Unit COMPUTATIONAL MECHANICS

Course
Civil engineering
Study-unit Code
A003325
Curriculum
In all curricula
Teacher
Nicola Cavalagli
Teachers
• Nicola Cavalagli
Hours
• 63 ore - Nicola Cavalagli
CFU
9
Course Regulation
Coorte 2023
Offered
2023/24
Learning activities
Caratterizzante
Area
Ingegneria civile
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
Knowledge of the Finite Element Method for linear static and dynamic analysis of structures. Knowledge of problems connected to implementation of numerical codes for solving structural systems by the Finite Element Method.
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
Hands-on practice and oral exam.
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.
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