MUH 302 - Continuum Mechanics

Course Objectives

1. To teach tensor operations and physical meaning of a tensor and its components.
2. To teach the basic equations related to the description of deformation and motion of a continuum.
3. To obtain the equation of conservation of mass, the equation of conservation of momentum the equation of conservation of angular momentum and the equation of conservation of energy.
4. To provide the concepts of stress vector and tensor.
5. To obtain fundamental equations of thermodynamics of continuous media.
6. To give constitutive equations of elastic solids, to give some examples.
7. To give constitutive equations of fluids, to give some examples.

Course Description

Deformation, length and angle changes, area and volume changes. Strain invariants, principal axes. Kinematics; velocity, acceleration, material derivative. Deformation rate, vorticity. Kinematics of volume integral. Stress tensor, principal stresses. Compatibility conditions. Equations of conservation of mass and balance of, momentum, angular momentum and energy. Entropy inequality, Constitutive equation of elastic solid, plane elastic waves, vibration of infinite plate. Elastic medium under large deformation. Extension and torsion of incompressible isotropic solid. Constitutive equations of fluids. Hydrostatic, Newtonian viscous fluids, Navier-Stokes equations of incompressible fluids, pathline, streamline, steady, unsteady, laminar and turbulent flow, some examples.