AIMS AND LEARNING OUTCOMES

Basic knowledge to evaluate the ultimate load-bearing capacity of solids and structures using nonlinear analyses. Analytical and numerical approaches to treat material and geometrical nonlinearities.

TEACHING METHODS

Lectures and laboratory sessions using the finite element code ANSYS.

SYLLABUS/CONTENT

The finite element method: introduction; brush up on the direct stiffness method (bar and MOM element and trusses), the variational formulation (bar element), plane stress and isoparametric elements and shape functions; finite element modeling; the nonlinear bar element; finite element solution of nonlinear problems: geometric nonlinearities; linearized buckling; post-buckling; plasticity; constraints and contact; continua with cracks. The finite element code ANSYS, introduction and applications. 

Stability and Buckling: basic concepts and response diagrams; stability of systems with n degrees of freedom; stability of trusses and frames; Von Mises arch and snapping instability. Applications with ANSYS.   

The elasto-brittle solid (introduction to fracture mechanics): stress concentration and intensification; fracture criteria; ductile-brittle transition in the structural collapse. Applications with ANSYS.  

The elasto-plastic solid: incremental analysis and limit analysis. Applications with ANSYS 

RECOMMENDED READING/BIBLIOGRAPHY

• Felippa C.A, Introduction to Finite Element Methods, University of Colorado at Boulder, sito web prof. Felippa.
• Felippa C.A., Nonlinear Finite Element Methods, University of Colorado at Boulder, sito web prof. Felippa.
• L. Nunziante, L. Gambarotta, A. Tralli, Scienza delle costruzioni, McGraw-Hill.
• Carpinteri A., Scienza delle Costruzioni 1,2, Pitagora Editrice, Bologna.
• L. Corradi dell'Acqua, Meccanica delle strutture vol. 3, McGraw-Hill.
• Z.P. Bazant, L. Cedolin, Stability of structures, Oxford Press.
• M. Jirasek, Z. P.Bazant, Inelastic analysis of structures, Wiley.
• Carpinteri A., Meccanica della Frattura, Pitagora