Unit COMPUTATIONAL MECHANICS
- Course
- Civil engineering
- Study-unit Code
- A003325
- Curriculum
- In all curricula
- Teacher
- Nicola Cavalagli
- Teachers
-
- Nicola Cavalagli
- Hours
- 72 ore - Nicola Cavalagli
- CFU
- 9
- Course Regulation
- Coorte 2025
- Offered
- 2025/26
- Learning activities
- Caratterizzante
- Area
- Ingegneria civile
- Sector
- ICAR/08
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
English- Contents
Finite Element Method for linear analysis of structures.
Time domain integration schemes for dynamic analysis.
Algorithms and programming codes for structural analysis.- Reference texts
J.S. Przemieniecki, Theory of matrix structural analysis, McGraw-Hill Inc., New York, 1968.
Klaus-Jürgen Bathe, Finite element procedures in engineering analysis, Prentice-Hall Inc., Englewood Cliffs, New Jersey 07632, 1982.- Educational objectives
Expected learning outcomes consist in understanding the finite element method in the linear field for the static and dynamic analysis of structures, as well as understanding the issues related to the development of computational codes for solving structures using the finite element method.
Specifically:
Acquisition of knowledge related to (Dublin descriptor 1):
_Discretization process of continuous structures;
_Matrix analysis and the finite element method;
_Determination of stiffness matrices for one-dimensional and three-dimensional structural elements;
_Shape functions in Cartesian and intrinsic coordinates;
_Interpolating functions;
_Techniques for numerical integration;
_Time-domain integration methods.
Skills in applying theoretical knowledge to practical cases concerning the solution of planar elastic structures (one-dimensional and two-dimensional) using matrix analysis and the finite element method (Dublin descriptor 2), and independent judgment in choosing the modeling approach that balances result accuracy with computational time (Dublin descriptor 3), with particular reference to:
_Discretization of continuous structures using one-dimensional and/or two-dimensional elements;
_Determination of stiffness matrices for one-dimensional and two-dimensional elements;
_Element assembly and solution techniques for structures subjected to static loads;
_Evaluation of time histories of structural response.- Prerequisites
In order to be able to understand and apply the majority of the techniques described within the Course, the following knowledge is recommended:
Maths: derivation and integration techniques for one-dimensional and bi-dimensional functions; differential equations.
Physics and Meccanica Razionale: vector calculus; equilibrium equation both for static and dynamic problems.
Structural Mechanics and Strength of Materials: equilibrium, compatibility and constitutive equations for the elastic continuum; beam elastic deflection equations.
Non-linear mechanics and structural dynamics: plane problems (plane stress and plane strain problems); equilibrium equation for discrete systems (multi degree fo freedom - MDOF); modal analysis and modal superposition technique.- Teaching methods
Face-to-face both theoretical and practical classes.- Other information
Attendance to classes: optional but strongly advised.- Learning verification modality
The assessment of the course’s learning objectives consists of a practical exercise and an oral examination.
The practical exercise involves the numerical solution of simple planar elastic frame structures subjected to static and dynamic loads, using procedures developed during the course. Its purpose is to help students apply theoretical knowledge to real-world problems using the finite element method (Dublin Descriptor 2), to encourage independent judgment in selecting the most appropriate structural models for the problem at hand (Dublin Descriptor 3), and to support the learning of the fundamental theoretical concepts covered in the course (Dublin Descriptor 5).
The oral examination, lasting approximately 45 minutes, is designed to assess several aspects:
i) the student’s understanding of the theoretical and methodological content of the course (Dublin Descriptor 1);
ii) the ability to explain solution techniques for structural problems using the finite element method (Dublin Descriptor 2);
iii) the capacity for independent judgment in proposing suitable models for different applications, with full awareness of the simplifying assumptions made, the physical meaning of the involved quantities, and the uncertainty of the results obtained (Dublin Descriptor 3).
Additionally, the oral exam evaluates the student’s ability to communicate effectively, to engage in a constructive discussion, and to summarize the practical implications of the theories studied (Dublin Descriptor 4), as well as their ability to learn and internalize the fundamental elements of the course content (Dublin Descriptor 5).
The final grade is expressed on a scale of 30 and is calculated as the average of the two components, weighted equally:
Practical exercise: weight = 0.5
Oral examination: weight = 0.5- Extended program
Structural analysis by the equilibrium method. Structural analysis by the Finite Element Method (FEM). Stiffness matrices for truss and beam elements. Shape functions. Plane elements. Lagrangian and Serendipity family. Isoparametric elements. Numerical integration.
Dynamic equilibrium equations. Mass matrices for truss and beam elements. Time domain integrations schemes: central difference method, Houbolt method, Wilson theta method, Newmark method. Modal superposition. Stability and accuracy of the time domain integration schemes.
Algorithms for numerical static and dynamic analysis of structures. Structural analysis by means of commercial software.