2025
Variational methods in dynamics
Dynamics has historically developed trough a series of steps, starting from Galilei and achieving the formulations of Lagrange, Hamilton and Einstein. While performing these steps, scientists have always recognized the importance of setting to the base the principle of “Least Action”. Although we have to (and must) remain in the inner of Classical Mechanics, the just mentioned principle is of fundamental importance for us. In this brief course, an introduction to the “Calculus of Variation” is given, touching the most emblematic physical problems that led to this tool. In the end, a brief hint to its application to the principle of least action will be given, leading to the canonical formulation of the “Lagrange Equations”.
- Docente: Prof. Rinaldo Garziera
- Crediti: 2
- Ore: 16
- Lingua: Inglese
- Date:
Computational mechanics
Coordinate transformation and rotations in 3D, Lie algebra and Lie groups. Discretization of PDEs, the Galerkin method.
Application to linear problems in heat and elasticity. Numerical methods for solving linear problems: direct methods, fixed point methods, Krylov methods, multigrid methods. Numerical methods for non-linear problems. Application to geometric and material nonlinearities in structural mechanics. ODE: time integration. Multistep integrators, implicit / explicit integrators. The Dahlquist barrier. DAE: index, A-stability, time integration schemes. Constrained dynamics and multibody problems. Outlook: parallel computing.
- Docente: Prof. Alessandro Tasora
- Crediti: 2
- Ore: 16
- Lingua: Inglese
- Date:
Elements of nonlinear continuum mechanics
The course aims to provide some basic notions of non-linear continuum mechanics. Topics that will be covered are the
following: analysis of the deformation; deformation gradient; polar decomposition, Green-Lagrange strain tensor; analysis of the state of stress; Piola transformation; first and second Piola Kirchhoff stress tensors; hyperelastic bodies; strain energy; constitutive equations; change of observer and invariance of material response; derivation of the linear theory of elasticity.
- Docente: Prof. Gianni Royer Carfagni
- Crediti: 2
- Ore: 16
- Lingua: Inglese
- Date:
Analytical modelling of sandwich and layered composites
The course aims to provide a comprehensive description of the analytical modelling of the response of sandwich and layered beams and plates, made by the composition of either elastic and viscoelastic layers, under bending and buckling.
- Docente: Prof. Laura Galuppi
- Crediti: 2
- Ore: 16
- Lingua: Inglese
- Date:
Elements of thermography and thermal imaging
These lessons provide a comprehensive foundation in quantitative thermography, exploring a wide range of applications from power electronics and heat transfer to building analysis, diagnostics, and prognostics.
- Docenti: Proff. F. Bozzoli, L. Cattani, A. Soldati
- Crediti: 2
- Ore: 16
- Lingua: Inglese
- Date: 27-31 gennaio 2025