The course is aimed at illustrating the main analytical and numerical methods for structural analysis, suitable for computer. The student will be able to write computer programs based on different numerical methods, understand the concepts of the most common commercial softwares, and use them for the structural analysis of mechanical components.
Numerical methods for beam structures calculation, foundamentals of finite element theory, techniques of finite element analysis.
BEAM STRUCTURES ANALYSIS
Analytical methods for statics: elastic line, corollary of Mohr, principle of virtual work, method of forces, method of displacements. Numerical methods for statics: finite difference. Finite difference method for buckling analysis.
FINITE ELEMENT BASE THEORY
Shape function and stiffness matrix. One-dimension finite elements: truss, bending, torsional, beam. Structural elements for plane stress an plane strain problems: triangles and rectangles of first and second order. Axisimmetric elements. Tridimensional elements. Isoparametric elements. Quadrature formulas. Assembly stiffness matrix. Loads and boundary conditions.
FINITE ELEMENT CALCULATION TECHNIQUES
Solvers: direct and iterative methods. Non-linear problems solution. Natural frequence and buckling analysis. Dynamical problems: methods of modal superposition and implicit-explicit numerical integration.
BENDING PLATES
Theory of bending plates. Finite difference solution. Kirchoff plate elements.
LABORATORY EXERCISES
Elaboration of calculation sheets for the solution of structural problems by numerical and analytical methods. Use of commercial software for finite element analysis.
E. Bazzaro, C. Gorla, S. Miccoli, Lezioni di tecnica delle costruzioni meccaniche - Parte generale - 2a edizione - Schoenfeld & Ziegler, 2004.
R.D. Cook, D.S. Malkus, M.E. Plesha, R.J. Witt, Concepts and applications of finite element analysis - 4th edition - John Wiley & sons, 2002.
Lezioni ed esercitazioni pratiche in laboratorio
Oral exam
None