Seminario di ingegneria matematica - Elementi di calcolo delle variazioni (Disciplinare) - Calculus of Variations and Elasticity
Responsabile didattico: Lorenzo Freddi
Durata: 28 ore
Periodo didattico: secondo semestre
Programma
First part: Mathematical foundations of the Calculus of Variations
- Calculus of Variations: an historical overview
- Critical points of functionals
- The First Variation and necessary conditions
- The Fundamental Lemma of the CoV
- Euler equations
- Natural boundary conditions
- Variational problems of higher order
- Constrained problems and Lagrange multipliers
- The Second Variation and sufficient conditions
- Convex Lagrangians
Second part: Variaton methods in three-dimensional linear elasticity
- Formulation of the static equilibrium problem in small deformations
- Variational principles in linear elasticity
- Uniqueness, existence and approximation of the solution
- Regularity of the solution
- Elements of unique continuation of the solution (if time permits)
Third part: Variational methods for slender curvilinear continua
- Direct approach to the theory of rods
- Balance laws and constitutive relations from the three-dimensional theory
- Variational formulation
- Element of stability of conservative systems (if time permits)
Prof. Lorenzo Freddi, modulo 1, 10 ore.
Prof. Antonino Morassi, modulo 2, 10 ore.
Prof. Michel Jabbour, ciclo conferenze, 8 ore.
