Non-linear Analysis of Structures
The course aims at integrating the basic skills of students with advanced methods for the analysis of structures relying upon nonlinear models and finite-element based computational tools.
Contents of the course of Continuum and structural Mechanics. Basic knowledge of Matlab programming.
Elastoplastic behavior. One-dimensional elastoplasticity. Ideal plasticity and hardening. Extension to the multi-dimensional case. Bending of elastoplastic beams. The concept of plastic hinge. Resistance domains. Limit analysis. Plastic collapse. Static and kinematic approach. Constitutive equations with internal variables. Energy and variational methods. Incremental analysis. Linearization. The theorem of virtual power. Introduction to non-linear mechanics. Conjugate strain and stress measures. Material and geometric stiffness. Equilibrium paths. Bifurcation and limit points. Snap through and snap back. Arc-length methods. Basics of the finite element method. Displacement-based and stress-based approaches. One-dimensional and two-dimensional elements. Numerical implementation of structural theories: The rod model, Euler-Bernoulli and Timoshenko beams. Plates and shells. Numerical integration.
Nonlinear material behaviour. Energy and variational methods.Basics of the finite element method.
The course includes both theoretical and practical sessions that are developed in parallel
L. Corradi Dell'Acqua, Meccanica delle strutture. McGraw-Hill. J. N. Reddy, An introduction to the finite element method, McGraw-Hill. J Lemaitre, J.L. Chaboche, Mechanics of Solid Materials, Cambridge University Press. Class notes.
Homework and oral examination