(Department) Biomedical Engineering (Division)
(Level and Major)
Course Title Theory of Elasticity
Number of Credits 3 Prerequisite
Course Topics:
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Mathematical Preliminaries, Kronecker Delta and Alternating Symbol
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Coordinate Transformations & Cartesian Tensors
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Vector, Matrix, and Tensor Algebra, Calculus of Cartesian Tensors
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Orthogonal Curvilinear Coordinates
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Deformation: Displacements and Strains
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Geometric Construction of Small Deformation Theory
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Strain Transformation, Principal Strains, Spherical and Deviatoric Strains
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Strain Compatibility
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Curvilinear Cylindrical and Spherical Coordinates
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Stress and Equilibrium
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Body and Surface Forces
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Traction Vector and Stress Tensor
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Stress Transformation, Principal Stresses, Spherical and Deviatoric Stresses
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Equilibrium Equations,
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Relations in Curvilinear Cylindrical and Spherical Coordinates
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Material Behavior—Linear Elastic Solids, Material Characterization
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Linear Elastic Materials—Hooke’s Law, Physical Meaning of Elastic Moduli
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Thermoelastic Constitutive Relations,
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Formulation and Solution Strategies,
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Review of Field Equations,
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Boundary Conditions and Fundamental Problem Classifications,
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Stress & Displacement Formulations
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Principle of Superposition,
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Saint-Venant’s Principle,
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General Solution Strategies,
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Strain Energy and Related Principles,
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Uniqueness of the Elasticity Boundary-Value Problem,
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Bounds on the Elastic Constants,
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Related Integral Theorems,
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Principle of Virtual Work,
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Principles of Minimum Potential and Complementary Energy,
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Rayleigh-Ritz Method,
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Two-Dimensional Formulation,
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Plane Strain & Plane Stress,
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Generalized Plane Stress,
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Antiplane Strain,
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Airy Stress Function,
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Polar Coordinate Formulation,
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Two-Dimensional Problem Solution,
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Cartesian Coordinate Solutions Using Polynomials,
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Cartesian Coordinate Solutions Using Fourier Methods,
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General Solutions in Polar Coordinates,
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Polar Coordinate Solutions,
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Extension, Torsion, and Flexure of Elastic Cylinders, General Formulation,
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Torsion Formulation & Torsion Solutions Derived from Boundary Equation,
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Torsion Solutions Using Fourier Methods,
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Torsion of Cylinders With Hollow Sections,
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Flexure Formulation & Flexure Problems Without Twist,
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Some Aspects of Objectivity, Change of Observer, and Objective Tensor Fields
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Objective Rates
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Invariance of Elastic Material Response
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Isotropic Hyperelastic Materials,
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Incompressible & Compressible Hyperelastic Materials,
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Some Forms of Strain-energy Functions,
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Elasticity Tensors,
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Transversely Isotropic Materials
- Hyperelastic Composite Materials with Two Families of Fibers
Reading Resources:
Evaluation:
30% Final Exam
60% Midterm Exam
10% Homework
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