# Advanced Mechanics Of Materials And Applied Elasticity

Advanced Mechanics Of Materials And Applied Elasticity

• Cartesian Tensors
• Definition And Rules Of Operation Of Tensors Of The Second Rank
• Transformation Of The Cartesian Components Of A Tensor Of The Second
• Rank Upon Rotation Of The System Of Axes To Which They Are Referred
• Definition Of A Tensor Of The Second Rank On The Basis
• Of The Law Of Transformation Of Its Components
• Symmetric Tensors Of The Second Rank
• Invariants Of The Cartesian Components Of A Symmetric Tensor
• Of The Second Rank
• Stationary Values Of A Function Subject To A
• Constraining Relation
• Stationary Values Of The Diagonal Components Of A
• Symmetric Tensor Of The Second Rank
• Quasi Plane Form Of Symmetric Tensors Of The Second Rank
• Stationary Values Of The Diagonal And The Non-Diagonal
• Components Of The Quasi Plane, Symmetric Tensors Of The
• Second Rank
• Mohr’s Circle For Quasi Plane, Symmetric Tensors Of The
• Second Rank
• Maximum Values Of The Non-Diagonal Components Of A
• Symmetric Tensor Of The Second Rank
• Problems
• Strain And Stress Tensors
• The Continuum Model
• The Displacement Vector Of A Particle Of A Body
##### Components Of Strain Of A Particle Of A Body
• Implications Of The Assumption Of Small Deformation
• Proof Of The Tensorial Property Of The Components Of Strain
• Traction And Components Of Stress Acting On A Plane Of
• A Particle Of A Body
• Proof Of The Tensorial Property Of The Components Of Stress
• Properties Of The Strain And Stress Tensors
• Components Of Displacement For A General Rigid Body
• Motion Of A Particle
• The Compatibility Equations
• Measurement Of Strain
• The Requirements For Equilibrium Of The Particles Of A Body
• Cylindrical Coordinates
• Strain–Displacement Relations In Cylindrical Coordinates
• The Equations Of Compatibility In Cylindrical Coordinates
• The Equations Of Equilibrium In Cylindrical Coordinates
• Problems
• Stress–Strain Relations
• Introduction
• The Uniaxial Tension Or Compression Test Performed
• In An Environment Of Constant Temperature
• Strain Energy Density And Complementary Energy Density For
• Elastic Materials Subjected To Uniaxial Tension Or Compression
• On The Response Of Materials Subjected To Uniaxial
• States Of Stress
##### Models Of Idealized Time-Independent Stress–Strain
• Relations For Uniaxial States Of Stress
• Stress–Strain Relations For Elastic Materials Subjected
• To Three-Dimensional States Of Stress
• Stress–Strain Relations Of Linearly Elastic Materials
• Subjected To Three-Dimensional States Of Stress
• Stress–Strain Relations For Orthotropic, Linearly
• Elastic Materials
• Stress–Strain Relations For Isotropic, Linearly
• Elastic Materials Subjected To Three-Dimensional
• States Of Stress
• Strain Energy Density And Complementary Energy
• Density Of A Particle Of A Body Subjected To External
• Forces In An Environment Of Constant Temperature
• Thermodynamic Considerations Of Deformation Processes
• Involving Bodies Made From Elastic Materials
• Linear Response Of Bodies Made From Linearly
• Elastic Materials
• Time–Dependent Stress-Strain Relations
• The Creep And The Relaxation Tests
• Yield And Failure Criteria
• Yield Criteria For Materials Subjected To Triaxial
• States Of Stress In An Environment Of Constant Temperature
• The Von Mises Yield Criterion
##### Failure Of Structures — Factor Of Safety For Design
• The Maximum Normal Component Of Stress Criterion
• For Fracture Of Bodies Made From A Brittle, Isotropic,
• Linearly Elastic Material
• The Mohr’s Fracture Criterion For Brittle Materials Subjected To
• States Of Plane Stress
• Formulation And Solution Of Boundary Value
• Problems Using The Linear Theory Of Elasticity
• Introduction
• Boundary Value Problems For Computing The Displacement
• And Stress Fields Of Solid Bodies On The Basis Of The
• Assumption Of Small Deformation
• Methods For Finding Exact Solutions For Boundary Value
• Problems In The Linear Theory Of Elasticity
• Solution Of Boundary Value Problems For Computing
• The Displacement And Stress Fields Of Prismatic Bodies
• Made From Homogeneous, Isotropic, Linearly Elastic Materials
• Problems An Environment Of Constant Temperature
• Mechanics Of Materials And Applied Elasticity
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• Applications Of Young’s Modulus Of Elasticity
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