ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
The main objective of the course will be the study of some mathematical models in solid mechanics, referred to static and dynamic problems. We will consider elastic and isotropic materials for which several simplifications can be introduced due to: the geometry of the piece, the volume forces, the boundary conditions, or the existence of symmetries. In addition, there will be an introduction to more general behaviour laws, to the formulation of non-linear boundary conditions, and to the inclusion of thermal effects. Finally, we will devote the last part of the course to study geometries with cracks, their advance and detection, and to the introduction of some damage models.
1. Linear elastodynamic equations.
2. Stresses and strains.
3. Strain tensor.
4. General methods of resolution in linear elasticity.
5. Plane problems in linear elasticity.
6. Axially symmetric problems.
7. Bending and torsion of cylindrical beams.
8. One-dimensional beam models.
9. Plate models.
10. Vibrations.
11. Thermoelasticity. Anisotropic elasticity.
12. Plasticity.
13. Non linear boundary conditions.
• Basic bibliography:
- Barral, P. y Quintela, P. Modelos Matemáticos na Mecánica de Sólidos. Curso Virtual de la Universidad de Santiago de Compostela. Curso 2017-18.
- Bower, A.F. Applied Mechanics of Solids. CRC Press. 2010.
• Complementary bibliography:
- Anderson, T.L. Fracture Mechanics. Taylor & Francis. 2005.
- Barber, J.R. Elasticity. Solid Mechanics and its applications. Kluwer Academic Publishers. 2010.
- Bermúdez de Castro, A. Continuum Thermomechanics. Progress in Mathematical Physics. Edit. Birkhäuser. 2005.
- Broek, D. The Practical Use of Fracture Mechanics. Kluwer Academic Publishers. 1988.
- Carpinteri, A. Structural Mechanics – A unified approach. Chapman & Hall. London, 1997.
- E.W.V. Chaves. Mecánica del Medio Continuo. Conceptos Básicos.
Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Barcelona. 2012.
- E.W.V. Chaves. Mecánica del Medio Continuo. Modelos Constitutivos. Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Barcelona. 2009.
- Fraeijs de Veubeke. A Course in Elasticity. Applied Mathematical Sciences, 29. Springer-Verlag 1979.
- Germain, P. Mecanique. Tomos I y II. École Polytechnique. Ellipses. 1986.
- Guiu Giralt, F. Fundamentos físicos de la mecánica de la fractura. Textos Universitarios. Consejo Superior de Investigaciones Científicas. 1997.
- Gurtin, M.E. An Introduction to Continuum Mechanics. Academic Press. New York, 1981.
- Henry, J.P. y Parsy, F. Cours d'Élasticité. Dunod Université. 1982.
- Lemaitre J. A A course on damage mechanics. Springer-Verlag, 1996.
- Lemaitre, J. y Chaboche, J.L. Mécanique des Matériaux Solides. Dunod. 2009.
- Lubliner, J. Plasticity Theory. Maxwell Macmillan International Editions. 1990.
- Quintela Estévez, P. Métodos matemáticos en mecánica de sólidos. Publicaciones del Departamento de Matemática Aplicada, nº 24. 1999. Revisada en 2004.
- Roger D. y Dieulesaint E. Elastic Waves in Solids I, II. Springer. 1999.
- Segel, L.A. Mathematics Applied to Continuum Mechanics. Macmillan Publishing Co., Inc. 2007.
- Sokolnikoff, I.S. Mathematical theory of elasticity. Krieger Publishing Company. 1956.
- Vinson, J.R. The Behavior of Thin Walled Structures, Beams, Plates and Shells. Kluwer academic publishers. 1989.
Modelling specialisation skills
CM1: To be able to extract, using different analytical techniques, both qualitative and quantitative information from the models.
CM2: Knowing how to model elements and complex systems leading to well-posed formulated problems.
General skills
CG1 Have knowledge that provide a basis or opportunity for originality in developing and / or applying ideas, often within a research context, knowing how to translate industrial needs in terms of R&D in the field of mathematics Industrial;
CG2 Be able to apply the acquired knowledge and abilities to solve problems in new or unfamiliar environments within broader contexts, including the ability to integrate multidisciplinary R & D in the business environment;
CG4 To have the ability to communicate the findings to specialist and non-specialist audiences in a clear and unambiguous way
CG5 To have the appropriate learning skills to enable them to continue studying in a way that will be largely self-directed or autonomous, and also to be able to successfully undertake doctoral studies.
Specific skills
CE1: To acquire a basic knowledge in an area of Engineering / Applied Science, as a starting point for an adequate mathematical modelling, using well-established contexts or in new or unfamiliar environments within broader and multidisciplinary contexts.
CE2: Model specific ingredients and make appropriate simplifications in the model to facilitate their numerical treatment, maintaining the degree of accuracy, according to previous requirements.
CE5: Being able to validate and interpret the results, comparing them with visualizations, experimental measurements and functional requirements of the physical engineering system.
The aforementioned competencies will be worked through:
Lectures : CE1, CE2, CE5, CM1, and CM2
Seminars: CE1, CE2, CE5, CM1 and CM2
Numerical simulation of practical cases: CE1, CE2, CE5, CM1 and CM2
Personal homeworks: CG1, CG2, CG4, CG5, CE1, CE2, CE5, CM1 and CM2
The classes will be given by videoconference, supported by a digital presentation and by COMSOL software package. Throughout the course, a progress test and an individual work will be proposed, which will be taken into account in the evaluation of personal work.
The course will have besides book and video notes that will facilitate its study; this makes possible to realize an online modality, although it is necessary to take the progress test, present the individual work proposed during the course, and undergo the final evaluation test.
In addition to the bibliography indicated, we will handle recent publications in scientific journals.
The evaluation will be with an exam, and it will be combined with the score of a progress test and the one obtained in the individual work presented. The exam will have a virtual test part, and a face-to-face part. The exam will represent the 60% of the final grade.
The assessment in the second opportunity will be with an exam that will represent the 60% of the final mark. This will be added to the 40% of that obtained in the development of the work done by the student during the course. Students will have the opportunity to present their personalised work until the day they take the face-to-face part of their exam.
The CG1, CG2, CG4, CG5, CE1, CE2, CE5, CM1 and CM2 competencies will be evaluated through the personal homework.
The competencies CE1, CE2, CE5, CM1 and CM2 competences will be assessed by the final exam.
Hours expositives: 18
Hours of laboratory: 24
Tutories: 6
Hours of personel work: 97.
Hours of evaluation: 5
Total volume of work: 150 hours.
Have knowledges of:
Ordinary differential equations / dynamic systems
Equations in partial derivatives
Tensor calculus and equilibrium equations of of the solids mechanics in Eulerian coordinates.
CONTINGENCY PLAN for the adaptation of this guide to the document "Bases para o desenvolvemento dunha docencia presencial segura no curso 2020-2021", approved by the Governing Council of the USC (entity to which both teachers of the subject belong) in ordinary session held on June 19, 2020:
• If scenario 2 is applied, the following adaptations to this guide will be made:
- The contents of each topic developed during this scenario will be maintained.
- The explanation of practical examples of the concepts studied would be limited depending on the software available for this purpose.
- The teaching methodology will be adapted to the criteria indicated by the University of Santiago, and to the guidelines of the Academic Commission of the Master of Industrial Mathematics.
• In case of application of scenario 3, in addition to the incidences already indicated for scenario 2, the following adaptations of this guide will be produced:
- When the Examination must be taken in this scenario, it will be done in a session combining the use of tools from the Virtual Course, to do a test part, and to propose a task to be completed in a Teams session, and to be handed in the Virtual Course itself of the subject before the end of the session. This affects both first and second chance students.
- In any case, the previous points will be adapted to the criteria indicated by the University of Santiago, and to the guidelines of the Academic Commission of the Master of Industrial Mathematics.
Patricia Barral Rodiño
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813213
- patricia.barral [at] usc.es
- Category
- Professor: University Lecturer
Peregrina Quintela Estevez
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813223
- peregrina.quintela [at] usc.es
- Category
- Professor: University Professor
| Tuesday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Wednesday | |||
| 11:00-12:30 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Thursday | |||
| 11:00-12:30 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Friday | |||
| 12:00-14:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| 03.22.2021 10:00-14:00 | Grupo /CLE_01 | Computer room 5 |
| 06.21.2021 16:00-20:00 | Grupo /CLE_01 | Computer room 5 |