压电材料高等力学 英文版2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

压电材料高等力学 英文版PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Chapter 1 Introduction to Piezoelectricity1

1.1 Background1

1.2 Linear theory of piezoelectricity4

1.2.1 Basic equations in rectangular coordinate system4

1.2.2 Boundary conditions7

1.3 Functionally graded piezoelectric materials8

1.3.1 Types of gradation9

1.3.2 Basic equations for two-dimensional FGPMs9

1.4 Fibrous piezoelectric composites11

References17

Chapter 2 Solution Methods21

2.1 Potential function method21

2.2 Solution with Lekhnitskii formalism23

2.3 Techniques of Fourier transformation28

2.4 Trefftz finite element method31

2.4.1 Basic equations31

2.4.2 Assumed fields31

2.4.3 Element stiffness equation33

2.5 Integral equations34

2.5.1 Fredholm integral equations34

2.5.2 Volterra integral equations36

2.5.3 Abel's integral equation37

2.6 Shear-lag model39

2.7 Hamiltonian method and symplectic mechanics41

2.8 State space formulation47

References51

Chapter 3 Fibrous Piezoelectric Composites53

3.1 Introduction53

3.2 Basic formulations for fiber push-out and pull-out tests55

3.3 Piezoelectric fiber pull-out59

3.3.1 Relationships between matrix stresses and interfacial shear stress59

3.3.2 Solution for bonded region61

3.3.3 Solution for debonded region62

3.3.4 Numerical results63

3.4 Piezoelectric fiber push-out63

3.4.1 Stress transfer in the bonded region64

3.4.2 Frictional sliding66

3.4.3 PFC push-out driven by electrical and mechanical loading69

3.4.4 Numerical assessment70

3.5 Interfacial debonding criterion76

3.6 Micromechanics of fibrous piezoelectric composites81

3.6.1 Overall elastoelectric properties of FPCs81

3.6.2 Extension to include magnetic and thermal effects89

3.7 Solution of composite with elliptic fiber94

3.7.1 Conformal mapping94

3.7.2 Solutions for thermal loading applied outside an elliptic fiber95

3.7.3 Solutions for holes and rigid fibers104

References105

Chapter 4 Trefftz Method for Piezoelectricity109

4.1 Introduction109

4.2 Trefftz FEM for generalized plane problems109

4.2.1 Basic field equations and boundary conditions109

4.2.2 Assumed fields111

4.2.3 Modified variational principle113

4.2.4 Generation of the element stiffness equation115

4.2.5 Numerical results117

4.3 Trefftz FEM for anti-plane problems118

4.3.1 Basic equations for deriving Trefftz FEM118

4.3.2 Trefftz functions119

4.3.3 Assumed fields119

4.3.4 Special element containing a singular corner121

4.3.5 Generation of element matrix123

4.3.6 Numerical examples125

4.4 Trefftz boundary element method for anti-plane problems127

4.4.1 Indirect formulation127

4.4.2 The point-collocation formulations of Trefftz boundary element method129

4.4.3 Direct formulation129

4.4.4 Numefical examples132

4.5 Trefftz boundary-collocation method for plane piezoelectricity137

4.5.1 General Trefftz solution sets137

4.5.2 Special Trefftz solution set for a problem with elliptic holes138

4.5.3 Special Trefftz solution set for impermeable crack problems140

4.5.4 Special Trefftz solution set for permeable crack problems142

4.5.5 Boundary collocation formulation144

References145

Chapter 5 Symplectic Solutions for Piezoelectric Materials149

5.1 Introduction149

5.2 A symplectic solution for piezoelectric wedges150

5.2.1 Hamiltonian system by differential equation approach150

5.2.2 Hamiltonian system by variational principle approach153

5.2.3 Basic eigenvalues and singularity of stress and electric fields154

5.2.4 Piezoelectric bimaterial wedge159

5.2.5 Multi-piezoelectric material wedge162

5.3 Extension to include magnetic effect166

5.3.1 Basic equations and their Hamiltonian system166

5.3.2 Eigenvalues and eigenfunctions167

5.3.3 Particular solutions170

5.4 Symplectic solution for a magnetoelectroelastic strip171

5.4.1 Basic equations171

5.4.2 Hamiltonian principle172

5.4.3 The zero-eigenvalue solutions175

5.4.4 Nonzero-eigenvalue solutions179

5.5 Three-dimensional symplectic formulation for piezoelectricity182

5.5.1 Basic formulations182

5.5.2 Hamiltonian dual equations183

5.5.3 The zero-eigenvalue solutions184

5.5.4 Sub-symplectic system187

5.5.5 Nonzero-eigenvalue solutions190

5.6 Symplectic solution for FGPMs192

5.6.1 Basic formulations192

5.6.2 Eigenvalue properties of the Hamiltonian matrix H194

5.6.3 Eigensolutions corresponding to μ＝0 and-α194

5.6.4 Extension to the case of magnetoelectroelastic materials197

References201

Chapter 6 Saint-Venant Decay Problems in Piezoelectricity205

6.1 Introduction205

6.2 Saint-Venant end effects of piezoelectric strips206

6.2.1 Hamiltonian system for a piezoelectric strip206

6.2.2 Decay rate analysis211

6.2.3 Numerical illustration216

6.3 Saint-Venant decay in anti-plane dissimilar laminates218

6.3.1 Basic equations for anti-plane piezoelectric problem218

6.3.2 Mixed-variable state space formulation219

6.3.3 Decay rate of FGPM strip220

6.3.4 Two-layered FGPM laminates and dissimilar piezoelectric laminates226

6.4 Saint-Venant decay in multilayered piezoelectric laminates231

6.4.1 State space formulation231

6.4.2 Eigensolution and decay rate equation234

6.5 Decay rate of piezoelectric-piezomagnetic sandwich structures237

6.5.1 Basic equations and notations in multilayered structures238

6.5.2 Space state differential equations for analyzing decay rate239

6.5.3 Solutions to the space state differential equations241

References246

Chapter 7 Penny-Shaped Cracks249

7.1 Introduction249

7.2 An infinite piezoelectric material with a penny-shaped crack250

7.3 A penny-shaped crack in a piezoelectric strip255

7.4 A fiber with a penny-shaped crack embedded in a matrix258

7.5 Fundamental solution for penny-shaped crack problem263

7.5.1 Potential approach263

7.5.2 Solution for crack problem265

7.5.3 Fundamental solution for penny-shaped crack problem266

7.6 A penny-shaped crack in a piezoelectric cylinder268

7.6.1 Problem statement and basic equation269

7.6.2 Derivation of integral equations and their solution272

7.6.3 Numerical results and discussion277

7.7 A fiber with a penny-shaped crack and an elastic coating279

7.7.1 Formulation of the problem279

7.7.2 Fredholm integral equation of the problem285

7.7.3 Numerical results and discussion286

References287

Chapter 8 Solution Methods for Functionally Graded Piezoelectric Materials291

8.1 Introduction291

8.2 Singularity analysis of angularly graded piezoelectric wedge292

8.2.1 Basic formulations and the state space equation292

8.2.2 Two AGPM wedges298

8.2.3 AGPM-EM-AGPM wedge system301

8.2.4 Numerical results and discussion303

8.3 Solution to FGPM beams308

8.3.1 Basic formulation308

8.3.2 Solution procedure308

8.4 Parallel cracks in an FGPM strip312

8.4.1 Basic formulation313

8.4.2 Singular integral equations and field intensity factors315

8.5 Mode Ⅲ cracks in two bonded FGPMs318

8.5.1 Basic formulation of the problem318

8.5.2 Impermeable crack problem320

8.5.3 Permeable crack problem324

References325

Index329