Lecture Schedule

1. Introduction
   Organization meeting
   continuous medium (continuum) and continuum mechanics
   course overview.
2. Vector and Tensor
   vertors; vector addition; scalar product; vector products; basis and component; change of basis
   tensors; rectangular Cartesian tensor components; dyadics; tensor properties
   vector and tensor calculus; differentiation; gradient; divergence and curl
   Integral transformation
   HW1: (P24) 5,6,7,11,15,20; (P46) 4,6,13; (P61) 3,5,7,11. (total of 13 problems)
3. Stress
   body forces and surface forces; traction; stress tensor
   principal axes of stress; invariants
   Mohr's circles; plane stress
   HW2: (P80) 1,5,9,13,17; (P93) 1,4,7,10,13; (P100) 1,4,7; (P111) 1,6 (total of 15 problems)
4. Strain and Deformation
   small strain and rotation; displacement gradient; strain tensor; rotation tensor
   kinematics of a continuous medium; material derivatives
   rate-of-deformation tensor; spin tensor; natural strain increment
   finite strain and deformation; Eulerian and Lagrangian formulations
   strain rate; geometric measures of strain; change in length, angle, volume, and area
   rotation and stretch tensors
   HW3: (P135) 1, 4, 6, 8, 11, 14, 17; (P152) 1, 3, 6(a), 9, 14, 16; (P170) 1, 3, 6, 9, 13 (total of 18 problems)
5. Mid-term Exam;
6. General Principles
   Introduction; flux; Reynolds transport theorem
   Conservation of mass; The continuity equation
   Momemtum principles; Equation of motion and equilibrium; Piola-Kirchhoff stress tensors
   Enery balance; First law of thermodynamics; Energy equation; Stress power
   HW4: (P212) 4,5,10,11; (P224) 3,7,11,13,14; (P236) 2,4,6,8 (total of 13 problems)
7. Constitutive Equations
   Introduction, ideal material; Isotropic tensor
   classic elasticity; ideal elastic; strain-energy function; symmetry group; thermal
   fluids; pressure in fluids; viscous fluid, Newtonian fluids, viscosity, Navier-Poisson Law
   linear viscoelastic response, creep, stress relaxation; Kevin/Maxwell models.
   HW5: (P278) 3; (P94) 2,10,11,12; (P304) 1,6,8; (P324) 3,5 (total of 10 problems)
8. Fluid Mechanics
   Field equations of Newtonian fluids; a 2-D incompressible steady channel flow
   Perfect fluid, Kelvin's theorem, Bernoulli equation
   acoustic wave of small amplitude; steady irrotational flow of compressible fluids
   irrotation flow of incompressible perfect fluid, the Green's identities; 2-D flow stream function
   similarity of flow fields; characteritic numbers; dimensional analysis, the pi theorem
   two limited cases (large Re and small Re), boundary-layer concept
   HW6: (P433) 3, 7; (P447) 2,4,10; (P461) 2,4,5; (P473) 3,6 (total of 10 problems)
9. Linearized Theory of Elasticity
   Field equations; uniqueness of the elastostatic problem; stress equation of elastostatic
   wave equations
10. Final Exam