功能梯度材料结构的解析和半解析解 仲政,聂国隽 编 专业科技 文轩网

1 Introduction
1.1 Functionally Graded Materials
1.2 Effective Material Properties of FGMs
1.2.1 The Ru1e of Mixtures
1.2.2 The Mori-Tanaka Scheme
1.2.3 The Self-Consistent Estimate
1.2.4 Mathematical Idealization of FGMs
1.3 A Review of Recent Research on FGM Structures
1.3.1 FGM Beams
1.3.2 Rectangu1ar FGM Plates
1.3.3 Circu1ar FGM Plates
1.3.4 FGM Cylmders
1.3.5 FGM Spheres
References
2 Fnndamentals for an Elastic FGM Body
2.1 Three-Dimensional Problems
2 1.1 Basic Assumptions
2 1.2 Equations in Cartesian Coordinates
2 1.3 Equations in Cylindrical Coordinates
2 1.4 Equations in Spherical Coordinates
2.2 Two-Dimensional Problems
2.2.1 Equations in Cartesian Coordinates
2.2.2 Equations in Polar Cosidinates
2.3 Boundary and Initial Conditions
2.3.1 Boundary Conditions
2.3.2 Initial Conditions
2.4 Mu1ti-field Coupling Media
2.5 Variational Principlsifsian FGM Body
2.5.1 Basic Equations
2.5.2 Principle of VJrtual Work
2.5.3 Unconventional Hamilton Variational Principles
2.5.4 Unconventional Hamilton Variational Principle in Phase Space
2.6 Uniqueness of Elasticity Solutions
2.7 Principle of Superposition
2.8 Principle of Saint-Venant
References
3 Governing Equations for Different Solution Schemes
3.1 Governing Equations in Terms of Displacements
3.1.1 Equations in Cartesian Coordinates
3.1.2 Equations in Cylindrical Coordinates
3.1.3 Equations in Spherical Coordinates
3.2 Governing Equations in Terms of Displacement Functions
3.2.1 Three-Dimensional Problem of Transversely Isotropic
3.2.2 Three-Dimensional Problem oflsotropic FGM Body
3.2.3 Plane Stress Problem of Orthotropic FGM Body
3.2.4 Axisymmetric Problem of Transversely Isotropic
3.2.5 Axisymmetric Problem oflsotropic FGM Body
3.3 Governing Equations in Terms of Stress Function
3.3.1 Two-Dimensional Problem in Cartesian Coordinates
3.3.2 Two-Dimensional Problem in Polar Coordinates
3.4 Governing Equations Expressed by State-Space Method
3.4.1 Equations in Terms of Mixed Variables in Cartesian Coordinates
3.4.2 Equations for Multifield Coupled Problem in Cartesian Coordinates
3.4.3 Equations in Terms of Displacements in Cylindrical Coordinates
3.4.4 Equations for Multifield Coupling Problem in Cylindrical Coordinates
References
4 Functionally Graded Beams
4.1 Analytical Solution of FGM Beams Using the Displacement Method
4.1.1 Formulation
4.1.2 Exact Solutions for FGM Beams
4.2 Analytical Solutions of FGM Beams Using the Displacement Function Method
4.2.1 Formulation
4.2.2 Solution
4.2.3 Boundary Conditions
4.2.4 Isotropic Cases
4.2.5 Numerical Examples
4.3 Analytical Solutions of FGM Beams Using the Stress Function Method
4.3.1 Formulation
4.3.2 Solution of Orthotropic FGM Beams
4.3.3 Examples of Orthotropic FGM Beams
4.4 Elasticity Solutions for FGM Beams Using the State Space Method
4.4.1 Formulation
4.4.2 Solution
4.5 Electroelastic Analysis of FGPM Beams Using the Stress Function Method
4.5.1 Formulation
4.5.2 Solution
4.5.3 Examples
References
5 Rectangular Functionally Graded Plates
5.1 Analytical Solutions oflsotropic Rectangular FGM Plates in Cylindrical Bending
5.1.1 Formulation
5.1.2 Solution Procedure
5.1.3 Numerical Examples and Discussion
5.2 Three-Dimensional Elastic Solution oflsotropic Rectangular FGM Plates
5.2.1 Formulation
5.2.2 Solution
5.2.3 Examples
5.3 Three-Dimensional Elastic Solution of Transversely Isotropic Rectangular FGM Plates
5.3.1 Formulation
5.3.2 Solution
5.3.3 Numerical Examples
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