ADAVANCED FINITE ELEMENTS ANALYSIS (MODULE 2)
Learning outcomes of the course unit
• Learn the underlying basis for the deformation of beams and shells.
• Understand how the beam/shell structure and microstructure affects is overall mechanical response.
• Students will gain judgment skills for the design of beam, membranes and thin materials whose deformation is primarily governed by bending.
Course contents summary
1. Concepts of differential geometry applied to curved structural elements.
2. Deformation measures on a curved beam/shell. Examples.
3. Stress and mechanical equilibrium.
4. Constitutive relation: from microstructure to macroscopic elastic behavior.
5. Numerical (iterative) solution for soft non-linear elastic beams and plane-strain shells.
6. Implementation using matlab.
7. Non-linear static analysis of the large deformation of beams and shells; examples and applications (in civil, mechanical engineering, material science and nature).
• A.E Green, W. Zerna. Theoretical elasticity, 2d edition Dover Publication, INC, New-York 1968
• D.D. Fox. A geometrically exact shell theory. Ph.D. Dissertation, Stanford university, 1990
• Lecture notes will be provided by the teacher.
The course is organized in theoretical and practical lessons (by making use slides or other kind of computer presentations); the exercises are either developed by the teacher and autonomously in class also by making use of the computer and at home by the students.
For every topic, the practical activities are properly scheduled in order to provide the students the ability to solve the proposed problems on the basis of the previously explained theoretical concepts.
Assessment methods and criteria
The final assessment consists in a single written test on all the topics covered by the course (with theoretical questions and simple numerical exercises). The students can also decide, on a voluntary basis, to improve the grading of their final exam by preparing a short report related to the analysis of a simple structure assigned by the teacher. This small project will contribute up to 30% of the final grading of the exam.