压电材料高等力学

Chapter 1 Introduction to Piezoelectricity

1.2 Linear theory ofpiezoelectricity

1.2.1 Basic equations in rectangular coordinate system

1.2.2 Boundary conditions

1.3 Functionally graded piezoelectric materials

1.3.1 Typesofgradation

1.3.2 Basic equations for two-dimensional FGPMs

1.4 Fibrous piezoelectric composites

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 Basicequations

2.4.2 Assumed fields

2.4.3 Element sti伍1ess equation

2.5 Integralequations

2.5.1 Fredholmintegralequations

2.5.2 Volterra integral equations

2.5.3 Abel's integralequation

2.6 Shear-Iagmodel

2.7 Hamiltonian method and symplectic mechanics

2.8 State space formulation

Chapter 3 Fibrous Piezoelectric Composites

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 fiberpush-out

3.4.1 Stress transferin the bonded regio

3.4.2 Frictionalsliding

3.4.3 PFC push-out driven by electrical and mechanicalloading

3.4.4 Numerical assessment

3.5 Interfacial debonding criterion

3.6 Micromecharucs offibrous piezoelectric composites

3.6.1 0verallelastoelectric properties ofFPCs

3.6.2 Extension to include magnetic and thermal effects

3.7.1 Conformalmapping

3.7.2 Solutions for thermalloading applied outside an elliptic fiber

3.7.3 Solutions for holes and rigid fibers References

Chapter 4 Treftz Method for Piezoelectricit

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 ofthe element stifffiness equation

4.2.5 Numerical results

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 comer

4.3.5 Generation ofelement matrix

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 GeneraI 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

Chapter 5 Symplectic Solutions for Piezoelectric Materials

Chapter 6 Saint-Venant Decay Problems in Piezoelectricity

Chapter 7 Penny-Shaped Cracks

Chapter 8 Solution Methods for Functionally Graded Piezoelectric Materials

Index

《压电材料高等力学（英文版）》主要阐述线性压电材料的基本理论和基本研究方法，其中包括Trefftz有限元法、辛力学模型、哈密顿系统；讨论了纤维增强压电复合材料、压电功能梯度材料、含币型裂纹压电材料、压电材料辛力学等问题。《压电材料高等力学（英文版）》的读者对象是物理、力学和材料类相关专业的研究人员和研究生。