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.
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 2024-25.
- 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.
A course will be available on the Virtual Campus of the Universidade de Santiago de Compostela and a team on the Teams platform to facilitate virtual tutorials.
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 grade of the personal work will be the average of the grades of a progress test and the grade obtained through individual work. The exam will be face-to-face, in the classroom assigned for this purpose at each site of the master's degree, and will have a multiple-choice test and a written part. In order to pass the subject it will be essential to obtain at least 4 points out of 10 in the exam. The final grade will be the maximum between the exam grade and the result of weighting the personal work with 40% and the exam with 60%.
In the second evaluation opportunity the student keeps the grade obtained with his personal work throughout the course. The final grade of the second opportunity will be governed by the same criteria as the first opportunity.
The grade is considered as not presented if the student did not take the progress test in the continuous evaluation, did not hand in the individual work, and did not take the exam.
For cases of fraudulent performance of exercises or tests, the provisions of the Regulations on the assessment of the academic performance of students and the review of qualifications of the University of Santiago de Compostela will apply.
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.
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
| Thursday | |||
|---|---|---|---|
| 11:00-12:30 | Grupo /CLE_01 | Spanish | Computer room 0 |
| Friday | |||
| 11:00-13:00 | Grupo /CLE_01 | Spanish | Computer room 5 |