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Numerical Simulation of Mechatronic Sensors and Actuators - Finite Elements for Computational Multiphysics
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Numerical Simulation of Mechatronic Sensors and Actuators - Finite Elements for Computational Multiphysics
von: Manfred Kaltenbacher
Springer-Verlag, 2015
ISBN: 9783642401701
600 Seiten, Download: 25411 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Preface to the Third Edition 5  
  Preface to the Second Edition 8  
  Preface to the First Edition 10  
  Contents 14  
  Notation 21  
  1 Introduction 26  
     References 30  
  2 The Finite Element (FE) Method 31  
     2.1 Finite Element Formulation 32  
     2.2 Finite Element Method for a 1D Problem 37  
     2.3 Nodal (Lagrangian) Finite Elements 44  
        2.3.1 Basic Properties 45  
        2.3.2 Quadrilateral Element in R2 47  
        2.3.3 Triangular Element in R2 50  
        2.3.4 Tetrahedron Element in R3 51  
        2.3.5 Hexahedron Element in R3 52  
        2.3.6 Wedge Element in R3 54  
        2.3.7 Pyramidal Element in R3 55  
        2.3.8 Global/Local Derivatives 56  
        2.3.9 Numerical Integration 58  
     2.4 Finite Element Procedure 60  
     2.5 Time Discretization 65  
        2.5.1 Parabolic Differential Equation 65  
        2.5.2 Hyperbolic Differential Equation 69  
     2.6 Integration over Surfaces 72  
     2.7 Edge Nédélec Finite Elements 73  
     2.8 Discretization Error 75  
     2.9 Finite Elements of Higher Order 79  
        2.9.1 Legendre Polynomials and Hierarchical Finite Elements 81  
        2.9.2 Lagrange Polynomials and Spectral Elements 89  
     2.10 Flexible Discretization 91  
        2.10.1 Mortar FEM 93  
        2.10.2 Nitsche Type Mortaring 106  
        2.10.3 Numerical Example 111  
     References 113  
  3 Mechanical Field 116  
     3.1 Navier's Equation 116  
     3.2 Deformation and Displacement Gradient 120  
     3.3 Mechanical Strain 121  
     3.4 Constitutive Equations 125  
        3.4.1 Plane Strain State 127  
        3.4.2 Plane Stress State 128  
        3.4.3 Axisymmetric Stress--Strain Relations 129  
     3.5 Waves in Solid Bodies 129  
     3.6 Material Properties 131  
     3.7 Numerical Computation 133  
        3.7.1 Linear Elasticity 133  
        3.7.2 Damping Model 135  
        3.7.3 Geometric Nonlinear Case 137  
        3.7.4 Numerical Example 143  
     3.8 Locking and Efficient Solution Approaches 144  
        3.8.1 Incompatible Modes Method 147  
        3.8.2 Enhanced Assumed Strain Method 149  
        3.8.3 Balanced Reduced and Selective Integration 151  
     References 157  
  4 Flow Field 159  
     4.1 Spatial Reference Systems 160  
     4.2 Reynolds' Transport Theorem 161  
     4.3 Conservation Equations 162  
        4.3.1 Conservation of Mass 162  
        4.3.2 Conservation of Momentum 163  
        4.3.3 Conservation of Energy 166  
        4.3.4 Constitutive Equations 167  
     4.4 Navier-Stokes Equations 167  
     4.5 Characterization of Flows by Dimensionless Numbers 168  
     4.6 Finite Element Formulation 169  
     4.7 Numerical Examples 173  
        4.7.1 Steady Channel Flow 173  
        4.7.2 Unsteady Flow Around a Square 176  
     References 178  
  5 Acoustic Field 180  
     5.1 Wave Theory of Sound 180  
        5.1.1 Conservation of Mass (Continuity Equation) 182  
        5.1.2 Conservation of Momentum (Euler Equation) 182  
        5.1.3 Pressure-Density Relation (State Equation) 183  
        5.1.4 Linear Acoustic Wave Equation 185  
        5.1.5 Acoustic Quantities 187  
        5.1.6 Plane and Spherical Waves 189  
     5.2 Quantitative Measure of Sound 193  
     5.3 Nonlinear Acoustic Wave Equation 197  
     5.4 Numerical Computation 202  
        5.4.1 Linear Acoustic Wave Equation 202  
        5.4.2 Linear Acoustic Conservation Equations 205  
        5.4.3 Nonlinear Acoustics 208  
        5.4.4 Non-conforming Grids 211  
        5.4.5 Discretization Error 215  
     5.5 Treatment of Open Domain Problems 219  
        5.5.1 Absorbing Boundary Conditions 220  
        5.5.2 Perfectly Matched Layer (PML) Technique 222  
     5.6 Numerical Examples 233  
        5.6.1 Transient Wave Propagation in Unbounded Domains 233  
        5.6.2 Harmonic Wave Propagation in Unbounded Domains 237  
        5.6.3 Nonlinear Wave Propagation in a Channel 239  
     References 244  
  6 Electromagnetic Field 247  
     6.1 Maxwell's Equations 247  
        6.1.1 Law of Ampère 249  
        6.1.2 Law of Faraday 250  
        6.1.3 Law of Gauss 253  
        6.1.4 Solenoidal Magnetic Field 254  
     6.2 Quasistatic Electromagnetic Fields 255  
        6.2.1 Magnetic Vector Potential 255  
        6.2.2 Skin Effect 256  
     6.3 Electrostatic Field 258  
     6.4 Material Properties 259  
        6.4.1 Magnetic Permeability 259  
        6.4.2 Electrical Conductivity 262  
        6.4.3 Dielectric Permittivity 263  
     6.5 Electromagnetic Interface Conditions 264  
        6.5.1 Continuity Relations for Magnetic Field 264  
        6.5.2 Continuity Relations for Electric Field 265  
        6.5.3 Continuity Relations for Electric Current Density 267  
     6.6 Numerical Computation: Electrostatics 267  
     6.7 Numerical Computation: Electromagnetics 269  
        6.7.1 Formulation 269  
        6.7.2 Discretization with Edge Elements 275  
        6.7.3 Discretization with Nodal Finite Elements 277  
        6.7.4 Newton's Method for the Nonlinear Case 280  
        6.7.5 Approximation of BH Curve 283  
        6.7.6 Higher Order Edge Elements 285  
        6.7.7 Modeling of Current-Loaded Coil 291  
        6.7.8 Computation of Global Quantities 292  
        6.7.9 Induced Electric Voltage 295  
        6.7.10 Voltage-Loaded Coil 295  
     6.8 Numerical Examples 297  
        6.8.1 Thin Iron Plate 297  
        6.8.2 TEAM-13 Benchmark Problem 300  
     References 302  
  7 Coupled Flow-Structural Mechanical Systems 304  
     7.1 Fluid-Solid Interaction 304  
     7.2 Coupling Types and Strategies 305  
     7.3 Grid Adaption 308  
     7.4 Numerical Examples 311  
        7.4.1 Solid Plunger 311  
        7.4.2 Flag in a Flow 312  
     References 315  
  8 Coupled Mechanical-Acoustic Systems 316  
     8.1 Solid--Fluid Interface 316  
     8.2 Coupled Field Formulation 318  
     8.3 Numerical Computation 319  
        8.3.1 Finite Element Formulation 319  
        8.3.2 Non-conforming Grids 321  
        8.3.3 Numerical Examples 322  
     References 327  
  9 Computational Aeroacoustics 328  
     9.1 Requirements for Numerical Schemes 328  
     9.2 Lighthill's Analogy 331  
     9.3 Curle's Theory 336  
     9.4 Vortex Sound 341  
     9.5 Perturbation Equations 343  
     9.6 Finite Element Formulation 346  
        9.6.1 Lighthills' Inhomogeneous Wave Equation 346  
        9.6.2 Perturbation Equations 349  
        9.6.3 Source Term Treatment 352  
     9.7 Comparison of Different Aeroacoustic Analogies 353  
     References 356  
  10 Coupled Electrostatic-Mechanical Systems 358  
     10.1 Electrostatic Force 358  
     10.2 Numerical Computation 365  
        10.2.1 Calculation Scheme 366  
        10.2.2 Voltage-Driven Bar 368  
     References 370  
  11 Coupled Magnetomechanical Systems 371  
     11.1 General Moving/Deforming Body 371  
     11.2 Electromagnetic Force 373  
     11.3 Numerical Computation 375  
        11.3.1 Force Computation Via the Principle of Virtual Work 375  
        11.3.2 Grid Adaption Techniques 378  
        11.3.3 Calculation Scheme 382  
        11.3.4 Moving Current/Voltage-Loaded Coil 384  
     References 391  
  12 Piezoelectric Systems 393  
     12.1 Constitutive Equations 393  
     12.2 Governing Equations: Linear Piezoelectricity 396  
     12.3 Piezoelectric Material Properties 397  
     12.4 Models for Nonlinear Piezoelectricity 402  
        12.4.1 Macroscopic Model with Hysteresis Operators 402  
        12.4.2 Micro-mechanical Switching Model 410  
     12.5 Numerical Computation 411  
        12.5.1 Linear Case 412  
        12.5.2 Macroscopic Hysteresis Based Approach 414  
        12.5.3 Micro-mechanical Switching Model 418  
     12.6 Numerical Examples 423  
        12.6.1 Computation of Impedance Curve 423  
        12.6.2 Piezoelectric Disc Actuator 426  
        12.6.3 Polarization and Depolarization Process 427  
     References 430  
  13 Algebraic Solvers 432  
     13.1 Preconditioned Conjugate Gradient (PCG) Method 432  
     13.2 Multigrid (MG) Method 434  
     13.3 Geometric MG Method 437  
        13.3.1 Geometric MG for Edge Elements 437  
        13.3.2 Case Study 440  
     13.4 Algebraic MG Method 443  
        13.4.1 Auxiliary Matrix 444  
        13.4.2 Coarsening Process 444  
        13.4.3 Prolongation Operators 448  
        13.4.4 Smoother and Coarse-Grid Operator 448  
        13.4.5 AMG for Nodal Elements 449  
        13.4.6 AMG for Edge Elements 450  
        13.4.7 AMG for Time-Harmonic Case 453  
        13.4.8 Case Studies 454  
     13.5 Block Preconditioner for Higher Order Edge Element Discretization 460  
     References 467  
  14 Industrial Applications 470  
     14.1 Electrodynamic Loudspeaker 470  
        14.1.1 Finite Element Models 471  
        14.1.2 Verification of Computer Models 473  
        14.1.3 Numerical Analysis of the Nonlinear Loudspeaker Behavior 475  
        14.1.4 Computer Optimization of the Nonlinear Loudspeaker Behavior 477  
     14.2 Noise Computation of Power Transformers 477  
        14.2.1 Finite Element Models 479  
        14.2.2 Verification of the Computer Models 482  
        14.2.3 Verification of the Calculated Winding and Tank-Surface Vibrations 482  
        14.2.4 Verification of the Sound-Field Calculations 484  
        14.2.5 Influence of Tap-Changer Position 485  
        14.2.6 Influence of Stiffness of Winding Supports 486  
     14.3 Fast-Switching Electromagnetic Valves 486  
        14.3.1 Modeling and Solution Strategy 487  
        14.3.2 Actuator Characteristics 489  
        14.3.3 Actuator Dynamics 491  
        14.3.4 Dynamics Optimization I: Electrical Premagnetization 492  
        14.3.5 Dynamics Optimization II: Overexcitation 494  
        14.3.6 Switching Cycle 495  
     14.4 Cofired Piezoceramic Multilayer Actuators 496  
        14.4.1 Polarization of a Stack Actuator 497  
        14.4.2 Stack Actuator: Hysteresis Based Approach 500  
     14.5 Capacitive Micro-machined Ultrasound Transducers 502  
        14.5.1 Requirements to Numerical Simulation Scheme 503  
        14.5.2 Single CMUT Cell 505  
        14.5.3 CMUT Array 507  
        14.5.4 Controlled CMUT Array 508  
     14.6 High-Intensity Focused Ultrasound 512  
        14.6.1 Piezoelectric Transducer and Input Impedance 512  
        14.6.2 Pressure Pulse Computation 514  
        14.6.3 High-Power Pulse Sources for Lithotripsy 515  
     14.7 Human Phonation 520  
        14.7.1 Mathematical Modeling 522  
        14.7.2 2D Fully Coupled Simulation 522  
        14.7.3 3D Driven Simulation 527  
     14.8 Aeroacoustics of Flow Around Obstacles 532  
        14.8.1 Square Cylinder Geometries 532  
        14.8.2 Edge Tone 540  
        14.8.3 Airframe Noise 547  
     References 550  
  15 Summary and Outlook 553  
     References 554  
  Appendix A Norms 555  
  Appendix B Scalar and Vector Fields 557  
  Appendix C Tensors and Index Notation 573  
  Appendix D Appropriate Function Spaces 578  
  Appendix E Solution of Nonlinear Equations 583  
  Appendix F Hysteresis Model 589  
  Index 594  


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