NUMERICAL METHODS FOR STRUCTURAL ANALYSIS (UNIT 2)
Learning outcomes of the course unit
The aim of the course is to give the basis for a correct numerical modelling of generic structures with the finite element method
Technical structural mechanics
Advanced design of structures
Course contents summary
Basic concepts of the finite element method
Structural discretisation with finite elements.
Use of finite elements in non linear problems
Some more aspects about the finite element method
Structural discretisation with finite elements.Choice of the finite element and of the shape functions. Shape functions in the local reference system and their derivatives. Examples of linear shape functions. Isoparametric elements: convergence requirements. Lagrangian and Serendipidy elements. Isoparametric elements in one, two and three dimensions.Numerical integration methods. Variable transformation in 1D, 2D, 3D. Gauss rule. Accuracy of the numerical integration. Examples.Use of finite elements in non linear problemsEigen analysis: linear buckling problems (geometry stiffness matrix), vibration mode shapes of a structure (mass matrix). Material non linear problems in static and dynamic situations.
Cook, R.D., Malkus D.S., Plesha, M.E.: “Concept and application of finite element analysis”, 4th edition, John Wiley & Sons, 2002.
Zienkiewicz, O.C.: “The finite element method”, Mc Graw-Hill, 2000.
Theoretical and practical Lectures, use of the pc for the finite element analysis of structural problems
Assessment methods and criteria
Development of a project and oral examination