Discrete and continuum mechanics with applications
- Unit Coordinator: Francesco Dell'Isola
- Programme: Double Degrees
- ECTS Credits: 9
- Semester: 2
- Year: 1
- Campus: University of L'Aquila
- Language: English
- Aims:
The goal of this course is to provide the concepts of solid Mechanics using the notion of continuum models as well as of discrete models. On successful completion of this module, the student should know the fundaments of the Analytic Mechanics and how to apply it to solve the problem of an elastically deformable body.
- Content:
- Space of configurations: the finite dimensional case.
- Space of configurations: the infinite dimensional case.
- The configuration space for the Euler-Bernoulli beam.
- Elements of model theory.
- The problem of the determination of the motion for finite dimensional systems.
- The principle of minimum action, Lagrangians: the finite dimensional case.
- Deduction of Euler- Lagrange conditions for the finite dimensional case. Numerical methods for solving ordinary differential equations.
- The principle of minimum action for infinite dimensional systems.
- Space of three-dimensional Continuous configurations.
- Euler theory of the deformable beam.
- Stable equilibrium as a minimum of energy.
- The concept of constraint for finite dimensional systems: the Dini theorem.
- Discretization of infinite-dimensional models.
- Timoshenko beam.
- Wave propagation: applications.
- Pre-requisites:
The student must know the basics of algebra and mathematical analysis. He must also have a basic knowledge of the mechanics of the material point and of the rigid body.
- Reading list:
Gurtin, Morton E. An introduction to continuum mechanics. Vol. 158. Academic press, 1982.
Sanjay Govindjee. A First Course on Variational Methods in Structural Mechanics and Engineering. University of California, Berkeley.
