Mechanics for Materials and Technologies

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