Variational principles in structural mechanics, numerical solution strategies and advanced topics

Lecturer: Dr. Panagiotis Koutsogiannakis (DICAM)

Timetable: 

June 3, 2024 (Monday) 9:00-12:00 
June 4, 2024 (Tuesday) 10:00-12:00 
June 6, 2024 (Thursday) 9:00-12:00 

Classes will be held on-site at DICAM in Room 1H and online. For more info please check the Syllabus attached.

Program:

The course introduces to the variational principles that emerge in structural mechanics and build up to numerical solutions of structural elements with emphasis to the case variable support.
The course starts with an introduction to variational analysis and calculus of variations. The notion of minimization problems is examined through basic examples from physics and mechanics.
Next, the Hamiltonian principle is discussed, and the Euler-Lagrange equations of motion are obtained. Then, the problem of variable support elements is introduced, and the equations of motion are obtained. This leads to the emergence of extra “interface” equations that are discussed in the context of configurational forces.
In the second part of the course, the numerical solution of the variable support elements is discussed. The notion of a reconstruction of field quantities from discrete Degrees of Freedom is presented and used to derive a Finite Element representation of the problem using the Galerkin method.
Course Delivery:
The course will be offered in a hybrid format. Synchronous, in-person lectures will be offered to PhD students at the University of Trento, Campus Mesiano. On-line video-streaming lectures will also be available to other students.

Duration: 8 hours (1 credit).

Registration: in order to register for the course please send an email to dicamphd [at] unitn.it.