NONLINEAR STRUCTURAL ANALYSIS
Learning outcomes of the course unit
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).
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).
Course contents summary
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.
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.
Form of teaching
Theory supported by exercises.