## 20801631 - COMPUTATIONAL MECHANICS

Computational Mechanics is a teaching aimed at providing a deep knowledge on physical-mathematical problem of civil engineering. The course is aimed mainly to develop the skills required for the implementation of numerical models with the software Mathematica for the solution of many mathematical models introduced during the teaching. The numerical methods proposed are based on variational formulation of the mathematical problems, finite elements methods (FEM) and finite difference Method.
The teaching belongs to the “Ingegneria Civile Per la Protezione dai Rischi Naturali” master course, which aims at training engineers towards high professional levels in the fields of the protection of both environment and civil infrastructures from hydrogeological and seismic hazards.
In such framework the teaching aims at defining suitable mathematical-numerical models in the framework of civil engineering and solve them with the help of the software Mathematica.
Upon successful completion of the course, students will be able to: 1) use Mathematica to solve many problems of civil engineering 2) to classify the mathematical models (elliptic, hyperbolic, parabolic…) 3) use suitable numerical schemes for the resolution of many mathematical problem (variational methods, FEM, finite difference method)

Curriculum

teacher profile | teaching materials

Programme

Classification of first order system of partial differential equations: elliptic, parabolic, hyperbolic system. Second order partial differential equations. Variational formulation of elliptic problems. Approximate variational methods: Galerkin and Ritz-Rayleigh method, finite element method FEM. Finite difference methods: consistence, convergence, stability. Examples and programs: deformation and vibrations of bars, plate and membranes, numerical solution of elliptic, hyperbolic and parabolic problems.

Core Documentation

teacher profile | teaching materials

Programme

Classification of first order system of partial differential equations: elliptic, parabolic, hyperbolic system. Second order partial differential equations. Variational formulation of elliptic problems. Approximate variational methods: Galerkin and Ritz-Rayleigh method, finite element method FEM. Finite difference methods: consistence, convergence, stability. Examples and programs: deformation and vibrations of bars, plate and membranes, numerical solution of elliptic, hyperbolic and parabolic problems.

Core Documentation