Mechanics of Materials and Structures.
The course aims to provide an introduction to the issues pertaining to the numerical solution of the problems of Structural Mechanics. The discretisation of engineering, physics and mathematical problems will be considered, backed up by systems of differential equations, through the transformation of the continuous (infinite number of degrees of freedom) to the discrete (finite number of degrees of freedom). Particular relevance will be placed on the so-called Finite Element Method, principally concerning displacements, with reference to the structural analysis of beams, frames, plates and continuum solids.
Revision of solid mechanics; framework of methods of discretion: Strong and weak forms, Principle of virtual work, variational principles, weighted residues Rayleigh-Ritz: interpolation of whole dominium, stationary . condition, generation of the linear system of resolving equations; finite elements method: approach to movements, functions of form, matrix of rigidity, assembly procedure of resolving system, phases of modeling for finite elements (for tri-dimensional analysis): triangular and quadrangular plate elements, tetraedrical and esaedrical elements, isoparametric elements, continuity requisites, accuracy and convergence, exactitude of solution, calculus routines for finite elements (developed with MatLab); analysis of specific problems (dynamics, non-linear behavior, plastic, large movements, thermal analysis etc). Revision of structural mechanics; same frame as above; finite elements (for tridimensional analysis): rod, beam and plate elements.
Front lessons.
Homeworks to be presented at the oral exams, including programme elaborations (typically using MatLab) and their applications.