.3 Solving the Nonlinear Equation
21.4 Conclusion
References
Chapter 22 Hydrogen Skin Effect vs. Hydrogen Diffusion
22.1 Introduction
22.2 The Theoretical Observation
22.2.1 Hydrogen Transport Model
22.2.2 Model Description
22.2.3 Computational Algorithm of the Model
22.3 Simulation Results
22.4 The Discussion of the Results
22.5 Conclusions
References
Chapter 23 Bending Waves in Mass-in-Mass Metamaterial
23.1 Introduction
23.2 Bending in Mass-in-Mass Chain
23.3 Dispersion Analysis
23.4 Discussion
References
Chapter 24 Numerical Investigations of Large Amplitude Oscillations of Planar Parametrically Excited Beams
24.1 Introduction and Model Description
24.1.1 Model of a Parametrically Excited Beam
24.1.2 Finite Element Formulation
24.1.3 Parameter Values and Non-Dimensionalization
24.2 Stability of the Trivial Solution
24.2.1 Analytical Approximation of the Stability Limit (Bolotin’s Method)
24.2.2 Numerical Determination of the Stability Boundaries
24.3 Calculation of Periodic Solutions Bifurcating from the Primary Resonance
24.3.1 FE Simulations and Use of a Boundary Value Problem Solver
24.3.2 Application of the Galerkin Method
24.3.3 Local Analytical Investigation of the Oscillation Equation Close to the 2 : 1-Resonance
24.3.4 Approximation by the Ritz Method
24.4 Conclusions and Further Research Goals
References
Chapter 25 Continuum Mechanics Applied for Studying Instabilities in Nanoparticles
25.1 Introduction
25.2 Methods and Models
25.2.1 Atomistic Approaches
25.2.2 Continnuum Mechanics Approaches
25.3 Mechanical Properties Used in Continuum Shell Models
25.3.1 Effective Elastic Properties and Thickness
25.3.2 Continuum Mechanics Models for van der Waals Interaction and the Intrinsic Curvature Induced Excess Surface Energy
25.4 Some Examples for Application of Continuum Mechanics to Nanoparticles
25.4.1 Carbon Crystallites
25.4.2 Carbon Onions
25.5 Conclusion
References
Chapter 26 Spectral Domain Approach for the Numerical Modeling of Elastodynamic Fields in Layered Structures
26.1 Introduction
26.2 Modeling
26.2.1 Governing Equations
26.2.2 Dimensional Analysis and Scaling
26.2.3 Conversion to Ordinary Differential Equations
26.2.4 Equation System and Green’s Function
26.2.5 Electrical Field Calculation
26.3 Examples
26.3.1 Electrical Capacitance Calculation of Interdigital Capacitors
26.3.2 Vibrating Fluid Sensor
26.3.3 Piezoelectric Fluid Sensor
References