Aims & Learning Objectives:
Aims: To introduce the general theory of continuum mechanics and, through this, the study of viscous fluid flow.
Students should be able to explain the basic concepts of continuum mechanics such as stress, deformation and constitutive relations, be able to formulate balance laws and be able to apply these to the solution of simple problems involving the flow of a viscous fluid.
Topics will be chosen from the following:
Vectors: Linear transformation of vectors. Proper orthogonal transformations. Rotation of axes. Transformation of components under rotation.
Cartesian Tensors: Transformations of components, symmetry and skew symmetry. Isotropic tensors.
Kinematics: Transformation of line elements, deformation gradient, Green strain. Linear strain measure. Displacement, velocity, strain-rate.
Stress: Cauchy stress; relation between traction vector and stress tensor.
Global Balance Laws: Equations of motion, boundary conditions.
Newtonian Fluids: The constitutive law, uniform flow, Poiseuille flow, flow between rotating cylinders.