Altenbach / Goldstein / Murashkin Mechanics for Materials and Technologies

1. Auflage 2017
ISBN: 978-3-319-56050-2
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 46, 460 Seiten, eBook

Reihe: Advanced Structured Materials

This book shows impressively how complex mathematical modeling of materials can be applied to technological problems. Top-class researchers present the theoretical approaches in modern mechanics and apply them to real-world problems in solid mechanics, creep, plasticity, fracture, impact, and friction. They show how they can be applied to technological challenges in various fields like aerospace technology, biological sciences and modern engineering materials.

Zielgruppe

Research

Autoren/Hrsg.

Altenbach, Holm

Goldstein, Robert V.

Murashkin, Evgenii

Inhaltsverzeichnis

1;Preface;6
2;Contents;12
3;List of Contributors;21
4;1Multi-Mode Symmetric and Asymmetric Solutions in the Jeffery-Hamel Problem for a Convergent Channel;28
4.1;Abstract;28
4.2;Key words:;28
4.3;1.1 Introduction and Statement of the Problem;29
4.4;1.2 Analytical Expressions, Asymptotic Expansions, and Integral;34
4.5;1.2 Analytical Expressions, Asymptotic Expansions, and Integral Estimates of the Solutions;34
4.5.1;1.2.1 Perturbation Method for Small Re;34
4.5.2;1.2.2 Perturbation Method for Small Aperture Angles;35
4.5.3;1.2.3 Asymptotic Behavior of the Solution for Large Re;36
4.5.4;1.2.4 Integral Estimates;36
4.6;1.3 Numerical-Analytical Accelerated Convergence Method and;38
4.7;1.3 Numerical-Analytical Accelerated Convergence Method andContinuation with Respect to a Parameter;38
4.8;1.4 Solutions Regularly Depending on the Reynolds Number;40
4.9;1.5 Construction of the Velocity Profiles and Analysis of the;44
4.10;1.5 Construction of the Velocity Profiles and Analysis of theFluid Flow Modes;44
4.11;1.6 Numerical-Analytical Solution of the Problem for theCritical Value of the Channel Angle;48
4.12;1.7 New Multi-Mode Asymmetric Solutions that Cannot be;51
4.13;1.7 New Multi-Mode Asymmetric Solutions that Cannot beRegularly Continued with Respect to Re;51
4.14;1.8 Kinematic and Force Characteristics of Steady Flows;56
4.15;1.9 Conclusions;57
4.16;Acknowledgements;57
4.17;References;57
5;2Riemann’s Method in Plasticity: a Review;59
5.1;Abstract;59
5.2;Key words:;59
5.3;2.1 Preliminary Remarks;59
5.4;2.2 Pressure-Independent Plasticity;61
5.5;2.3 Pressure-Dependent Plasticity;66
5.6;2.4 Planar Ideal Flows;71
5.7;2.5 Conclusions;72
5.8;Acknowledgements;72
5.9;References;72
6;3Homogenization of Corrugated Plates Based on the Dimension Reduction for the Periodicity Cell Problem;74
6.1;Abstract;74
6.2;Key words:;74
6.3;3.1 Introduction;75
6.4;3.2 Statement of the Problem;77
6.5;3.3 Dimension Reduction for the Periodicity Sell Problem;78
6.6;3.4 Symmetric Corrugation;83
6.7;3.5 Numerical Example 1 - Computation of Effective Stiffness ofthin Corrugated Shells;86
6.8;3.6 Computation of the Effective Stiffnesses D2 1212, D2 2121 for Thin Plates;87
6.9;3.7 Numerical Example 2 - Corrugated Plates of ArbitraryThickness;89
6.10;3.8 Universal Relations Between the Effective Stiffness of Corrugated Plates made of Materials with the same Poisson’s Ratio;95
6.11;3.9 Conclusions;96
6.12;Acknowledgements;96
6.13;References;97
7;4Consideration of Non-Uniform and Non-Orthogonal Mechanical Loads for Structural Analysis of Photovoltaic Composite Structures;98
7.1;Abstract;98
7.2;Key words:;98
7.3;4.1 Introduction;99
7.3.1;4.1.1 Motivation;99
7.3.2;4.1.2 Objective and Structure;101
7.3.3;4.1.3 Preliminaries and Notation;102
7.4;4.2 Mechanical Loads at Photovoltaic Modules;104
7.4.1;4.2.1 Loading at Natural Weathering;104
7.4.1.1;4.2.1.1 Snow Loads;105
7.4.1.2;4.2.1.2 Wind Loads;105
7.4.2;4.2.2 Mathematical Description of Mechanical Loads;106
7.4.2.1;4.2.2.1 Load Vector;106
7.4.2.2;4.2.2.2 Direction of Loads;106
7.4.2.3;4.2.2.3 Amplitude and Spatial Distribution of Loads;107
7.5;4.3 Solution Approach with eXtended LayerWise Theory;109
7.5.1;4.3.1 Prerequisites;109
7.5.2;4.3.2 Degrees of Freedom;111
7.5.3;4.3.3 Kinematical Measures;111
7.5.4;4.3.4 Balance Equations and Kinetic Measures;111
7.5.5;4.3.5 Constitutive Equations;114
7.5.6;4.3.6 Boundary Conditions;115
7.5.7;4.3.7 Kinematical Constraints;116
7.5.8;4.3.8 Introduction of Mean and Relative Measures;117
7.5.9;4.3.9 Principle of Virtual Work;118
7.6;4.4 Numerical Implementation;120
7.6.1;4.4.1 Basic Procedure in Finite Element Method;120
7.6.2;4.4.2 Shape Functions;120
7.6.3;4.4.3 JACOBI Transformation;121
7.6.4;4.4.4 Discretisation;122
7.6.4.1;4.4.4.1 Degrees of Freedom;122
7.6.4.2;4.4.4.2 KinematicalMeasures;123
7.6.5;4.4.5 Constitutive Equations for FEM;124
7.6.6;4.4.6 Element Stiffness Relation;125
7.6.7;4.4.7 Surface Load Vector;126
7.6.8;4.4.8 Assembling;127
7.6.9;4.4.9 Numerical Integration and Artificial Stiffening Effects;128
7.7;4.5 Structural Analysis;130
7.7.1;4.5.1 Test Structure;130
7.7.2;4.5.2 Discretisation and Convergence;131
7.7.3;4.5.3 Case Studies;133
7.7.4;4.5.4 Results and Discussion;134
7.7.4.1;4.5.4.1 Degrees of Freedom;134
7.7.4.2;4.5.4.2 Kinetic and Kinematic Quantities;137
7.8;4.6 Conclusion;140
7.9;Acknowledgements;143
7.10;4.A Appendix;143
7.10.1;4.A.1 Constitutive Matrices;143
7.10.2;4.A.2 Auxiliary Matrices;144
7.11;References;145
8;5 Block Element Method for the Stamps of the no Classical Form;148
8.1;Abstract;148
8.2;Key words:;148
8.3;5.1 Introduction;149
8.4;5.2 Statement of the Problem;150
8.5;5.3 Properties of the Integral Equations;151
8.6;5.4 The Block Element Method for a System of Integral Equations;153
8.7;5.5 Study of the Properties of the Solution of the System of Integral Equations and a Boundary Value Problem;154
8.8;5.6 Acknowledgments;156
8.9;References;157
9;6 On the Irreversible Deformations Growth in the Material with Elastic, Viscous, and Plastic Properties and Additional Requirements to Yield Criteria;158
9.1;Abstract;158
9.2;Key words:;158
9.3;6.1 Introduction;158
9.4;6.2 Large Deformations Kinematics;159
9.5;6.3 Governing Equations;163
9.6;6.4 The Flow of Elastic-Viscous-Plastic Solids Inside the Cylindrical Tube;167
9.7;6.5 Viscometric Deformation of the Incompressible Cylindrical Layer;171
9.8;6.6 Conclusion;175
9.9;References;176
10;7On Nonlocal Surface Elasticity and Propagationof Surface Anti-Plane Waves;177
10.1;Abstract;177
10.2;Key words:;177
10.3;7.1 Introduction;177
10.4;7.2 Governing Equations;179
10.5;7.3 Anti-Plane Surface Waves in an Elastic Half-Space;181
10.6;7.4 Conclusions;184
10.7;References;184
11;8Deformation of Spherical Inclusion in an ElasticBody with Account for Influence of InterfaceConsidered as Infinitesimal Layer withAbnormal Properties;187
11.1;Abstract;187
11.2;Key words:;187
11.3;8.1 Introduction;187
11.4;8.2 Model of the Interface Elasticity;188
11.5;8.3 Problem of Spherical Inclusion. Various Solutions;190
11.6;8.4 Conclusion;192
11.7;Acknowledgements;192
11.8;References;192
12;9Analysis of Internal Stresses in a ViscoelasticLayer in Sliding Contact;194
12.1;Abstract;194
12.2;Key words:;194
12.3;9.1 Introduction;194
12.4;9.2 Problem Formulation;195
12.5;9.3 Method of Solution;196
12.6;9.4 Analysis of Internal Stresses;199
12.7;9.5 Conclusions;202
12.8;Acknowledgements;203
12.9;References;203
13;10On the Problem of Diffusion in Materials UnderVibrations;205
13.1;Abstract;205
13.2;Key words:;205
13.3;10.1 Introduction;205
13.4;10.2 The Equation of Impurity Motion;206
13.5;10.3 Statement of the Problem: Governing Equations;208
13.6;10.4 Localization of Diffusion Process;210
13.7;10.5 Structural Transformations of Materials;213
13.8;10.6 Conclusion;214
13.9;Acknowledgements;214
13.10;References;215
14;11A Study of Objective Time Derivatives inMaterial and Spatial Description;216
14.1;Abstract;216
14.2;Key words:;217
14.3;11.1 Introduction and Outline to the Paper;217
14.4;11.2 Frames of Reference – Fundamental Definitions;218
14.4.1;Definition 11.1.;218
14.4.2;Definition 11.2.;219
14.4.3;Definition 11.3.;219
14.4.4;Definition 11.4.;220
14.4.5;Definition 11.5.;220
14.5;11.3 Changing Frames of Reference;223
14.5.1;11.3.1 Kinematic Quantities and Their Images;224
14.5.2;11.3.2 Rotation of one Reference Frame with Respect to Another;228
14.5.3;11.3.3 Motion of FoRs with Respect to Each Other;231
14.6;11.4 Frame Indifference of Operators;233
14.6.1;11.4.1 Transformation Properties of Spatial Gradients;233
14.6.2;11.4.2 Transformation Properties of the Total and Material Time Derivatives;240
14.7;11.5 Conclusions and Outlook;245
14.8;9.A Appendix;246
14.8.1;9.A.1 Rotational Tensors and Angular Velocity Vectors;246
14.9;References;249
15;12On Electronically Restoring an ImperfectVibratory Gyroscope to an Ideal State;251
15.1;Abstract;251
15.2;Key words:;251
15.3;12.1 Introduction;252
15.4;12.2 Notation;254
15.5;12.3 Kinetic Energy, Prestress and Potential Energy;256
15.6;12.4 Tangentially Anisotropic Damping;257
15.7;12.5 Electrical Energy;258
15.8;12.6 Eliminating Frequency Split;262
15.9;12.7 Parametric Excitation;265
15.10;12.8 Principal and Quadrature Vibration;266
15.11;12.9 Numerical Experiment;266
15.12;12.10 Averaging;270
15.13;12.11 Graphical Comparisons and Quantitative Analysis of theExact and Averaged ODE;271
15.14;12.12 Isotropic Damping and the Meander Electrodes;274
15.15;12.13 Conclusion;274
15.16;Acknowledgements;274
15.17;References;275
16;13ShockWave Rise Time and the Viscosity ofLiquids and Solids;277
16.1;Abstract;277
16.2;Key words:;277
16.3;13.1 Introduction;277
16.4;13.2 Experiments and Their Results;278
16.5;13.3 Conclusions;282
16.6;Acknowledgements;282
16.7;References;283
17;14Lowest Vibration Modes of StronglyInhomogeneous Elastic Structures;284
17.1;Abstract;284
17.2;Key words:;284
17.3;14.1 Introduction;284
17.4;14.2 Antiplane Shear Motion;285
17.4.1;14.2.1 Stiffer Outer Domain;287
17.4.2;14.2.2 Stiffer Inner Domain;289
17.5;14.3 Model Examples;290
17.5.1;14.3.1 Two-Layered Circular Cylinder;290
17.5.2;14.3.2 Square Cylinder with a Circular Annular Inclusion;292
17.6;14.4 Concluding Remarks;294
17.7;12.A Appendix;294
17.8;References;295
18;15Geometrical Inverse Thermoelastic Problem forMultiple Inhomogeneities;297
18.1;Abstract;297
18.2;Key words:;297
18.3;15.1 Introduction;297
18.4;15.2 Mathematical Formulation of the Direct Problem;298
18.5;15.3 Reciprocity Principle and Reciprocity Gap Functional;300
18.6;15.4 Statement of the Inverse Problem and a Method of itsSolving;302
18.7;15.5 Numerical Procedure and Numerical Examples;306
18.8;15.6 Conclusions;312
18.9;Acknowledgements;312
18.10;References;312
19;16Indentation of the Regular System of Punchesinto the Foundation with Routh Coating;314
19.1;Abstract;314
19.2;Key words:;314
19.3;16.1 Statement of the Problem;315
19.4;16.2 Dimensionless Form and Operator Representation;317
19.5;16.3 Transformation of Main Equation and Special Basis;318
19.6;16.4 Solving the Problem;320
19.7;16.5 Main Results and Conclusions;325
19.8;Acknowledgements;325
19.9;References;325
20;17Physical Modeling of Rock Deformation andFracture in the Vicinity of Well for DeepHorizons;326
20.1;Abstract;326
20.2;Key words:;326
20.3;17.1 Introduction;326
20.4;17.2 Experimental Facility and Loading Programs for Specimens;327
20.5;17.3 Rock Specimens Test Results;330
20.6;17.4 Conclusion;333
20.7;Acknowledgements;333
20.8;References;334
21;18Full Axially Symmetric Contact of a RigidPunch with a Rough Elastic Half-Space;335
21.1;Abstract;335
21.2;Key words:;335
21.3;18.1 Introduction;335
21.4;18.2 Problem Formulation;336
21.5;18.3 Some Generalizations;340
21.6;References;342
22;19Geometric Aspects of the Theory ofIncompatible Deformations in Growing Solids;343
22.1;Abstract;343
22.2;Key words:;343
22.3;19.1 Introduction;344
22.4;19.2 Naive Geometric Motivation;345
22.5;19.3 Material Manifold;347
22.6;19.4 Growing Solids;350
22.7;19.5 Mappings Between Manifolds;351
22.8;19.6 Deformations;353
22.9;19.7 Material Connection;355
22.10;19.8 Example;357
22.11;References;361
23;20Free Vibrations of a Transversely Isotropic Platewith Application to a Multilayer Nano-Plate;364
23.1;Abstract;364
23.2;Key words:;364
23.3;20.1 Introduction;364
23.4;20.2 Equations of Motion and Their Transformation;366
23.5;20.3 Principal Natural Frequency in the Dependence of Boundary Conditions;368
23.6;20.4 Numerical Results and Their Discussion;370
23.7;20.5 The Generalized Kirchhoff–Love (GKL) Model for a Multilayer Plate;372
23.8;20.6 Continuum Model of a Multilayer Graphene Sheet (MLGS) Vibrations;373
23.9;20.7 Identification of Graphite and Graphene Parameters and some Numerical Results;374
23.10;20.8 Numerical Results and Their Discussion;375
23.11;Acknowledgements;376
23.12;References;376
24;21On Thermodynamics of Wave Processes of HeatTransport;378
24.1;Abstract;378
24.2;Key words:;379
24.3;21.1 Preliminary Remarks;379
24.4;21.2 Thermodynamic Orthogonality and Constitutive Equationsof the Perfect Plasticity;380
24.5;21.3 Internal Entropy Production for a Heat Transport Processin Thermoelastic Continua;384
24.6;21.4 Constitutive Equations for Type-III Thermoelasticity byVirtue of Thermodynamic Orthogonality;387
24.7;21.5 Conclusions;389
24.8;References;390
25;22The Technological Stresses in a VaultedStructure Built Up on a Falsework;392
25.1;Abstract;392
25.2;Key words:;392
25.3;22.1 Introduction;392
25.4;22.2 Statement of the Problem;393
25.5;22.3 Boundary Value Problem for the Built-up Structure;395
25.6;22.4 Analytical Solution of the Problem. Determining theStresses in the Vault Supported by the Falsework;398
25.7;22.5 Residual Stresses in the Finished Structure;399
25.8;Acknowledgements;400
25.9;References;400
26;23Reversible Plasticity Shape-Memory Effect inEpoxy Nanocomposites: Experiments, Modelingand Predictions;402
26.1;Abstract;402
26.2;Key words:;403
26.3;23.1 Introduction;403
26.4;23.2 Experimental Methods;405
26.4.1;23.2.1 Material Selection and Sample Preparation;405
26.4.2;23.2.2 Material Characterization;405
26.4.3;23.2.3 RPSM Characterization;406
26.5;23.3 Mechanism;407
26.6;23.4 Model Description;407
26.6.1;23.4.1 Kinematics;407
26.6.2;23.4.2 Structural Relaxation and Thermal Deformation;409
26.6.3;23.4.3 Constitutive Equations for Stress;409
26.6.4;23.4.4 Flow Rule;411
26.7;23.5 Results and Discussions;411
26.7.1;23.5.1 Mechanical Properties;411
26.7.2;23.5.2 Thermal Properties;413
26.7.3;23.5.3 Morphological Properties;414
26.7.4;23.5.4 RPSM Properties;415
26.8;23.6 Conclusion;423
26.9;18.A Appendix;423
26.9.1;18.A.1 Parameter Determination and Effect of MWCNT on theMaterial Parameters;423
26.9.2;18.A.2 Determination of ?r, k, G and l;424
26.9.3;18.A.3 Determination of C1, C2, tos, ag and ar;425
26.9.4;18.A.4 Determination of hg, ss, Q and h;427
26.10;References;427
27;24The Dynamics of an Accreting Vibrating Rod;431
27.1;Abstract;431
27.2;Key words:;432
27.3;24.1 Introduction;432
27.4;24.2 Equations of Motion and Their Transformations;433
27.5;24.3 Theoretical Treatment: Solution of Mixed Problem to;435
27.6;24.4 Numerical Simulations and Discussions;438
27.7;24.5 Conclusion;443
27.8;Acknowledgements;443
27.9;References;444
28;25A New, Direct Approach Toward ModelingRate-Dependent Fatigue Failure of Metals;446
28.1;Abstract;446
28.2;Key words:;446
28.3;25.1 Introduction;446
28.4;25.2 New Rate-Dependent Elastoplasticity Model;448
28.5;25.3 Failure Under Monotone and Cyclic Loadings;451
28.5.1;25.3.1 Governing Equations in the Uniaxial Case;451
28.5.2;25.3.2 Parameter Identification with Monotone Strain Data;452
28.5.3;25.3.3 Predictions for Fatigue Failure Under Cyclic Loadings;453
28.6;25.4 Numerical Results;454
28.6.1;25.4.1 Failure Under Monotone Strain;454
28.6.2;25.4.2 Predictions for Fatigue Failure Under Cyclic Loadings;455
28.7;25.5 Concluding Remarks;458
28.8;Acknowledgements;458
28.9;References;459

Über Autor(innen)

With contributions of W. Müller, Heng Xiao, D.M. Klimov, V.F. Zhuralev, B.D. Annin, V.A. Babeshko, I.G. Goryacheva, V.P. Matveenko, N.F. Morozov, N.N. Bolotnik, A.A. Burenin, R.V. Goldstein, D.A. Indeicev, G.I. Kanel, E.V. Lomakin, A.V. Manzhirov, K.E. Kazankov, V.I. Karev, S.A. Lychev, E.V. Murashkin, D.A. Parshin, Yu.N. Radaev, H. Altenbach, I. Kudish, Yu. Kaplunov, N.K. Gupta, R. Velmurugan, and S. Kapuria