MECCANICA COMPUTAZIONALE DELLE STRUTTURE

Objectives of the course:

1. give to the students the basic knowldge of numerical methods in mechanics and of the approximations related to their use.

2. give to the students the skills for performing numerical analyses of complex structures, in the linear and non.linear range.

3. give to the students the ability to understand the basic principles of a numerical code of structural analysis, in order to use it with awereness.

The course includes lectures, written exercises and computer practice.

1. METHODS OF STRUCTURAL ANALYSIS

1. Displacement method
2. Variational methods. Energy principles.
3. The principle of virtual works

2. STIFFNESS AND MASS MATRICES

1. Direct construction of the stiffness matrix and of the mass matrix. Mechanical interpretation.
2. Positive semidefiniteness of the stiffness matrix.
3. Band width.

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

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

4. VARIATIONAL METHODS OF SOLUTION FOR CONTINUOUS SYSTEMS

1. Interpolation methods. Finite differences
2. Residual methods
3. Ritz method
   1. The Ritz-Galerkin method
   2. The Petrov-Galerkin method
4. The Finite Element Method (F.E.M.)
5. Convergence and stability of the solution. Numerical issues-

5. ANALYSIS OF CONTINUA 2D

1. The Finite Element Method for continuous systems
   1. Lagrangian elements
   2. Isoparametric elements. Numerical integration
   3. Equivalent nodal forces
   4. Post-processing. Stress evaluation and recovery
   5. Error estimates and Rate of convergence
   6. Locking issues
2. Stationary problems
3. Time-dependent problems. Semidiscretization

6. FRAMES

1. Hermite shape functions. Continuity requirements.
2. General method for the calculation of the shape functions.
3. Higher order beam models.
4. Stiffness and Mass matrices
5. Equivalent nodal forces
6. Post-proecssing of the resulta and errors.

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

1. Elements of incremental analysis
   1. Newton's method
   2. Implicit and explicit methods

8. PLATES

1. The equations of the elastic plate
   1. Kirchhoff-Love hupotheses
   2. Generalized strains and stresses
   3. Equilibrium equations of thin plates and boundary conditions
   4. Rectangular plates with various boundary conditions
   5. Variational solutions
2. Stability of plates
   1. von Karman equations
3. Shell finite elements
   1. degrees of freedom
   2. Interpolation of the normal
   3. Shear locking - mixed elements.

1. J.N. Reddy – An Introduction to the Finite Element Method

2. L. Corradi Dell’Acqua – Meccanica delle Strutture - Vol. 2 e Vol. 3

3. Zinkiewicz – Taylor – The Finite Element Method , Vol. 1

4. Timoshenko, S.P., Theory of Plates and Shells.

5. Heyman J., Equilibrium of shell structures, cap.I