Engineering Elasticity: Elasticity with less Stress and Strain

Preface for Students
Preface for Instructors
Contents
About the Author
Chapter 1: Getting Ready (Mostly Review)
	Linear Algebra
		Scalars, Vector, and Matrices
		Addition and Subtraction of Vectors
		Multiplication of a Scalar Times a Vector
		Multiplication of Vectors
		Addition and Subtraction of Matrices
		A Scalar Times a Matrix
		Multiplication of Matrices
		Multiplication of a Matrix Times a Vector
		Transpose of a Matrix
		Inverse of a Matrix
		Length of a Vector
		A Vector Field and Matrix Field
		A Matrix Times a Vector Field
		A Matrix Field Times a Vector Field
	Calculus-Based Physics 1 Review
		Newton´s Laws in Equation Form
		Force, Work, and Energy
	Miscellaneous
		The Difference Between Point, Point Vector, and a General Vector
		Material Properties
		Isotropic and Anisotropic Materials
		Homogeneous and Non-homogeneous Materials
		Taylor Expansion and Physical Interpretation
			Derivative of a Vector by a Scalar
	Problems
Chapter 2: Deformations
	A Map
		Mathematics of a Mapping
		The Application of a Mapping
	Problems
Chapter 3: Forces
	Problems
Chapter 4: Force-Energy Relationships
	Springs
	Young´s Modulus
	Internal Forces
	Energy from Surface Forces
	Equation of Motion in Terms of Energy
	Problems
Chapter 5: Isotropic Materials
	Rotations and Translations
	Rotational Invariants
	Problems
Chapter 6: Minimizing Energy
	Spring Model
	Discrete 3D Model
	Continuous 3D Model
	Problems
Chapter 7: Simulations
	Introduction
	User Input
	Define Nodes and Their Connectivity
	Position Boundary Conditions
	Force Boundary Conditions
	Calculate Initial Volumes
	Calculate Deformation Energy per Unit Initial Volume
	Define Variable List
	Gravity
	Go
	Plots
		Simulating Incompressible Materials
		Scaling in Simulations
	Problems
Chapter 8: Quasi-static Simulation Examples
	Introduction
	Single Grid Study
	Cylindrical Compression Test
	Real Compression
	Matching Fig. 2.1
	Bending Paper
	Extrusion Study
	Water Drop
	Problems
Chapter 9: The Invariants
	Another Set of Invariants
	Problems
Chapter 10: Experiments
	Experiments
	Compression Experiment
	Extension Experiments
		Extension in One Direction
		Extending in Two Directions
		Checking Forces
	Simulations
	Problems
Chapter 11: Time-Dependent Simulations
	Example in 1D
	Notation Alert
	Equivalence of Equations of Motion
	Force on Fixed Nodes
	Numerical Simulation
	Problems
Chapter 12: Anisotropic Materials
	Anisotropic Materials
	Measuring the Energy of Deformation of an Anisotropic Material
	How to Find the Jig Coordinates Within a Sample
		Vector Projection
		Example 1: Layered Anisotropy
		Example 2: Fibrous Sample
	Finding  (Gram-Schmidt QRD)
	Example Deformation of a Simple Spring Model
	Numerical Simulation Example
	Alternate Set of Anisotropic Invariants
	Alternate Experimental Jig
	Problems
Chapter 13: Plot Deformation, Displacements, and Forces
	Deformation of Local Regions
	Internal Forces on Local Regions
	Displacement of Nodes
	Boundary Forces
	Grid Refinement and the Finite Element Method
	Problems
Chapter 14: Euler-Lagrange Elasticity
	Euler-Lagrange Equations
	Define Point Locations Within the Body
	Equations of Motion
	Force
	Quasi-static Deformations
	Force Boundary Conditions in Simulations
	Discrete Energy Equations Used in Numerical Simulations
	Energy per Unit Initial Volume
	Problems
Chapter 15: Linear Elasticity
	Comparison to Linear Elasticity
		Linear Elasticity
		Zeroth-Order Term in Equation 15.5
		First-Order Term in Equation 15.5
		Second-Order Term in Equation 15.5
		Comparison to Standard Linear Elasticity Equations
		Landau´s Energy Equation Leads to Linear Elastic Force-Displacement Equations
	Some Limitations of Linear Elasticity
	Advantage of Linear Elasticity
		Small Deformations with Rotations
	Problems
Chapter 16: Classical Finite Elasticity
	Classical Elasticity
	Direct Comparisons with Classical Elasticity
		Stress
		The Invariants
	Direct Comparisons with Rubber Elasticity
	Problems
Appendices
	Appendix A: Deformation in Jig Coordinates
	Appendix B: Origins of Anisotropic Invariants
		Why ?
		Gram-Schmidt QRD
		Example of Gram-Schmidt QRD
		Subroutine for Calculating Gram-Schmidt QRD
		Subroutine for Calculating Equation 12.21 Values
		General Numerical Proof That Equation 12.21 Provides the Same  Matrix as Gram-Schmidt QRD
		Why Cannot We Just Apply Gram-Schmidt QRD to m Instead of jig?
	Appendix C: Euler-Lagrange Equations
		Euler-Lagrange Equations in 1D
		Euler-Lagrange Equations in 2D
		Euler-Lagrange Equations with Two Dependent and One Independent Variables
	Appendix D: Finite Element Example
	Appendix E: Project Ideas
		Chapter 2
		Chapter 3
		Chapter 4
		Chapter 5
		Chapter 6
		Chapter 7
		Chapter 8
		Chapter 9
		Chapter 10
		Chapter 11
		Chapter 12
		Chapter 13
		Chapter 14
		Chapter 15
		Chapter 16
Index