Identifying Data 2019/20
Subject (*) Continuum mechanics Code 614855205
Study programme
Mestrado Universitario en Matemática Industrial (2013)
Descriptors Cycle Period Year Type Credits
Official Master's Degree 1st four-month period
 First Optional 6
Language
Spanish
Teaching method Face-to-face
Prerequisites
Department Matemáticas
Coordinador
Arregui Alvarez, Iñigo
 E-mail
inigo.arregui@udc.es
Lecturers
Arregui Alvarez, Iñigo
Rodriguez Seijo, Jose Manuel
 E-mail
inigo.arregui@udc.es
jose.rodriguez.seijo@udc.es
Web http://http://www.m2i.es/docs/modulos/MESimNumerica/MMContinuos/Mecanica%20de%20los%20medios%20continuos.pdf
General description

Study programme competencies
Code Study programme competences
A1 Alcanzar un conocimiento básico en un área de Ingeniería/Ciencias Aplicadas, como punto de partida para un adecuado modelado matemático, tanto en contextos bien establecidos como en entornos nuevos o poco conocidos dentro de contextos más amplios y multidisciplinares.
A2 Modelar ingredientes específicos y realizar las simplificaciones adecuadas en el modelo que faciliten su tratamiento numérico, manteniendo el grado de precisión, de acuerdo con requisitos previamente establecidos.
A9 Conocer, saber seleccionar y saber manejar las herramientas de software profesional (tanto comercial como libre) más adecuadas para la simulación de procesos en el sector industrial y empresarial.
B3 Ser capaz de integrar conocimientos para enfrentarse a la formulación de juicios a partir de información que, aun siendo incompleta o limitada, incluya reflexiones sobre las responsabilidades sociales y éticas vinculadas a la aplicación de sus conocimientos.

Learning aims
Learning outcomes Study programme competences
Reaching a basic knowledge in mechanics, as a starting point for an adequate mathematical modelling AC1
AC2
AC9
Be able to integrate knowledges to proceed to the formulation of decissions. AC1
AC2
 BC2

Contents
Topic Sub-topic
Introduction Tensor algebra and analysis. Polar decomposition, divergence and Stokes theorems
Curvilinear coordinates Vector bases and curvilinear coordinates. Vector fields. Differential operators in curvilinear coordinates
Kinematics Material bodies. Motion and deformation, types of motions. Transport theorems. Isochoric motions, spin, circulation, vorticity
Conservation laws Mass. Linear and angular moments. Force and stress. Moment equilibrium and its consequences. Piola-Kirchhoff tensor. Energy conservation, Clausius-Duhem inequality
Change of observer Change of observer. Material indifference pinciple
Some simple models Constitutive hypotheses. Ideal fluids. Navier-Stokes equations. Elastic bodies. Thermoelasticity

Planning
Methodologies / tests Competencies Ordinary class hours Student’s personal work hours Total hours
Problem solving A9 B3 13 45 58
Mixed objective/subjective test A1 A2 B3 4 4 8
Guest lecture / keynote speech A1 A2 41 42 83
 
Personalized attention 1 0 1
 
(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies
Methodologies Description
Problem solving Resolution, by the student, of some exercises of continuum mechanics
Mixed objective/subjective test Theorical-practical control
Guest lecture / keynote speech Exposition, by the teacher, of the contents and resolution of some exercises

Personalized attention
Methodologies
Problem solving
Description
The teacher will help the students, when necessary, in the resolution of the proposed exercises

Assessment
Methodologies Competencies Description Qualification
Problem solving A9 B3 Resolución de exercicios e cuestións teórico-prácticas por parte do alumno, con axuda de bibliografía 40
Mixed objective/subjective test A1 A2 B3 Resolución de exercicios e cuestións teórico-prácticas nunha proba presencial 60
 
Assessment comments

To surpass the matter, the student will have to obtain at least a qualification of 4 in the mixed objective/subjective proof.

Both methodologies of evaluation will be taken into account, with the indicated percentages, in all the opportunities empoyed by the student.

Sources of information
Basic O. López Pouso (2002). "An Introduction to Continuum Mechanics" de M. E. Gurtin. Ejercicios Resueltos (capí­tulos I-VI). Publicacións Docentes do Departamento de Matemática Aplicada. Univ. de Santiago de Compostela
M. E. Gurtin (1981). An Introduction to Continuum Mechanics. Academic Press. Boston

Complementary Y. C. Fung (1994). A First Course in Continuum Mechanics. Prentice Hall
K. Hutter, K. Jöhnk (2004). Continuum Methods of Physical Modeling. Springer
A. Bermúdez de Castro (2004). Continuum Termomechanics. Birkhauser
N. Bobillo Ares (2003). Introducción a la geometría y cinemática de medios continuos. Servicio de Publicaciones de la Unviersidad de Oviedo
R. Temam, A. Miranville (2001). Mathematical Modeling in Continuum Mechanics. Cambridge University Press
L. A. Segel (1987). Mathematics Applied to Continuum Mechanics. Dover, New York
G. Duvaut (1990). Mécanique des Milieux Continus. Masson, París


Recommendations
Subjects that it is recommended to have taken before

Subjects that are recommended to be taken simultaneously
Partial differential equations/614855203

Subjects that continue the syllabus
Fluid mechanics/614855206
Solid mechanics/614855207

Other comments


(*)The teaching guide is the document in which the URV publishes the information about all its courses. It is a public document and cannot be modified. Only in exceptional cases can it be revised by the competent agent or duly revised so that it is in line with current legislation.