Academic Year 2015/2016 - 2° Year

ICAR/08 - 9 CFU - 1° Semester

**1. METHODS OF STRUCTURAL ANALYSIS**

- Displacement method
- Variational methods. Energy principles.
- The principle of virtual works

**2. STIFFNESS MATRIX**

- Positive semidefiniteness of stiffness matrix
- Direct construction of the stiffness matrix
- Band width

**3. STRUCTURES WITH FINITE NUMBER OF DOF'S - TRUSSES**

- Assemblage of stiffness matrix
- Loads, imposed deformations and displacements: equivalent nodal forces
- Post-processing and analysis of the results
- Mass matrix

**4. VARIATIONAL METHODS OF SOLUTION FOR CONTINUOUS SYSTEMS**

- Interpolation methods. Finite differences
- Residual methods
- Ritz method
- The Ritz-Galerkin method
- The Petrov-Galerkin method

- The Finite Element Method (F.E.M.)
- Convergence and stability of the solution. Numerical issues-

**5. ANALYSIS OF CONTINUA 2D**

- The Finite Element Method for continuous systems
- Lagrangian elements
- Isoparametric elements. Numerical integration
- Equivalent nodal forces
- Post-processing. Stress evaluation and recovery
- Error estimates and Rate of convergence
- Locking issues

- Stationary problems
- Time-dependent problems. Semidiscretization

**6. FRAMES**

- Hermite shape functions
- General method for the calculation of the shape functions
- Stiffness and Mass matrices
- Equivalent nodal forces
- Post-proecssing of the resulta and errors.

**7. NON LINEAR ANALYSIS WITH F.E.M.**

- Elements of incremental analysis
- Newton's method
- Inplicit and explicit methods

- Material non linearities
- Elastic-plastic material
- Elastic-plastic trusses
- Elastic-plastic beams with concentrated hinges and with diffused plasticity
- Fundamentals of plasticity for continuous systems

- Geometric non linearities
- Geometric stiffness matrix
- Linearized stability analysis
- Incremental analysis and P-Delta effects

**8. PLATES**

- The equations of the elastic plate
- Kirchhoff-Love hupotheses
- Generalized strains and stresses
- Equilibrium equations of thin plates and boundary conditions
- Rectangular plates with various boundary conditions
- Variational solutions

- Stability of plates
- von Karman equations

- Shell finite elements
- degrees of freedom
- Interpolation of the normal
- Shear locking - mixed elements

1. J. N. Reddy – An Introduction to the Finite Element Method [Reddy] |
2. L. Corradi Dell’Acqua – Meccanica delle Strutture - Vol. 2 e Vol. 3 [MdS] |
3. Zinkiewicz – Taylor – The Finite Element Method , Vol. 1 [ZFEM] |