Introduzione ai problemi non lineari ed all'analisi: cambi finiti di configurazione ed equilibrio nella configurazione deformata; linearizzazione (rigidezza elastica/geometrica), analisi incrementale passo-passo; analisi di path following con metodo pseudo-arclength. Esempi: pendolo, von Mises truss structure. Meccanica del continuo non-lineare: deformazioni finite; tension secondo Cauchy, tensione nominale secondo Piola-Kirchhoff; equazioni costitutive (materiali iperelastici non lineari, e.g., polimeri, gomme); formulazione Updated e Total Lagrangian; teorema delle potenze virtuali. Nonlinear models of cables/beams/plates/shells: nonlinear models of cables, straight beams, plates, shells; Cauchy’s equations of motion and linearization about any equilibrium state. Computational methods for static/dynamic structural problems The method of weighted residuals for nonlinear problems: the Galerkin method; the Rayleigh-Ritz method. The method of finite elements: the co-rotational formulation for beams. Applications: tether problem, nonlinear static response and frequency response for beams/panels/shells under static/dynamic differential pressures; contact problems: finite element multibody simulations of landing gear system. Limit states due to elastic and dynamic instabilities: stability of equilibrium states; critical points on equilibrium paths; limit points; imperfect systems; snap-through; critical loads and buckling mode shapes; flexural-torsional instability of compressed beams or open thin-walled beams; buckling of cylindrical shells, flutter/galloping in nonconservative structures, torsional divergence vs flutter. Applications: 2-dof nonlinear airfoil model, panels under supersonic flows. Visco-elasticity: Rheological models due to Kelvin, Maxwell, visco-elastic standard model; four-parameter model; differential and integral formulation of visco-elastic laws. Applications: Visco-elastic analysis of a composite membrane. Limit states due to elasto-plastic failure: elasto-plastic materials or with work hardening; multiaxial elasto-plastic laws and the plastic flux; kinematic and static theorems for limit analysis; plastic interaction domains. The elasto-plastic beam problem: Elasto-plastic bending of Saint-Venant cylinders; elasto-plastic torsion; elasto-plastic extension and bending; elasto-plastic analysis of beams; plastic hinges; static and kinematic theorems for the plastic failure; limit design.

W. Lacarbonara, Nonlinear Structural Mechanics, Springer, New York, 2013.