35401 - Computational structural mechanics M

Learning outcomes

The course is an introduction to computational mechanics of solids and structures. The goal of the course is to provide the students with the fundamental concepts and operating tools to solve current structural problems.

Course contents

The direct stiffness method. Linear elastic rods and beams (Eulero-Bernoulli and Timoshenko beam theories). Three dimensional truss and frame structures. Specific topics: restraints, constraints, offsets, semi-rigid connections and joint flexibility.

Weak and variational formulations. Displacement based formulations: principle of virtual works and minimum of total potential energy. Mixed and hybrid formulations. Flexibility approach. Applications to common structural elements (beams, plates and shells).

Variational methods. Rayleigh-Ritz and Galerkin methods. The finite element method (assumed displacement finite elements). Eulero-Bernoulli and Timoshenko beam elements. Curved arch elements. Finite elements for two- and three-dimensional elasticity. Kirchhoff and Mindlin plate elements. Shell elements. Finite element modelling and performance. Convergence requirements. Patch test.

Nonlinear analysis. Solution methods. Incremental methods and general control. Geometric nonlinearity. Finite deformations. Total and updated Lagrangian formulation. A total Lagrangian truss element. Geometric stiffness and stability analysis of frame structures. Material nonlinearity. Elasto-plasticity. Pushover and limit analyses.

Linear and nonlinear dynamic analysis. Modal and transient analyses. Time stepping methods.

Readings/Bibliography

- Lecture slides and notes

- M. Capurso, Introduzione al Calcolo Automatico delle Strutture, Cremonese, Roma, 1977

- K.J. Bathe, Finite Element Procedures, Prentice-Hall Inc., 1996

- O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, 5a edizione, Butterworth-Heinemann, 2000

 

During the lectures, some reading assignments will be made from selected papers in the published literature.

Teaching methods

The course content will be entirely covered by the lectures. The course includes some laboratory sessions, which will cover the practical aspects of the lectures. The instructors will tutor the students.

Assessment methods

There will be a final oral examination, based on questions intended to assess the knowledge and understanding of the topics covered by the course.

Teaching tools

The teaching tools are overhead projector, projector and PC.

The course includes some laboratory sessions, at the Laboratory of Computational Mechanics ( www.lamc.ing.unibo.it ).

Links to further information

http://www.lamc.ing.unibo.it

Office hours

See the website of Francesco Ubertini