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
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 shearstress
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 ellipticfiber
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 boundaryelement method
4.4.3 Direct formulation
4.4.4 Numerical examples
4.5 Trefftz:boundary-collocation method for planepiezoelectricity
4.5.1 GeneraI Trefftz solution sets
4.5.2 Special Trefftz solution set for a problem with ellipticholes
4.5.3 Special Trefftz solution set for impermeable crackproblems
4.5.4 Special Trefftz solution set for permeable crackproblems
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 PiezoelectricMaterials
Index
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