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Non-linear analysis of structures ( 5 CFU ) Finalità

To present basic concepts of the non-linear behaviour of structures, with reference to material and geometric non-linearities. The aim of the course is to supply the tools for evaluating the load-carrying capacity of a structure, related to the attainment of material strength (plastic limit analysis) or to the loss of structural stiffness (stability of equilibrium).

Programma

Plastic limit analysis.

Perfectly plastic behaviour and plastic collapse. Plastic collapse of beams under bending: plastic hinge, limit moment for symmetric and non-symmetric cross-sections, combined actions and limit curves. Incremental analysis of elastic-plastic frames. Collapse mechanisms. Theorems of limit analysis (static and kimenatic theorems). Frames under proportional point loads (method of the combination of mechanisms) and under distributed loads. Frames under non-proportional loads. Limit loads of plates (yield line theory). Numerical methods for calculating the collapse load. Cyclic loads and shake-down.

Stability of equilibrium.

Discrete elastic systems: stationarity and minimum of total potential energy, theory of the second order, critical Euler load (static and energetic criteria). Flexural stability of axially compressed beams: fundamental cases, frames, beams with curved axis. Torsional stability of beams under axial compressive load or bending. Stability of plates. Determination of the critical load: Rayleigh-Ritz method, finite element method. Post-critical behaviour. Beams under axial compressive load and bending: effects of material non-linearity and imperfections on load-carrying capacity, stability curves. Snap-through instability of shallow arches.

Perfectly plastic behaviour and plastic collapse. Plastic collapse of beams under bending: plastic hinge, limit moment for symmetric and non-symmetric cross-sections, combined actions and limit curves. Incremental analysis of elastic-plastic frames. Collapse mechanisms. Theorems of limit analysis (static and kimenatic theorems). Frames under proportional point loads (method of the combination of mechanisms) and under distributed loads. Frames under non-proportional loads. Limit loads of plates (yield line theory). Numerical methods for calculating the collapse load. Cyclic loads and shake-down.

Stability of equilibrium.

Discrete elastic systems: stationarity and minimum of total potential energy, theory of the second order, critical Euler load (static and energetic criteria). Flexural stability of axially compressed beams: fundamental cases, frames, beams with curved axis. Torsional stability of beams under axial compressive load or bending. Stability of plates. Determination of the critical load: Rayleigh-Ritz method, finite element method. Post-critical behaviour. Beams under axial compressive load and bending: effects of material non-linearity and imperfections on load-carrying capacity, stability curves. Snap-through instability of shallow arches.

Attività d'esercitazione

Theory supported by exercises.

Modalità d'esame

Oral examination.

Propedeuticità

Analisi A-B, Analisi C, Geometria, Meccanica Razionale, Scienza delle Costruzioni A-B (Structural Mechanics A-B), Progettazione Strutturale Avanzata A (Advanced Structural Analysis A).

Testi consigliati

M. JIRASEK - Z.P. BAZANT: “Inelastic analysis of structures”, J.Wiley & Sons, New York, 2001.

D.O. BRUSH – B.O. ALMROTH: “Buckling of bars, plates and shells”, McGraw-Hill, New York, 1975.

A. CARPINTERI: "Analisi non-lineare delle strutture”, Ed. Pitagora, Bologna, 1998.

L. CORRADI DELL’ACQUA: “Instabilità delle strutture”, CLUP, Milano, 1978.

L. CORRADI DELL’ACQUA: “Meccanica delle strutture”, Voll. 1,3, McGraw-Hill, Milano, 1995.

S.P. TIMOSHENKO – J.M. GERE: “Theory of elastic stability”, McGraw-Hill, New York, 1961.

D.O. BRUSH – B.O. ALMROTH: “Buckling of bars, plates and shells”, McGraw-Hill, New York, 1975.

A. CARPINTERI: "Analisi non-lineare delle strutture”, Ed. Pitagora, Bologna, 1998.

L. CORRADI DELL’ACQUA: “Instabilità delle strutture”, CLUP, Milano, 1978.

L. CORRADI DELL’ACQUA: “Meccanica delle strutture”, Voll. 1,3, McGraw-Hill, Milano, 1995.

S.P. TIMOSHENKO – J.M. GERE: “Theory of elastic stability”, McGraw-Hill, New York, 1961.