Altenbach / Carrera / Kulikov Analysis and Modelling of Advanced Structures and Smart Systems

1. Auflage 2018
ISBN: 978-981-10-6895-9
Verlag: Springer Nature Singapore
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 81, 380 Seiten

Reihe: Advanced Structured Materials

This book presents selected papers presented at the 8th International Conference 'Design, Modeling and Experiments of Advanced Structures and Systems' (DeMEASS VIII, held in Moscow, Russia in May 2017) and reflects the modern state of sciences in this field. The contributions contain topics like Piezoelectric, Ferroelectric, Ferroelastic and Magnetostrictive Materials, Shape Memory Alloys and Active Polymers, Functionally Graded Materials, Multi-Functional Smart Materials and Structures, Coupled Multi-Field Problems, Design and Modeling of Sensors and Actuators, Adaptive Structures.

Autoren/Hrsg.

Altenbach, Holm

Carrera, Erasmo

Kulikov, Gennady

Inhaltsverzeichnis

1;Preface;6
2;Contents;7
3;List of Contributors;14
4;1Bending of a Three-Layered Plate with Surface Stresses;18
4.1;1.1 Introduction;18
4.2;1.2 Surface Elasticity;19
4.3;1.3 Equilibrium of a Symmetric Three-Layered Plate;20
4.3.1;1.3.1 Static Equations for a Three-Dimensional Plate-Like Solid;20
4.3.2;1.3.2 Transition to the Two-Dimensional Static Equations;22
4.3.3;1.3.3 Effective Stiffness Parameters;23
4.4;1.4 Conclusions and Future Steps;25
4.5;References;26
5;2A Numerical Study on the Potential of Acoustic Metamaterials;28
5.1;2.1 Introduction;28
5.2;2.2 Models for the Parametric Studies;31
5.3;2.3 Numerical Results;35
5.3.1;2.3.1 Influence of the Distribution of the Spherical Inclusions;35
5.3.2;2.3.2 Influence of the Material Properties of the Spherical Inclusions;41
5.3.3;2.3.3 Influence of a Fixed Density-Volume-Product;42
5.3.4;2.3.4 Influence of the Volume of the Inclusions;44
5.3.5;2.3.5 Influence of the Number of Layers with Different Material Properties;45
5.3.6;2.3.6 Discussion;46
5.4;2.4 Conclusions;47
5.5;References;49
6;3Electromechanical Degradation of Piezoelectric Patches;52
6.1;3.1 Introduction;52
6.2;3.2 Experimentation;54
6.3;3.3 Results and Discussions;57
6.4;3.4 Conclusions;59
6.5;References;60
7;4 Hybrid-Mixed Solid-Shell Element for Stress Analysis of Laminated Piezoelectric Shells through Higher-Order Theories;62
7.1;4.1 Introduction;63
7.2;4.2 Sampling Surface Shell Formulation;65
7.3;4.3 Hu-Washizu Variational Equation;67
7.4;4.4 Hybrid-Mixed Solid-Shell Element Formulation;69
7.5;4.5 Numerical Examples;74
7.5.1;4.5.1 Three-Layer Piezoelectric Cylindrical Shell;74
7.5.2;4.5.2 Three-Layer Piezoelectric Spherical Shell;78
7.6;4.6 Conclusions;82
7.7;References;82
8;5Finite Element Approach for Composite Magneto-Piezoelectric Materials Modeling in ACELAN-COMPOS Package;86
8.1;5.1 Introduction;87
8.2;5.2 Piezomagnetoelectric Boundary Problems;88
8.3;5.3 Finite Element Approximations;90
8.4;5.4 Homogenization of Two-Phase Piezomagnetoelectric Materials;92
8.5;5.5 Inhomogenious Polarization;95
8.6;5.6 Three-Dimensional Models for Composite Materials;98
8.7;5.7 Conclusions;103
8.8;References;104
9;6Robust Displacement and Mixed CUF-Based Four-Node and Eight-Node Quadrilateral Plate Elements;106
9.1;6.1 Introduction;106
9.2;6.2 Variable Kinematics Plate Model;110
9.2.1;6.2.1 Variational Statements;110
9.2.2;6.2.2 Variable Kinematics Assumptions;112
9.2.3;6.2.3 The Stress and Strain Fields;113
9.3;6.3 Finite Element Approximations;115
9.3.1;6.3.1 Displacement-Based Finite Elements;115
9.3.2;6.3.2 RMVT-Based Finite Elements;118
9.4;6.4 Numerical Results;119
9.4.1;6.4.1 Eigenvalues of the Stiffness Matrix;120
9.4.2;6.4.2 Transverse Shear Locking Test;123
9.4.3;6.4.3 The Distortion Tests;128
9.5;6.5 Conclusion;130
9.6;Appendix 1;132
9.7;Appendix 2;132
9.8;References;133
10;7Effect of Magnetic Field on Free and Forced Vibrations of Laminated Cylindrical Shells Containing Magnetorheological Elastomers;136
10.1;7.1 Introduction;137
10.2;7.2 Structure of Laminated Shell;138
10.3;7.3 Basic Hypotheses;140
10.4;7.4 Governing Equations;141
10.4.1;7.4.1 Governing Equations in Terms of Stress Resultants and Couples;141
10.4.2;7.4.2 Governing Equations in Terms of Displacements;143
10.4.3;7.4.3 Equations of Technical Shell Theory;144
10.4.4;7.4.4 Error of Governing Equations;146
10.5;7.5 Free Vibrations of MRE-based Laminated Cylindrical Shells and Panels;147
10.5.1;7.5.1 Lengthy Simply Supported Cylinders;147
10.5.2;7.5.2 Medium-Length Cylindrical Panels;151
10.5.3;7.5.3 Vibrations of Medium-Length Cylindrical Shells in Nonuniform Magnetic Field;153
10.6;7.6 Forced Vibrations;158
10.7;7.7 Conclusions;162
10.8;References;163
11;8Impact-Induced Internal Resonance Phenomena in Nonlinear Doubly Curved Shallow Shells with Rectangular Base;166
11.1;8.1 Introduction;166
11.2;8.2 Problem Formulation and Governing Equations;169
11.3;8.3 Method of Solution;173
11.3.1;8.3.1 Solution of Equations at Order of ?;174
11.3.2;8.3.2 Solution of Equations at Order of ?2;176
11.3.3;8.3.3 Impact-induced internal resonance ?1 = 2?2;176
11.3.4;8.3.4 Solution of Equations at Order of ?3;187
11.4;8.4 Conclusion;200
11.5;References;202
11.6;Appendix;204
12;9Ferrous Material Fill: Magnetization Channels, Layer-by-Layer and Average Permeability, Element-to-Element Field;207
12.1;9.1 Introduction. Qualitative Assessment of Typical Intervals for the Volume Fraction of a Ferrous Component;208
12.2;9.2 Quantitative Assessment of Characteristic Intervals for the Volume Fraction of a Ferrous Component and its Values for the Filling Materials;209
12.3;9.3 Selective (in the Form of Chains of Channels) Magnetization of Ferrous Material. Concept of Layer-Tube Channels;210
12.4;9.4 Data of the In-Channel (Core and Layer-Tube) Magnetic Flux, Average Induction, and Permeability;212
12.5;9.5 Magnetizing Channel Layer Tubes: Local Permeability, Radial Profile;215
12.6;9.6 Magnetization Channel Core: Average Magnetic Permeability;217
12.7;9.7 Generalized Dependencies for Comparison of the Calculated and Experimental Data;219
12.8;9.8 Magnetization Channel and Harness of the Channels (in the Ferromaterial Filling): Average Magnetic Permeability;220
12.9;9.9 The Physical Meaning of the Profile Permeability. Relative Field Strength Between Ferroelements;222
12.10;9.10 Conclusions;224
12.11;References;225
13;10Modeling and Simulation of a Chemically Stimulated Hydrogel Bilayer Bending Actuator;227
13.1;10.1 Introduction;227
13.2;10.2 Chemo-Electro-Mechanical Field Formulation;229
13.2.1;10.2.1 Chemical Field;230
13.2.2;10.2.2 Electrical Field;230
13.2.3;10.2.3 Mechanical Field;231
13.2.4;10.2.4 Numerical Solution Procedure;232
13.3;10.3 Numerical Simulation of a Chemically Stimulated Bilayer;233
13.4;10.4 Conclusion;240
13.5;References;240
14;11Mathematical Modelling of Piezoelectric Generators on the Base of the Kantorovich Method;243
14.1;11.1 Introduction;243
14.2;11.2 Mathematical Modelling of PEG;245
14.2.1;11.2.1 The Boundary-Value Problem in the Theory of Electroelasticity;245
14.2.2;11.2.2 Modeling of Cantilever Type PEGs;246
14.2.3;11.2.3 Modelling of Stack Type PEG;263
14.3;11.3 Summary;271
14.4;References;273
15;12Modeling of Dielectric Elastomers Accounting for Electrostriction by Means of a Multiplicative Decomposition of the Deformation Gradient Tensor;275
15.1;12.1 Introduction;275
15.2;12.2 Electromechanical Coupling by Electrostatic Force;277
15.2.1;12.2.1 Kinematics in Nonlinear Elasticity;277
15.2.2;12.2.2 Electro-Elastic Balance Laws;279
15.2.3;12.2.3 Lagrangian (Material) Framework;282
15.2.4;12.2.4 Constitutive Relations;283
15.3;12.3 Electromechanical Coupling Using a Multiplicative Decomposition of the Deformation Gradient Tensor;285
15.3.1;12.3.1 Total Stress;288
15.3.2;12.3.2 Intermediate Configuration;289
15.4;12.4 Electrostriction;290
15.4.1;12.4.1 Homogeneously Deformed Plate;292
15.5;12.5 Electromechanical Stability;296
15.5.1;12.5.1 Stiffening Effect of Electrodes;301
15.6;12.6 Conclusion and Outlook;303
15.7;References;304
16;13Mechanics of Axially Moving Structures at Mixed Eulerian-Lagrangian Description;307
16.1;13.1 Introduction;307
16.2;13.2 Linear Waves in a Moving String;309
16.3;13.3 Large Vibrations of an Axially Moving String;310
16.3.1;13.3.1 Mixed Eulerian-Lagrangian Description of the Kinematics of Motion;312
16.3.2;13.3.2 Mixed Form of the Variational Equation of Virtual Work;313
16.3.3;13.3.3 Finite Element Approximation;314
16.3.4;13.3.4 Lagrange’s Equation of Motion of the Second Kind;315
16.3.5;13.3.5 Example Solution;316
16.4;13.4 Finite Deformations of an Axially Moving Plate;318
16.4.1;13.4.1 Kinematic Description;319
16.4.2;13.4.2 Deformation and Strain Energy;321
16.4.3;13.4.3 Finite Element Scheme;324
16.4.4;13.4.4 Benchmark Problem;326
16.4.5;13.4.5 Time Stepping and Boundary Conditions;327
16.4.6;13.4.6 Simulation of a Moving Plate;329
16.5;13.5 Mixed Eulerian-Lagrangian Formulation in the Analysis of a Belt Drive;331
16.5.1;13.5.1 Problem Statement;332
16.5.2;13.5.2 Problem-Specific Coordinate System;333
16.5.3;13.5.3 Mixed Lagrangian-Eulerian Kinematic Description;335
16.5.4;13.5.4 Finite Element Approximation and Energy;335
16.5.5;13.5.5 Simulation Results;336
16.5.6;13.5.6 Work in Progress and Outlook;337
16.6;References;339
17;14A software platform for the analysis of porous die-cast parts using the finite cell method;342
17.1;14.1 Introduction;342
17.2;14.2 The Finite Cell Method;344
17.2.1;14.2.1 Fundamentals of the Finite Cell Method;344
17.2.2;14.2.2 Numerical Integration;347
17.3;14.3 Concept of the Software Platform;348
17.4;14.4 Trouble Shooting the STL Data Set;350
17.5;14.5 Verification of the Software Platform;352
17.6;14.6 Summary and Outlook;354
17.7;References;356
18;15Refined One-Dimensional Models for the Multi-Field Analysis of Layered Smart Structures;357
18.1;15.1 Introduction;357
18.2;15.2 Thermo-Piezo-Elastic One-Dimensional Model;360
18.2.1;15.2.1 Kinematic Approximation;361
18.2.2;15.2.2 Geometrical Relations;364
18.2.3;15.2.3 Constitutive Relations;365
18.2.4;15.2.4 Governing Equation;366
18.2.5;15.2.5 Loading Vector;368
18.2.6;15.2.6 Rotation and Assembly of the Fundamental Nucleus;369
18.2.7;15.2.7 The Stiffness Matrix Assembly;370
18.3;15.3 Numerical Results;370
18.3.1;15.3.1 Piezo-Elastic Model Assessment;371
18.3.2;15.3.2 Cantilever Beams with Piezo-Patches;372
18.3.3;15.3.3 Thermo-Piezo-Elastic Model Assessment;375
18.4;15.4 Conclusions;377
18.5;References;377