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, External department linked to the degrees
Areas: Applied Mathematics, Área externa M.U en Matemática Industrial
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
Numerical simulation of various Benchmark examples of applications in industry and civil engineering will be carried out.
The practicals of the subject will cover applications in linear and non-linear elasticity with the following objectives:
1- To know and to use the necessary procedures for the solving in computer of solid mechanics problems.
2- To know and to apply the problems solving methodology of the commercial packages: APEX, PATRAN-NASTRAN or MENTAT-MARC.
3- To interpret and post-process correctly the numerical results obtained with the simulation programs.
Part 1. Linear stationary and dynamic elasticity.
1.a. 3D models of elasticity.
1.b. 2D models of plane strain and plane stress.
1.c. 2D models of plates and shells.
1.d. 2D models for axially symmetric behaviour
1.e. 1D models of beams.
1.f. Multidimensional models.
1.g. Calculation of eigenfrequencies and eigenmodes of vibration.
1.h. Linear thermoelasticity.
1.i. Anisotropy.
Part 2. Non-linear elasticity
2.a. Non-linear materials: elastoplastic materials, von Mises' and Tresca's creep laws. Hill's criterion.
2.b. Isotropic and kinematic hardening.
2.c. Contact problems. Contact with rigid solid or deformable solid.
BASIC BIBLIOGRAPHY
• Barral, P. and Quintela, P. Modelos Matemáticos na Mecánica de Sólidos. Virtual Course of the University of Santiago de Compostela. Academic year 2024-25.
• Bower, A.F. Applied Mechanics of Solids. CRC Press. 2010.
• García Barachina, L. Introducción a Patran / Nastran en el cálculo de estructuras. Editorial Paraninfo. 2014.
• Quintela, P. Guide of practical cases in Solid Mechanics. Virtual Course of the University of Santiago de Compostela. Academic year 2024-25.
COMPLEMENTARY BIBLIOGRAPHY
• Bermúdez de Castro, A. Continuum Thermomechanics. Progress in Mathematical Physics. Edit. Birkhäuser. 2005.
• 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.
• Kikuchi, N.,Oden, J.T. (1988) Contact problems in elasticity. SIAM.
• Lemaitre J. A A course on damage mechanics. Springer-Verlag, 1996.
• Lemaitre, J., Chaboche, J.L. (1994) Mechanics of solids materials. Cambridge University Press.
• Sokolnikoff, I.S. Mathematical theory of elasticity. Krieger Publishing Company. 1956.• Timoshenko, S., Goodier,J.N. (1975) Teoría de la elasticidad. URMO.
• Tutorials and use cases of APEX, Patran, Nastran, Mentat and Marc. https://www.mscsoftware.com/
• Vinson, J.R. The Behavior of Thin Walled Structures, Beams, Plates and Shells. Kluwer academic publishers. 1989.
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;
CG3 Being able to integrate knowledge in order to state opinions using information that even incomplete or limited, include reflecting on social and ethical responsibilities linked to the application of their knowledge;
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.
CE4: Being able to select a set of numerical techniques, languages and tools, appropriate to solve a mathematical model.
CE5: Being able to validate and interpret the results, comparing them with visualizations, experimental measurements and functional requirements of the physical engineering system.
Numerical Simulation specialisation skills
CS1: To know, be able to select or use how to handle most suitable professional software tools (both commercial and free) for the simulation of processes in the industrial and business sector.
CS2: To adapt, modify and implement software tools for numerical simulation.
The sessions will be telematic from the classrooms assigned for this purpose by the USC (Part 1) and by UVigo (Part 2). The class sessions will be taught through the telematic teaching platforms available at the USC and UVigo (see Observations).
They will consist of three different parts:
A. Explanation of physical problems: mathematical modelling and design of academic tests. The aim is to develop the competences CG1, CG2, CG4, CG5, CE1 and CE2.
B. Planning of the tasks that allow solving them with the software packages: Patran-Nastran and Mentat-Marc. The competences CG1, CG2, CG4, CG5, CE4, CS1 and CS2 are handled.
C. Computer resolution and analysis of the results. In this section the competences CG1, CG2, CG3, CG4, CG5, CE5, CS1 and CS2 are worked on.
The classes will be supported by a digital presentation that will be made available to the student through a virtual course of the subject. Throughout the course an individual work corresponding to Part 1 will be proposed and will be taken into account in the assessment of the personal work.
The course will have video notes of at least sections A and B of Part 1 of the subject, which will facilitate their study.
The USC Virtual Campus will be used and a team will be created in Teams to facilitate virtual tutorials (Part 1) and the UVigo Remote Campus.
Attendance is not compulsory, although, it is recommended that as far as possible students attend in person at USC (Part 1) or UVigo (Part 2). The exam can be taken from the classrooms of the participating universities.
In the supervision by the teacher of the class work, the students will show their handling of the competences CE1, CE2, CE4, CE5, CS1 and CS2.
A computer-based test will be given to all students, based on the exercises proposed throughout the course. This test will assess the competences CE1, CE2, CE4, CE5 and CS1.
Students will have to carry out a practical work corresponding to Part 1 of the subject. The final grade for Part 1 will be calculated considering 40% of the practical work grade plus 60% of the exam grade.
The subject grade for Part 2 will be that of the final computer-based test at both the first and second opportunity.
The final grade for the subject will be the average of the grades obtained in Parts 1 and 2.
Warning: In cases of fraudulent performance in the tests (plagiarism or improper use of technology), the "Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións" (Regulations for the assessment of students' academic performance and revision of qualifications) will apply.
Presence/virtual Hours: Theoretical: 7; Practices: 35.
Non-presence Hours of Student Work: 90.
Assessment Hours: 5.
1- To consult thebibliography and the online documentation of the programmes.
2- To solve the problems proposed.
3- To use the tutorial timetable.
Peregrina Quintela Estevez
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813223
- peregrina.quintela [at] usc.es
- Category
- Professor: University Professor
| Tuesday | |||
|---|---|---|---|
| 15:00-18:00 | Grupo /CLE_01 | Spanish | Computer room 5 |
| Thursday | |||
| 11:00-14:00 | Grupo /CLE_01 | Spanish | Computer room 5 |