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


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.




Elenco corsi 2017/2018