Unit STRUCTURAL MECHANICS AND NUMERICAL METHODS

COMPUTATIONAL STRUCTURAL MECHANICS

Code	A001145
CFU	6
Teacher	Massimiliano Gioffre'
Teachers	Massimiliano Gioffre' Federico Cluni (Codocenza)
Hours	49 ore - Massimiliano Gioffre' 14 ore (Codocenza) - Federico Cluni
Language of instruction	Italian
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.

CFU

3

Teacher

Massimiliano Gioffre'

CFU

3

Teacher

Massimiliano Gioffre'

MECHANICS OF STRUCTURES

Code	70000409
CFU	6
Teacher	Massimiliano Gioffre'
Teachers	Massimiliano Gioffre' Massimiliano Gioffre'
Hours	54 ore - Massimiliano Gioffre' 36 ore - Massimiliano Gioffre'
Learning activities	Caratterizzante
Area	Analisi e progettazione strutturale per l'architettura
Academic discipline	ICAR/08
Type of study-unit	Opzionale (Optional)
Language of instruction	Italian
Contents	Basics of Continuum mechanics. Displacements in elastic beams and structures. Statically indeterminate structures. Barré de Saint Venant problem. Plasticity and strength criteria. Stability of the elastic equilibrium.
Reference texts	R. Baldacci, Scienza delle Costruzioni, Volumi I e II, UTET, Torino. L. Nunziante, L. Gambarotta, A. Tralli, Scienza delle Costruzioni, McGraw-Hill Leone Corradi dell'Acqua - Meccanica delle strutture, Mc Graw Hill M. Capurso, Lezioni di Scienza delle Costruzioni, Pitagora, Bologna.
Educational objectives	Understanding the base principles and concepts of Mechanics aimed to manage the tools needed for structural analysis (design and verifications) of both one-dimensional elements and bi-, tri-dimensional continua.
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. Geometry: vector spaces and linear operations; matrices and linear operators; linear systems; algebraic curves: conic curves.
Teaching methods	Face-to-face both theoretical and practical classes.
Other information	Attendance to classes: optional but strongly advised.
Learning verification modality	Written test and oral exam.
Extended program	Strain analysis. Stress analysis. Principle of virtual works. Elastic bodies and energy related theorems. Elastic Beams. Energy based methods for systems of beams. Statically indeterminate structures and their solution. Barré de Saint Venant problem: axial force, bending moment, eccentric axial force, shear force and bending moment, torsion. Plasticity and strength criteria. Strength of materials. Safety assessment. Stability of the elastic equilibrium: buckling loads, Euler buckling.