Buch, Englisch, 480 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1008 g
Buch, Englisch, 480 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1008 g
Reihe: Advanced Structured Materials
ISBN: 978-3-031-43735-9
Verlag: Springer
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.
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Weitere Infos & Material
1 A Semi-Empirical Fluid Force Model for Vortex-Induced Vibration of an Elastic Structure Andrei K. Abramian and Sergey A. Vakulenko1.1 Introduction 1.2 A Fluid Force Model 1.2.1 Formulation of the Problem 1.2.2 Solution of the Structure Motion Equation 1.2.2.1 Pure Resonance Case 1.2.2.2 Near Resonance Case 1.2.2.3 Non-Resonant Case 1.2.3 Effect of Variation of an Added Mass with the Reduced Velocity 1.3 An Example 1.4 Conclusion and Discussion References
2 Nonlinear Buckling and Equilibria of Layered Shallow Parabolic Arches with Interlayer Slip Christoph Adam, Ivan Paulmichl, and Thomas Furtmüller2.1 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
3 On the General Strategies to Formulate Shell and Plate Theories Holm Altenbach and Victor A. Eremeyev3.1 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
4 Conceptual Generalizations of the Kapitsa Problem Alexey V. Babenko, Oksana R. Polyakova, and Tatyana P. Tovstik4.1 Introduction 4.2 Mathieu Equation 4.3 Model of the Flexible Rod of the Kapitsa Pendulum4.4 Asymptotic Expansion4.5 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 Conclusions4.7 Some Hypotheses Regarding the Possible Application of the Kapitsa Pendulum Effect in Modern and Advanced Technology References
5 Dynamic Properties of Periodic Structures with Symmetric InclusionsLudmila Ya. Banakh and Igor S. Pavlov5.1 Introduction 5.2 Oscillations of Symmetric ???-gon Frames 5.3 Oscillations of Periodic Systems Containing Symmetric Subsystems5.4 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 6 Mathematical Model for Myopia Correction with MyoRing Implants Svetlana M. Bauer, Liudmila A. Venatovskaya, Eva B. Voronkova, Vladimir V. Kornikov, Larisa A. Avershina, and Anna E. Terenteva6.1 Introduction 6.2 Problem Statement 6.3 Results and Discussion 6.4 Conclusion References
7 Numerical Modeling the Stresses in Incompressible and Rigid Bodies Nikolai M. Bessonov and Yaroslava I. Litvinova7.1 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
8 Three-Dimensional Numerical Analysis of Natural Vibrations and Stability of Cylindrical Shells Interacting with Fluid Sergey A. Bochkarev, Sergey V. Lekomtsev, Valerii P. Matveenko, and Alexander N. Senin8.1 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
9 On the Problem of Modeling the Influence of Ice Cover and Surface Waves of a Liquid on the Dynamics of a Floating Body Anastasiia A. Chevrychkina, Nikolai M. Bessonov, and Andrei K. Abramian9.1 Introduction 9.2 Statement of the Problem 9.3 Numerical Method 9.4 Results 9.5 Conclusion References
10 Nonlinear Stationary Waves in a Thin-Walled Bar Affected by Deplanation of Its Cross-Section in Torsion Vladimir Erofeev, Boris Lampsi (Jr.), Anna Leonteva, and Nadezhda Semerikova10.1 Introduction 10.2 Differential Equation for Torsional Vibrations of a Bar Taking into Account the Nonlinearity and Deplanation of the Bar Cross Section10.3 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
11 Linear Reduced Elastic Isotropic Cosserat Medium Subjected to the External Follower Viscoelastic Torque as a Smart Acoustic Metamaterial Elena F. Grekova and Sabina M. Isaeva11.1 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 O = O1 and O = 1 11.4.2.1 Real Part of the Wave Number 11.4.2.2 Imaginary Part of the Wave Number 11.4.2.3 Logarithmic Decrement 11.4.3 Small Dissipation near the Lower Characteristic Frequency O1 11.4.4 Small Dissipation near the Upper Characteristic Frequency O = 1 11.5 Conclusions References
12 Nonlinear Vibrations of Bimodular Continua by Means of Isogeometric Analysis Rudolf Heuer and Galeb El Chabaan12.1 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
13 On the Equivalence Between Singular Waves Propagating in Force Loaded Viscoelastic Bodies and in Elastic Bodies Additionally Loaded by Eigenstrains Hans Irschik, Michael Krommer, and Astrid S. Pechstein13.1 Introduction 13.2 Basic Relations 13.3 An Equivalence Problem and its Solution 13.4 1D Shock Wave Propagating in a Semi-Infinite Half-Space or Rod References
14 Influence Tensors for the Analytical Mechanics of Anisotropic Eigenstressed Composites with Inclusions of Various Shapes and Orientations Nabor Jiménez Segura, Bernhard L.A. Pichler, and Christian Hellmich14.1 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 Q???????? 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
15 Computation of Eigenstrains for Static Shape Control of Arbitrarily Shaped Sub-Domains of Force-Loaded Elastic Bodies Michael Krommer, Astrid S. Pechstein, and Hans Irschik15.1 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 15.3.1.1 Variational Formulation 15.3.1.2 Numerical Example15.3.2 Displacement Tracking 15.3.2.1 Optimization 15.3.2.2 Numerical Example References
16 Flexural Deformations and Vibrations of a Three-Layer Beam-Strip with a Stiff Core and Soft Skins Gennadi Mikhasev, Marina Botogova, and Nguyen Le16.1 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 Vibrations16.5 Conclusions References
17 Maxwell’s Equations Through the Ages Wolfgang H. Müller and Elena N. Vilchevskaya17.1 Introduction and Scope of the Paper 17.2 Physical Principles of Electromagnetism 17.2.1 Conservation of Electromagnetic Flux17.2.2 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 Notations17.5 Conclusions and Outlook References
18 Multi-Objective Optimization of the Helix Shape of Cylindrical Milling Tools Chigbogu Ozoegwu and Peter Eberhard18.1 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 ???????? 18.4 Optimization 18.4.1 The Objective Functions 18.4.2 The Optimization Problem 18.5 Numerical Results 18.6 Conclusions References
19 Experimental and Numerical Studies on the Tensile Strength of Lap Joints of PEEK Plates and CF Fabric Prepregs Formed by Ultrasonic Welding Sergey V. Panin, Svetlana A. Bochkareva, Iliya L. Panov, Vladislav O. Alexenko, Anton V. Byakov, and Boris A. Lyukshin19.1 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 Simulation19.3.1 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 19.3.3.1 The Effect of the Prepreg Thickness on the Tensile Strength of the USW Lap Joints 19.3.3.2 The Effect of the Adhesion Level Between the Prepreg and the PEEK Adherends on the Tensile Strength of the USW Lap Joints 19.3.3.3 The Effect of the Adhesion Level Between the CF Fabric and the PEEK ‘Facing’ Layer on the Tensile Strength of the USW Lap Joints19.3.3.4 The Effect of the Adhesion Heterogeneity Between the Prepreg and the PEEK Adherends on the Tensile Strength of the USW Lap Joints 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) 19.3.4.1 The Effect of the Prepreg’s Elastic Modulus on the Tensile Strength of the USW Lap Joints19.3.4.2 The Effect of the Partial Interlayer Contact on the Tensile Strength of the USW Lap Joints in the Case of the Short PEEK Adherends 19.4 Conclusions References
20 On two Approaches for Determination of the Effective Conductivity of a Polycrystalline Material by Homogenization Methods Dmitry Pashkovsky, Ksenia Frolova, and Elena Vilchevskaya20.1 Introduction 20.2 Problem Statement 20.3 Results20.4 Conclusion References
21 The Functionally Invariant Solutions and Nonlinear Wave Equations Yuri V. Pavlov21.1 Introduction 21.2 Functionally Invariant Solutions 21.3 Solving the Nonlinear Equation 21.4 Conclusion References
22 Hydrogen Skin Effect vs. Hydrogen Diffusion Vladimir A. Polyanskiy, Dmitry G. Arseniev, Anastasiia A. Chevrychkina, and Yuri A. Yakovlev22.1 Introduction 22.2 The Theoretical Observation 22.2.1 Hydrogen Transport Model 22.2.2 Model Description22.2.3 Computational Algorithm of the Model 22.3 Simulation Results22.4 The Discussion of the Results 22.5 Conclusions References
23 Bending Waves in Mass-in-Mass Metamaterial Alexey V. Porubov and Yuting Zhao23.1 Introduction 23.2 Bending in Mass-in-Mass Chain 23.3 Dispersion Analysis 23.4 Discussion References
24 Numerical Investigations of Large Amplitude Oscillations of Planar Parametrically Excited Beams Alois Steindl, Roman Buchta, Michael Ruttmann, and Yury Vetyukov24.1 Introduction and Model Description 24.1.1 Model of a Parametrically Excited Beam 24.1.2 Finite Element Formulation24.1.3 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 24.2.2.1 Simulation with Fixed Values of Frequency ???? 24.2.2.2 Simulation of the FE Equations with Slowly Varying Frequency 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
25 Continuum Mechanics Applied for Studying Instabilities in Nanoparticles Melanie Todt, Markus A. Hartmann, and Franz G. Rammerstorfer25.1 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 Models25.3.1 Effective Elastic Properties and Thickness 25.3.2 Continuum Mechanics Models for van der Waals Interaction and the Intrinsic Curvature Induced Excess Surface Energy25.4 Some Examples for Application of Continuum Mechanics to Nanoparticles 25.4.1 Carbon Crystallites 25.4.2 Carbon Onions 25.5 Conclusion References
26 Spectral Domain Approach for the Numerical Modeling of Elastodynamic Fields in Layered Structures Thomas Voglhuber-Brunnmaier and Bernhard Jakoby26.1 Introduction 26.2 Modeling 26.2.1 Governing Equations 26.2.1.1 Linear Elastodynamics 26.2.1.2 Electrodynamics 26.2.1.3 Piezoelectric Media 26.2.2 Dimensional Analysis and Scaling 26.2.2.1 Non-Dimensionalization 26.2.2.2 Scaling of Physical Units 26.2.3 Conversion to Ordinary Differential Equations 26.2.4 Equation System and Green’s Function 26.2.5 Electrical Field Calculation 26.2.5.1 Method of Moments 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
