Continuum Mechanics

Credits

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/07 Mathematical Physics.

Examination method

Oral exam.

Learning
objectives

The course aims to provide methodologies and skills in Continuum Mechanics with reference to applications. Laboratory work is an integral part of the course.

Syllabus

Kinematics and deformations of a continuous system. Integral balance laws for simple continua and their local Eulerian and Lagrangian formulation. Euler equations for perfect fluids. Main results on the statics and dynamics of a perfect fluid, and applications. Plane motions, velocity potentials and Stokes potentials. Aerofoil theory. D’Alembert’s paradox. Hadamard’s theory for PDEs. Acoustic tensor, wave fronts and the eikonal equation. Energy balance and the laws of thermodynamics. Constitutive axioms. Reduced dissipation inequality and applications to viscous fluids and elastic continua. Navier-Stokes and Navier-Cauchy equations. Boundary layer and Prandtl’s hypothesis. Prandtl and Blasius equations. Wave propagation in perfect fluids and in linear elastic continua. Computer applications.

Expected learning
outcomes

On completion of the course, students must demonstrate that they

understand and know the general issues relating to the thermomechanics of continuous systems;
can apply the knowledge acquired to the mathematical description of the evolution of some real-world continuous material systems;
can communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
can identify the most appropriate methods to analyse and solve a problem relating to the course topics and interpret the results correctly.

Learning outcomes
to be assessed

Ability to use the techniques provided during the course for the study of the evolution of systems; clarity, correctness and completeness in the oral presentation of the course topics.

Continuum Mechanics