Continuum Mechanics
ME 69700/ 3 Cr.
This course will covers the formal, consistent and unified mathematical treatment of the mechanics of continuous solids and fluids.
- Available Online: No
- Credit by Exam: No
- Laptop Required: No
Topics
- Naive set theory
- Linear spaces
- Points, vectors, and tensors in Euclidian space
- Direct vs. indicial notation
- Bodies, configurations, motions
- Mass and mass density
- The deformation gradient
- The Jacobian
- The polar decomposition
- Lagrange and Almansi strain tensors
- Velocity gradient and vorticity
- Superposed rigid body motions and change of reference frame
- Reynold's transport theorem
- Conservation of mass
- Euler's laws
- Traction vector
- Stress tensor
- Localization theorem and local forms of balance laws
- Stress measures in the reference and current configuration
- Invariance and relationship to constitutive laws
- The balance of energy
- Directional (Gâteux) derivatives
- Consistent linearization
- Inviscid fluid
- Viscous fluid
- Elastic solids
- Linear Elastic Solids
