Front Matter
Chapter 1 Introduction to Piezoelectricity
1.1 Background
1.2 Linear theory of piezoelectricity
1.2.1 Basic equations in rectangular coordinate system
1.2.2 Boundary conditions
1.3 Functionally graded piezoelectric materials
1.3.1 Types of gradation
1.3.2 Basic equations for two-dimensional FGPMs
1.4 Fibrous piezoelectric composites
References
Chapter 2 Solution Methods
2.1 Potential function method
2.2 Solution with Lekhnitskii formalism
2.3 Techniques of Fourier transformation
2.4 Trefftz finite element method
2.4.1 Basic equations
2.4.2 Assumed fields
2.4.3 Element stiffness equation
2.5 Integral equations
2.5.1 Fredholm integral equations
2.5.2 Volterra integral equations
2.5.3 Abel’s integral equation
2.6 Shear-lag model
2.7 Hamiltonian method and symplectic mechanics
2.8 State space formulation
References
Chapter 3 Fibrous Piezoelectric Composites
3.1 Introduction
3.2 Basic formulations for fiber push-out and pull-out tests
3.3 Piezoelectric fiber pull-out
3.3.1 Relationships between matrix stresses and interfacial shear stress
3.3.2 Solution for bonded region
3.3.3 Solution for debonded region
3.3.4 Numerical results
3.4 Piezoelectric fiber push-out
3.4.1 Stress transfer in the bonded region
3.4.2 Frictional sliding
3.4.3 PFC push-out driven by electrical and mechanical loading
3.4.4 Numerical assessment
3.5 Interfacial debonding criterion
3.6 Micromechanics of fibrous piezoelectric composites
3.6.1 Overall elastoelectric properties of FPCs
3.6.2 Extension to include magnetic and thermal effects
3.7 Solution of composite with elliptic fiber
3.7.1 Conformal mapping.
3.7.2 Solutions for thermal loading applied outside an elliptic fiber
3.7.3 Solutions for holes and rigid fibers
References
Chapter 4 Trefftz Method for Piezoelectricity
4.1 Introduction
4.2 Trefftz FEM for generalized plane problems.
4.2.1 Basic field equations and boundary conditions
4.2.2 Assumed fields
4.2.3 Modified variational principle
4.2.4 Generation of the element stiffness equation
4.2.5 Numerical results
4.3 Trefftz FEM for anti-plane problems
4.3.1 Basic equations for deriving Trefftz FEM
4.3.2 Trefftz functions
4.3.3 Assumed fields
4.3.4 Special element containing a singular corner
4.3.5 Generation of element matrix
4.3.6 Numerical examples
4.4 Trefftz boundary element method for anti-plane problems
4.4.1 Indirect formulation
4.4.2 The point-collocation formulations of Trefftz boundary element method
4.4.3 Direct formulation
4.4.4 Numerical examples
4.5 Trefftz boundary-collocation method for plane piezoelectricity
4.5.1 General Trefftz solution sets
4.5.2 Special Trefftz solution set for a problem with elliptic holes
4.5.3 Special Trefftz solution set for impermeable crack problems
4.5.4 Special Trefftz solution set for permeable crack problems
4.5.5 Boundary collocation formulation
References
Chapter 5 Symplectic Solutions for Piezoelectric Materials
5.1 Introduction
5.2 A symplectic solution for piezoelectric wedges
5.2.1 Hamiltonian system by differential equation approach
5.2.2 Hamiltonian system by variational principle approach
5.2.3 Basic eigenvalues and singularity of stress and electric fields
5.2.4 Piezoelectric bimaterial wedge
5.2.5 Multi-piezoelectric material wedge
5.3 Extension to include magnetic effect
5.3.1 Basic equations and their Hamiltonian system
5.3.2 Eigenvalues and eigenfunctions
5.3.3 Particular solutions
5.4 Symplectic solution for a magnetoelectroelastic strip
5.4.1 Basic equations
5.4.2 Hamiltonian principle
5.4.3 The zero-eigenvalue solutions
5.4.4 Nonzero-eigenvalue solutions
5.5 Three-dimensional symplectic formulation for piezoelectricity
5.5.1 Basic formulations
5.5.2 Hamiltonian dual equations
5.5.3 The zero-eigenvalue solutions
5.5.4 Sub-symplectic system
5.5.5 Nonzero-eigenvalue solutions
5.6 Symplectic solution for FGPMs
5.6.1 Basic formulations
5.6.2 Eigenvalue properties of the Hamiltonian matrix H
5.6.3 Eigensolutions corresponding to μ =0 and–α
5.6.4 Extension to the case of magnetoelectroelastic materials
References
Chapter 6 Saint-Venant Decay Problems in Piezoelectricity
6.1 Introduction
6.2 Saint-Venant end effects of piezoelectric strips
6.2.1 Hamiltonian system for a piezoelectric strip
6.2.2 Decay rate analysis
6.2.3 Numerical illustration
6.3 Saint-Venant decay in anti-plane dissimilar laminates
6.3.1 Basic equations for anti-plane piezoelectric problem
6.3.2 Mixed-variable state space formulation
6.3.3 Decay rate of FGPM strip
6.3.4 Two-layered FGPM laminates and dissimilar piezoelectric laminates
6.4 Saint-Venant decay in multilayered piezoelectric laminates
6.4.1 State space formulation
6.4.2 Eigensolution and decay rate equation
6.5 Decay rate of piezoelectric-piezomagnetic sandwich structures
6.5.1 Basic equations and notations in multilayered structures
6.5.2 Space state differential equations for analyzing decay rate
6.5.3 Solutions to the space state differential equations
References
Chapter 7 Penny-Shaped Cracks
7.1 Introduction
7.2 An infinite piezoelectric material with a penny-shaped crack
7.3 A penny-shaped crack in a piezoelectric strip
7.4 A fiber with a penny-shaped crack embedded in a matrix
7.5 Fundamental solution for penny-shaped crack problem
7.5.1 Potential approach
7.5.2 Solution for crack problem
7.5.3 Fundamental solution for penny-shaped crack problem
7.6 A penny-shaped crack in a piezoelectric cylinder
7.6.1 Problem statement and basic equation.
7.6.2 Derivation of integral equations and their solution
7.6.3 Numerical results and discussion
7.7 A fiber with a penny-shaped crack and an elastic coating
7.7.1 Formulation of the problem
7.7.2 Fredholm integral equation of the problem
7.7.3 Numerical results and discussion
References
Chapter 8 Solution Methods for Functionally Graded Piezoelectric Materials
8.1 Introduction
8.2 Singularity analysis of angularly graded piezoelectric wedge
8.2.1 Basic formulations and the state space equation
8.2.2 Two AGPM wedges
8.2.3 AGPM-EM-AGPM wedge system
8.2.4 Numerical results and discussion
8.3 Solution to FGPM beams
8.3.1 Basic formulation
8.3.2 Solution procedure
8.4 Parallel cracks in an FGPM strip
8.4.1 Basic formulation
8.4.2 Singular integral equations and field intensity factors
8.5 Mode Ⅲ cracks in two bonded FGPMs
8.5.1 Basic formulation of the problem
8.5.2 Impermeable crack problem
8.5.3 Permeable crack problem
References
Index
版权
