Learning objectives
<br />To present basic concepts and tools for structural analysis by means of numerical procedures (finite element method, finite difference method)
Prerequisites
Scienza delle costruzioni, Tecnica delle costruzioni, Fondamenti di informatica.
Course unit content
<br />1) Analysis of structural problems.<br />Formulation of fundamental equations of structural problems. Exact and approximate solutions. Fourier series method. Indeterminate coefficient method. Ritz’s method. Indeterminate function method.<br />2) Finite difference method.<br />The differences of a function. Interpolation formulas. The numerical solution of differential equations. Boundary conditions. Analysis of membranes and slabs.<br />3) Matricial analysis of frames.<br />Stiffness matrix of beam and truss element.Assembly. Stiffness matrix of frame. Displacement boundary conditions. Flexibility matrix. Coordinate trasformation. Elastic foundation.<br />4) Finite element method.<br />Basic concepts of finite element analysis; discretization; interpolation functions; shape functions. Element stiffness matrices; assembly of elements.Completeness and compatibility, convergence requirements.<br />5) Static analysis by finite element method in linear elasticity.<br />a) Linear finite elements. Truss elements; Eulero-Benoulli’s beam elements; Timoshenko’s beam elements.<br />b) Bidimensional finite elements. Triangle finite element; isoparametric Serendipity and Lagrangian finite elements.<br />c) Tridimensional finite elements. Tetrahedral finite elements; hexahedral isoparametric elements; prismatic elements.<br />d) Finite elements for axially symmetric problems.<br />e) Finite elements for bending plates. Kirchhoff plate element. Mindlin plate element..<br />f) Finite elements for shell structures. Flat elements for shell.. Elemento finito di Pecknold finite elements. Isoparametric Mindlin skhell elements.<br />6) Introduction to advanced advanced topics in the finite element method.<br />Natural frequency and mode shapes. Stress stiffening and buckling. Orthotropic material and nonlinear problems.<br /> Practice lectures<br />Introduction to matrices and linear algebra, programming by FORTRAN and MATLAB enviroments, numerical analysis. Emphasis is placed on developing computational algorithms to solve problems using the above techniques and comparing the solutions to those obtained from commercial state-of-art general purpose finite element software packages available in the course. <br />
Bibliography
<br /> - Documentation provided by the teacher.<br />- D. FERRETTI, I. IORI, M. MORINI: “La stabilità delle strutture. Il caso delle costruzioni in cemento armato”. Mc Graw-Hill, 2002.<br />- R.D. COOK: 'Concepts and applications of finite element analysis', John Wiley & Sons, 1981.<br />- O.C. ZIENKIEWICZ: 'The Finite Element Method',3rd ed.,Mc Graw-Hill, 1977.<br />- C.A. BREBBIA, J.J. CONNOR: 'Fondamenti del metodo degli elementi finiti', CLUP, 1979.<br />- G. TONIOLO: 'Analisi strutturale con l'elaboratore elettronico', Masson, 1984.<br />- G. TONIOLO, P. MALERBA: 'Metodi di discretizzazione dell’analisi strutturale', Masson, 1981.<br />- J.K. BATHE: “Finite element procedures”, Prentice Hall, Englewood Cliffs, New Jersey, 1996.
