This book focuses on nonlinear finite element analysis of thin-walled smart structures integrated with piezoelectric materials. Two types of nonlinear phenomena are presented in the book, namely geometrical nonlinearity and material nonlinearity.
Geometrical nonlinearity mainly results from large deformations and large rotations of structures. The book discusses various geometrically nonlinear theories including von Kármán type nonlinear theory, moderate rotation nonlinear theory, fully geometrically nonlinear theory with moderate rotations and large rotation nonlinear theory. The material nonlinearity mainly considered in this book is electroelastic coupled nonlinearity resulting from large driving electric field. This book will be a good reference for students and researchers in the field of structural mechanics.
Downloa
Author(s): Shun-Qi Zhang
Series: Springer Tracts in Mechanical Engineering
Publisher: Springer Singapore
Year: 2021
Language: English
Pages: 191
City: Singapore
Acknowledgements
Contents
Acronyms
List of Figures
List of Tables
1 Introduction
1.1 Background
1.2 History of Smart Structures
1.3 Objectives and Outline
References
2 Literature Review
2.1 Plate/Shell Hypotheses and Applications to Linear Analysis
2.1.1 Kirchhoff-Love Hypothesis
2.1.2 Reissner-Mindlin Hypothesis
2.1.3 Higher-Order Shear Deformation Hypothesis
2.1.4 Zigzag Hypothesis
2.1.5 Bernoulli and Timoshenko Beam Hypotheses
2.2 Geometrically Nonlinear Modeling in Composites
2.2.1 Simplified Nonlinear Modeling
2.2.2 Large Rotation Nonlinear Modeling
2.2.3 Shear Locking Phenomena
2.3 Geometrically Nonlinear Modeling for Smart Structures
2.3.1 Von Kármán Type Nonlinear Theory
2.3.2 Moderate Rotation Nonlinear Theory
2.3.3 Fully Geometrically Nonlinear Theory with Moderate Rotations
2.3.4 Large Rotation Nonlinear Theory
2.4 Electroelastic Materially Nonlinear Modeling
2.4.1 Linear Piezoelectric Constitutive Equations
2.4.2 Strong Electric Field Models
2.5 Multi-physics Coupled Modeling
2.5.1 Functionally Graded Structures
2.5.2 Electro-Thermo-Mechanically Coupled Structures
2.5.3 Magneto-Electro-Elastic Composites
2.5.4 Aero-Electro-Elastic Coupled Modeling
2.6 Modeling of Piezo-Fiber Composite Bonded Structures
2.6.1 Types of Piezo Fiber Composite Materials
2.6.2 Homogenization of Piezo Fiber Composite
2.6.3 Modeling of Piezo Composite Laminated Plates and Shells
2.7 Vibration Control of Piezo Smart Structures
2.7.1 Conventional Control Strategies
2.7.2 Advanced Control Strategies
2.7.3 Intelligent Control Strategies
References
3 Geometrically Nonlinear Theories
3.1 Shear Deformation Hypotheses
3.2 Mathematical Preliminaries
3.2.1 Introduction of Coordinates
3.2.2 Base Vectors and Metric Tensor in Shell Space
3.2.3 Base Vectors and Metric Tensor at Mid-surface
3.2.4 Quantities in Deformed Configurations
3.3 Kinematics of Shell Structures
3.3.1 Through-Thickness Displacement Distribution
3.3.2 Shifter Tensor
3.4 Strain Field
3.5 Shell Theories
3.6 Normalization
3.7 Summary
References
4 Nonlinear Constitutive Relations
4.1 Piezoelectricity
4.1.1 History of Piezoelectricity
4.1.2 Piezoelectric Effects
4.2 Fundamental Theory of Piezoelectricity
4.3 Coordinate Transformation in Plates and Shells
4.4 Constitutive Relations for Macro-fiber Composites
4.4.1 Configurations of Macro-fiber Composites
4.4.2 Constitutive for Plates and Shells
4.4.3 Piezo Constants for MFC-d31 Type
4.4.4 Piezo Constants for MFC-d33 Type
4.4.5 Parameter Configuration
4.4.6 Multi-layer Piezo Composites
4.5 Electroelastic Nonlinear Constitutive Relations
4.6 Summary
References
5 Finite Element Formulations
5.1 Resultant Vectors
5.2 Rotation Description
5.3 Shell Element Design
5.4 Variational Formulations
5.5 Total Lagrangian Formulation
5.6 Geometrically Nonlinear FE Models
5.6.1 Dynamic FE Model
5.6.2 Static FE Model
5.7 Geometrically and Electroelastic Nonlinear FE Model
5.8 Numerical Algorithms
5.8.1 Newmark Method
5.8.2 Central Difference Algorithm
5.8.3 Newton-Raphson Method
5.8.4 Riks-Wempner Method
5.9 Summary
References
6 Nonlinear Analysis of Piezoceramic Laminated Structures
6.1 Benchmark Problems
6.1.1 Asymmetric Cross-Ply Laminated Plate
6.1.2 Hinged Thin Arch
6.1.3 Spherical Shell with a Hole
6.2 Buckling and Post-buckling Analysis
6.2.1 Hinged Panel with Cross-Ply Laminates
6.2.2 Hinged Panel with Angle-Ply Laminates
6.3 Geometrically Nonlinear Analysis of Smart Structures
6.3.1 Cantilevered Smart Beam
6.3.2 Fully Clamped Smart Plate
6.3.3 Fully Clamped Cylindrical Smart Shell
6.3.4 PZT Laminated Semicircular Cylindrical Shell
6.4 Electroelastic Nonlinear Analysis of Smart Structures
6.4.1 Validation Test
6.4.2 Piezolaminated Semicircular Shell
6.5 Summary
References
7 Numerical Analysis of Macro-fiber Composite Structures
7.1 Linear Analysis of MFC Structures
7.1.1 Validation Test
7.1.2 Isotropic Plate Bonded with MFC-d31 Patches
7.1.3 Isotropic Plate with MFC-d33 Patches Having Arbitrary Fiber Orientation
7.1.4 Composite Plate with MFC-d33 Patches Having Arbitrary Fiber Orientation
7.2 Nonlinear Analysis of MFC Structures
7.2.1 Cantilevered Plate Bonded with Multi-MFC Patches
7.2.2 Cantilevered Semicircular Cylindrical Shell with Multi-MFC Patches
7.3 Summary
References
8 Conclusion and Future Work
8.1 Future Research
Appendix A Geometric Quantities
A.1 Plate Structure
A.2 Cylindrical Structure
A.3 Spherical Structure
Appendix B Strain Fields of LRT56 Theory
Appendix C Normalization
C.1 Physical Components of the Strains
C.2 Physical Components of the Displacements
