Analysis of Composite Laminates: Theories and Their Applications

Front_cover
Front-Matter_2022_Analysis-of-Composite-Laminates
Copyright_2022_Analysis-of-Composite-Laminates
Dedication_2022_Analysis-of-Composite-Laminates
	Dedication
Contents_2022_Analysis-of-Composite-Laminates
	Contents
Biography_2022_Analysis-of-Composite-Laminates
	Biography
Acronyms_2022_Analysis-of-Composite-Laminates
	Acronyms
Preface_2022_Analysis-of-Composite-Laminates
	Preface
Chapter-1---Composite-analysis-overview_2022_Analysis-of-Composite-Laminates
	1 Composite analysis overview
		1.1 Introduction
			1.1.1 History of composites
			1.1.2 Applications of composites in aircrafts
		1.2 Composite laminates
			1.2.1 Definition and constituents
			1.2.2 Plies
			1.2.3 Laminates
		1.3 Analysis schemes
			1.3.1 Basic analysis schemes
			1.3.2 Basic equations
			1.3.3 Existing analysis theories
			1.3.4 Challenges
			1.3.5 Future developments
		1.4 General Hooke's law
			1.4.1 Hyperelastic materials
			1.4.2 Monoclinic materials
			1.4.3 Orthotropic materials
			1.4.4 Isotropic materials
			1.4.5 Plane stress-reduced constitutive relations
			1.4.6 Transformation of material coefficients
		1.5 Energy principles
			1.5.1 Virtual displacement principle
			1.5.2 Hamilton's principle
			1.5.3 Mixed variational principles
		References
Chapter-2---Shear-deformation-theories_2022_Analysis-of-Composite-Laminates
	2 Shear deformation theories
		2.1 Introduction
		2.2 Classical laminated plate theory
			2.2.1 Displacement fields
			2.2.2 Kinematic equation
			2.2.3 Constitutive equations
			2.2.4 Governing equations
		2.3 First-order shear deformation theory
			2.3.1 Displacement fields
			2.3.2 Kinematic equation
			2.3.3 Shear correction factors
			2.3.4 Constitutive equations
			2.3.5 Governing equations
		2.4 High-order shear deformation theories
			2.4.1 Second-order shear deformation theory
			2.4.2 Third-order shear deformation theory
			2.4.3 Higher-order shear deformation theories
		2.5 Finite element formulations
			2.5.1 CLPT
			2.5.2 FSDT
			2.5.3 TSDT
			2.5.4 Numerical examples
		References
Chapter-3---State-space-theory_2022_Analysis-of-Composite-Laminates
	3 State space theory
		3.1 Introduction
		3.2 Hamiltonian canonical equation of laminated plates
			3.2.1 Hamiltonian canonical equation of individual layer
			3.2.2 Exact solution of simply support single layer plates
			3.2.3 Hamiltonian canonical equation of laminated plates
		3.3 H-R variational principle of laminated plates
			3.3.1 H-R variational principle in rectangular coordinate system
			3.3.2 H-R variational principle in cylindrical coordinate system
			3.3.3 Numerical examples
		3.4 Finite element formulation of state space theory
			3.4.1 Hamiltonian isoparametric element
			3.4.2 Governing equations
			3.4.3 Boundary conditions
			3.4.4 Precise time-integration
			3.4.5 Free vibration
			3.4.6 Numerical examples
		3.5 Meshfree formulation of state space theory
			3.5.1 Interpolation using radial basis functions
			3.5.2 Radial basis functions
			3.5.3 Numerical examples
				Example I: Single layer plates
				Example II: Cross-ply composite laminated square plate
		3.6 Bonding imperfection in composite laminates
			3.6.1 Bonding imperfection
			3.6.2 State space equation of bonding imperfection problems
			3.6.3 Numerical examples
				Example I: Static problem
				Example II: Free vibration problem
		References
Chapter-4---Layerwise-theories_2022_Analysis-of-Composite-Laminates
	4 Layerwise theories
		4.1 Introduction
		4.2 Integrate layerwise methods
			4.2.1 Generalized laminate plate theory
			4.2.2 Layerwise FEM
			4.2.3 Other ILWMs
		4.3 Reddy's layerwise theory
			4.3.1 Displacement fields
			4.3.2 Euler equations
			4.3.3 Constitutive equations
			4.3.4 Finite formulations
			4.3.5 Numerical examples
				Examples I: Plates
				Examples II: Cylindrical shells
		4.4 Discrete layerwise theories
			4.4.1 Development of DLWM
			4.4.2 Displacement-based DLWM
			4.4.3 Carrera's unified formulation
			4.4.4 Three-field variables DLWM
			4.4.5 Multiparticle model of multilayered materials
		References
Chapter-5---Extended-layerwise-method_2022_Analysis-of-Composite-Laminates
	5 Extended layerwise method
		5.1 Introduction
		5.2 Extended layerwise method of laminated plates
			5.2.1 Displacements fields
			5.2.2 Description of transverse crack
			5.2.3 Hamilton's principle and Euler–Lagrange equations
			5.2.4 Constitutive equations
			5.2.5 Finite element formulations
			5.2.6 Time integrations
			5.2.7 Numerical examples
				Example I: Static problems
				Example II: Free vibration analysis
				Example III: Transient analysis
		5.3 Extended layerwise method of doubly-curved laminated shells
			5.3.1 Geometric equations of laminated shells
			5.3.2 Hamilton's principle and Euler–Lagrange equations
			5.3.3 Constitutive equations
			5.3.4 Governing equations
			5.3.5 Full extended layerwise method
			5.3.6 Numerical examples
				Example I: Isotropic and orthotropic shells without damage
				Example II: Cylindrical shells with delaminations and/or transverse crack
				Example III: Spherical shells with delaminations and/or transverse crack
				Example IV: Full-XLWM
		5.4 Fracture analysis of composite laminates
			5.4.1 Equivalent domain integral method
			5.4.2 Interaction integral method of isotropic materials
			5.4.3 Interaction integral method of orthotropic materials
			5.4.4 Interaction integral method of dynamic problems
			5.4.5 Local remeshing scheme
			5.4.6 Maximum circumferential tensile stress criterion
			5.4.7 VCCT based on XLWM
			5.4.8 Determination of delamination front
			5.4.9 Numerical examples
				Example I: Rectangular plates with a edge transverse crack
				Example II: Cylindrical shell with transverse cracks
				Example III: Edge cracked plate under mechanical shock
				Example IV: Arbitrary growth of transverse crack
				Example V: Delamination growth of laminates with transverse crack
		5.5 Fast uniform-grid delamination scheme
			5.5.1 The fast uniform-grid delamination scheme
			5.5.2 Delamination region identification
			5.5.3 Numerical examples
				Example I: Rectangular delamination region
				Example II: Circular delamination region
				Example III: Doubly circular delamination region
		5.6 Microfracture analysis of composite laminates
			5.6.1 Force-bearing mechanisms of fibers
			5.6.2 Modeling scheme
			5.6.3 Fibers modeling
			5.6.4 Governing equations
			5.6.5 Numerical examples
				Example I: Unidirectional laminates without damage
				Example II: Unidirectional laminates with matrix crack
				Example III: Unidirectional laminates with fiber breakage or transverse crack
		References
Chapter-6---Multiphysical-analysis_2022_Analysis-of-Composite-Laminates
	6 Multiphysical analysis
		6.1 Introduction
		6.2 Thermomechanical analysis
			6.2.1 Variational principles considering temperature effect
			6.2.2 Displacement fields
			6.2.3 Euler equations
			6.2.4 Constitutive equations
			6.2.5 Finite element formulations
			6.2.6 Time integrations
			6.2.7 Evaluation of SIF for thermomechanical dynamic problems
			6.2.8 Numerical examples
				Example I: Steady-state thermomechanical problems
				Example II: Laminates with delamination and transverse crack
		6.3 Piezoelectric analysis
			6.3.1 Displacement and potential fields
			6.3.2 Electromechanical variational principle
			6.3.3 Constitutive equations
			6.3.4 Finite element formulation
			6.3.5 Coupling modeling of laminated plates with piezoelectric patch
			6.3.6 Thermo-electromechanical dynamic analysis
			6.3.7 Numerical examples
				Example I: Piezoelectric plates with delaminations and transverse cracks
				Example II: Laminates with piezoelectric patch
				Example III: Thermo-electromechanical dynamic analysis of piezoelectric laminates
		6.4 Chemo-thermomechanical analysis
			6.4.1 Chemo-thermomechanical fields
			6.4.2 Hamilton principle and Euler equations
			6.4.3 Constitutive equations
			6.4.4 Finite element formulations
			6.4.5 Times integration
			6.4.6 Chemomechanical analysis
			6.4.7 Numerical examples
				Example I: Dynamic chemomechanical problems
				Example II: Multilayered TBC plate without damage
				Example III: TBC plate with multiple interface cracks and transverse crack
		References
Chapter-7---Analysis-of-complex-composite_2022_Analysis-of-Composite-Laminat
	7 Analysis of complex composites
		7.1 Introduction
		7.2 Layerwise/solid-element method of composite stiffened shells
			7.2.1 Modeling scheme
			7.2.2 Finite element formulations of the stiffener
			7.2.3 LW/SE method
			7.2.4 Numerical examples
				Example I: Semimonocoque construction
				Example II: XLW/SE
		7.3 Dynamic thermomechanical analysis of stiffened plates
			7.3.1 Dynamic thermomechanical three-dimensional elements
			7.3.2 Dynamic thermomechanical XLW/SE
			7.3.3 Numerical examples
				Example I: Stiffened plates with transverse crack or/and delamination
				Example II: Composite stiffened plates with various damage
		7.4 Analysis methods of sandwich structures
			7.4.1 DLWM for the sandwich plates
			7.4.2 Layerwise/solid-element of composite sandwich plates
			7.4.3 LW/SE of sandwich plates with multilayer cores
			7.4.4 Modeling of the sandwich structures
			7.4.5 Numerical examples
				Example I: Rectangular sandwich plate
				Example II: XLW/SE of truss sandwich plate
				Example III: XLW/SE of honeycomb sandwich plate
		7.5 Dynamic thermomechanical analysis of sandwich plates
			7.5.1 LW/SE method of sandwich plates with single core
			7.5.2 LW/SE method of sandwich plates with multiply cores
			7.5.3 Numerical examples
				Example I: Verifications
				Example II: Composite sandwich plates with various damage
				Example III: Composite sandwich plates with double layer honeycomb cores
		7.6 Dynamic thermo-chemomechanical coupling analysis on aeroengine turbine
			7.6.1 Three-dimensional thermo-chemomechanical formulations
			7.6.2 Transformation of coordinate system
			7.6.3 Modeling of aeroengine turbine with TBCs
			7.6.4 Numerical examples
				Example I: Verifications
				Example II: TBCs with various damage
		References
Chapter-8---Progressive-failure-analysis_2022_Analysis-of-Composite-Laminate
	8 Progressive failure analysis
		8.1 Introduction
		8.2 Continuous damage mechanics analysis framework
			8.2.1 Damage constitutive
			8.2.2 Damage initiation
				Maximum stress and maximum strain theories
				Tsai–Hill criterion
				Tsai–Wu criterion
				Hoffman criterion
				Hashin criteria
			8.2.3 Damage evolution law
		8.3 Progressive failure analysis of low-velocity impact
			8.3.1 Mathematic model of impact problem
			8.3.2 Contact force based on Hertz's law
			8.3.3 FEM implementation
			8.3.4 Numerical examples
				Example I: Verifications
				Example II: Composite laminated plates with stiffeners
		8.4 Progressive failure analysis of composites
			8.4.1 Discrete damage zone model
			8.4.2 DDZM-XLWM
			8.4.3 Fatigue analysis based on DDZM-XLWM
			8.4.4 Fatigue parameters
			8.4.5 Numerical examples
				Example I: Contact problems
				Example II: Verifications
				Example III: Composite plate with multiple delamination and transverse crack
				Example IV: Fatigue of delamination in DCB
		8.5 Progressive thermomechanical DDZM-XLWM
			8.5.1 Problems descriptions
			8.5.2 Interfacial heat transfer
			8.5.3 Governing equations
			8.5.4 Numerical examples
				Example I: Thermomechanical contact problems
				Example II: Verification
				Example III: Composite plate with delamination
		References
Chapter-9---Multiscale-analysis_2022_Analysis-of-Composite-Laminates
	9 Multiscale analysis
		9.1 Introduction
		9.2 Layerwise multiscale analysis method
			9.2.1 Multiscale analysis based on EST
			9.2.2 Homogenization method
			9.2.3 Layerwise multiscale analysis method
			9.2.4 Implementation
			9.2.5 Numerical examples
		9.3 Two-scale C2 of a laminated curved beams
			9.3.1 TSDT of curved beams
			9.3.2 Displacement decomposition
			9.3.3 Finite element formulations
			9.3.4 Nonlocal quadrature
		9.4 Three-scale C2 of laminated curved beams
			9.4.1 Displacement decomposition
			9.4.2 Finite element formulations
			9.4.3 Numerical examples
				Example I: Quasiisotropic curved beam
				Example II: Woven-curved beam
		9.5 C2 of laminated plates
			9.5.1 Framework of C2 for laminated plates
			9.5.2 Two-scale analysis of laminated plates
			9.5.3 Three-scale analysis of laminated plates
		References
Chapter-10---Sensitivity-analysis_2022_Analysis-of-Composite-Laminates
	10 Sensitivity analysis
		10.1 Introduction
		10.2 Sensitivity analysis based on FEM
			10.2.1 Static responses
			10.2.2 Frequency and mode shape
		10.3 Evaluation methods
			10.3.1 AM
			10.3.2 FDM
			10.3.3 SAM
			10.3.4 Step sizes of SAM and FDM
		10.4 Sensitivity analysis based on SST
			10.4.1 Hybrid governing equations
			10.4.2 Hybrid governing equation of bonding imperfection problems
			10.4.3 Implement of sensitivity analysis
			10.4.4 Numerical examples
				Examples I: Laminates without damage
				Examples II: Static problems of laminated plates with imperfections
				Examples III: Free vibration problems of laminated plates with imperfections
		References
Chapter-11---Analysis-codes_2022_Analysis-of-Composite-Laminates
	11 Analysis codes
		11.1 Overall framework
		11.2 Data structures and pre/post process
			11.2.1 Matrix storage formats
			11.2.2 Preprocess
			11.2.3 Post-process tool
		11.3 Solver models
			11.3.1 Solver_sdt
			11.3.2 Solver_sst
			11.3.3 Solver_rlw
			11.3.4 Solver_xlw
		References
Index_2022_Analysis-of-Composite-Laminates
	Index
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