( english version )
Structural Mechanics C ( 5 CFU )
Prof. Roberto Brighenti
     Tel. 0521 905910 - Fax. 0521 905924           E-mail. brigh@unipr.it

To present concepts and tools for structural design, with particular emphasis to the computational techniques applied to the analysis of structures with elastic or elasto-plastic behaviour and to buckling problems.

Overview and study of topics treated in the course Structural Mechanics A-B.
General aspects of the problem of nonuniform torsion and of the bending-torsion instability beams with a opened thin-walled cross-section. Plasticity problems, yielding function, isotropic and kinematic hardening, flow rule, plastic deformations; examples of plasticity models for common structural materials.

Fundamentals of computational mechanics
Weak and strong formulations of a problem described by differential equations. Natural and essential boundary conditions. Variational principles. Theorem of virtual work. Residual method.

Rayleigh-Ritz method for elastic structures.
Principle of the minimum of the total potential energy. Displacement field approximation. The Rayleigh-Ritz method applied to bending of beams and plates.

Fundamentals of the finite element method
Discretisation of a structure with finite elements. 1-D, 2-D and 3-D isoparametric finite elements. Algebraic static and dynamic equilibrium equations, initial stress effects of a structural system discretised with finite elements. Convergence of the finite element method. Eigenvalues analysis: buckling problems (critical load multipliers, geometric stiffness matrix), vibration mode shapes of a structure (mass matrix). Study of the flow-chart of a simple finite element program.

Applications : numerical modelling of generic structures
Use of commercial software programmes to model generic structures. Convergence tests for the solutions. Analysis and critical interpretation of the finite element results, precision evaluation. Substructuring. Non-linear analysis, buckling analysis, determination of eigenfrequencies. Post-processing of the results.

Attività d'esercitazione
Theory supported by exercises. During the course practical exercises will be held with the aid of programs running on PCs to get the students confident with numerical techniques applied to the analysis of structures.

Modalità d'esame
Oral examination.

Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A-B (Structural Mechanics A-B).

Testi consigliati
Documentation provided by the teacher.
A. CARPINTERI: “Scienza delle Costruzioni”, Vol. 1 e 2, Ed. Pitagora, Bologna.
A. CARPINTERI, “Structural Mechanics”, E&FN Spon, London.
M. CAPURSO: “Lezioni di Scienza delle Costruzioni”, Ed. Pitagora, Bologna.
L. CORRADI DELL’ACQUA: “Meccanica delle strutture”, Vol. 1,2 e 3, Mc Graw-Hill, 1995.
F. CESARI: “Introduzione al metodo degli elementi finiti”, Pitagora Ed., Bologna.
R. COOK,, D.S. MALKUS, M.E. PLESHA: “Concept and application of finite element analysis”, John Wiley & Sons.
V. FRANCIOSI: “Fondamenti di Scienza delle Costruzioni”, Ed. Liguori, Napoli.
T.J.R. HUGHES: “The finite element method. linear static and dynamic finite element analysis”, Prentice Hall, 1987.

A. MACERI: “Scienza delle Costruzioni”, Accademica, Roma.
D.R.J. OWEN, E. HINTON: “Finite elements in plasticity”, Pineridge Press, 1980.
O.C. ZIENKIEWICZ: “The finite element method”, Mc Graw-Hill, 1986.

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