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COMPUTATIONAL METHODS IN STRUCTURAL ANALYSIS

Degree course Civil Engineering
Curriculum IDRAULICA
Learnings Orientamento unico
Academic Year 2014/2015
ECTS 6
Scientific Disciplinary Sector ICAR/08
Year Second year
Time unit Second semester
Class hours 48
Educational activity Formative educational activities

Single group

Professor ALBA SOFI
Objectives N.D.
Programme 1. Elastic problem and variational principles
Review: basic equations governing the elastic problem, force method, displacement method. Finite difference method. Elements of calculus of variations. Fundamental identity of Mechanics. Principle of virtual displacements. Principle of virtual forces. Principle of minimum total potential energy. Principle of minimum total complementary energy.

2.Variational methods and matrix methods
Weighted-Integral formulation. Weak formulation. The Rayleigh-Ritz method. The Weighted Residuals method: Petrov-Galerkin method; Galerkin method; Least-Squares method; Collocation method; Sub-domains method.
Matrix formulation of the displacement method. Element stiffness matrix. Equivalent nodal forces. Transformation from local to global coordinate system. Assembly procedure. Imposition of boundary conditions and solution. Post-processing of the solution: evaluation of stress and strain distributions. Applications to the analysis of truss structures and frame structures.

3.The finite element method
Introduction to the finite element method: the displacement approach. The discretization process. Formulation of the finite element model: weak form of the governing equations; derivation of the interpolation functions; derivation of the finite element equations and computation of the element properties (stiffness matrix and equivalent nodal forces). Assembly of element equations: interelement continuity and equilibrium conditions. Imposition of boundary conditions and solution. Post-processing of the solution. Mono-dimensional finite elements: derivation of interpolation functions and properties. Truss element. Beam element: Timoshenko beam; Euler-Bernoulli beam. Convergence conditions of the method: validity of finite elements, conformity and geometric isotropy. Two-dimensional finite elements: derivation of interpolation functions and properties. Triangular element. Rectangular element. Plate finite elements. Natural coordinates. Derivation of shape functions in natural coordinates. Families of rectangular finite elements: Lagrangian family and Serendipity family. Isoparametric finite elements. Numerical integration. Limitations of the displacement approach. Modelling, errors and accuracy. Hints on: mixed finite element methods, equilibrated and hybrid models. “Locking” phenomena. Structure and main features of a commercial finite element software (ABAQUS. Finite Element Software. Student Edition). Elaboration and discussion of illustrative examples during exercise classes.
Books -K.J. Bathe, Finite Element Procedures, Prentice-Hall, Upper Saddle River, New Jersey, 2006.
-L. Corradi Dell’Acqua, Meccanica delle strutture. Le teorie strutturali e il metodo degli elementi finiti. Volume 2. Second Edition. McGraw-Hill, Milano, 2010.
-J.N. Reddy, An Introduction to the Finite Element Method, Third Edition, McGraw-Hill, Singapore, 2006.
-O.C. Zienkiewicz, R.L. Taylor & J.Z. Zhu, Finite Element Method. Its Basis & Fundamentals, Sixth Edition, Elsevier, Oxford, 2005.
Traditional teaching method Yes
Distance teaching method No
Mandatory attendance No
Written examination evaluation No
Oral examination evaluation Yes
Aptitude test evaluation No
Project evaluation Yes
Internship evaluation No
Evaluation in itinere No
Practice Test No

Further information

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