


Politecnico di Torino  
Academic Year 2017/18  
03AGFMX Computational methods in structural engineering design 

Master of sciencelevel of the Bologna process in Civil Engineering  Torino 





Esclusioni: 01PEZ 
Subject fundamentals
The course aims to teach the fundamentals of computational mechanics, especially for what it concerns automatic design of structures.

Expected learning outcomes
Knowledge and understanding:
The course aims to give the basis of structural analysis performed with numerical techniques in linear field; it is also oriented to give to the student the tools to understand technical and scientific books and/or papers in the field of computational mechanics in order to let him independently deepen his knowledge. Applying knowledge and understanding: At the end of the course the student should be able to correctly model structural elements using the finite elements method; in particular he should be able to choose the most proper finite element for each kind of problem/structure and to accurately model boundary conditions and material mechanical properties. The specific purpose of the course is to give to the students the knowledge necessary to model and solve typical structures (1D, 2D and 3D) using commercial finite element codes and to read critically the outputs of the analysis. Communication skills: At the end of the course the student should have assimilated the scientific/technical language related to computational mechanics in order to correctly approach complex commercial design tools and to understand their theoretical background. 
Prerequisites / Assumed knowledge
For a proper understanding of the course is necessary a basic knowledge of structural analysis for what concerns: stresses, strains, internal actions, deformation energy, potential energy. A basic knowledge of matrix calculus and numerical computation is also needed to follow the course.

Contents
The program of the course is structured as follows:
1. Displacement method a. Spring systems b. Formulation of the beam element c. Analysis of frames with the displacement method d. Application of boundary conditions to the stiffness matrix 2. Introduction to the Finite Element Method 3. Finite elements in generalized coordinates a. 1D elements (truss, beam, beam on elastic foundation, beam with variable stiffness, arch elements) b. 2D elements (plane stress) c. Axisymmetric elements d. 3D elements (tetrahedron, hexahedron elements) e. Plate elements (rectangular and triangular elements) 4. Definition of the displacement functions (convergence criteria and patch tests) 5. Interpolation tecniques (Lagrange and Hermite polynomials) 6. Isoparametric finite elements a. 1D elements (linear and quadratic) b. 2D plane stress elements (linear and quadratic serendipity elements) c. Solid elements (hexahedron elements with 8 and 20 nodes, degenerate elements) d. Transition elements e. Timoshenko beam element f. Kirchoff and Mindlin plate elements g. Mixed elements h. Shell elements 7. Numerical integration (applications to the FEM). 
Delivery modes
Il course is organized in theory lessons (held projecting the slides on a screen) and practice lessons where typical structural problems are addressed on a commercial finite element program.

Texts, readings, handouts and other learning resources
The books that are suggested for a better understanding of the topics of the course are:
F. Cesari  Introduzione al metodo degli elementi finiti – Pitagora  1997 G. Belingardi  Il metodo degli elementi finiti nella progettazione meccanica Levrotto & Bella  1998 K.J. Bathe  Finite Elemente Procedures in Engineering Analysis  Prentice Hall  1982 O. C. Zienkiewicz, R. L. Taylor, J. Z. Zhu  The finite element method : its basis and fundamentals  McGrawHill – 2005 The blueprint of the slides used during both theory and practice lessons are also given to the students. 
Assessment and grading criteria
The exam is an individual oral colloquium of about 3035 minutes, during which a series of questions on the theoretical and practical part of the course are asked.

