MECH4101 Continuum mechanics and thermodynamics Emneplan

This course covers the fundamentals of continuum mechanics and thermodynamics. Focus is on solid mechanics of deformable bodies treated as continuous distribution of matter disregarding their molecular structure and is intended to be a comprehensive treatment of the subject at an intermediate level. While mathematicians deal with geometric continuum mechanics using differential geometry and Lie derivatives and engineers study it using traditional strength of material approach, the course here is an in-between approach, covering enough of the general theory to be able to solve problems of interest in solid mechanics.

Knowledge 

The candidate:  

• can explain the linear elastic theory of continuum mechanics
• can explain the fundamental thermodynamic potentials and Legendre transforms
• can recognize the difference between continuous and discrete systems, can identify each of them through examples and can identify the equations for the former
• can explain the formalism associated with change of configuration (kinematics), the concepts of stress and constitutive relations
• can explain the difference between modelling dimensions and restrictions imposed on deformation fields for reductions as plane strain, axisymmetry and shell
• can identify the limitations and explain the meaning of such restrictions imposed on constitutive models through the principles of thermodynamics.

Skills 

The candidate:  

• can calculate the values for fundamental parameters i.e., stress, strain, and displacement in static problems of linear elasticity in 1-, 2-, and 3-D domains
• can solve the governing differential equations for the field variables at various locations analytically for simple geometries
• can conduct an independent, limited research project under supervision and in accordance with applicable norms for research ethics
• can apply relevant mathematical methods, such as partial differentiation, multiple integration, or Fourier analysis, in derivation and solution of governing PDEs

General competence 

The candidate:  

• can reflect upon, explain, and critically assess the solution and its procedure applied to solid mechanics problems in 1-, 2-, and 3-D using the appropriate methods
• can communicate independent research work using the correct terminology with peers and academics and to some extent with non-experts
• can explain what continuum mechanics and thermodynamics are used for and how the formulation of continua differs from that of discrete systems conceptually and mathematically.

Lectures and tutorials.

The following coursework requirements must have been approved for the student to take the exam: Each student must give an individual presentation on an advanced topic related to continuum mechanics and/or thermodynamics. Peer Q&A. 15 minutes presentation + 10 minutes Q&A will follow the presentations.

Written 3-hour exam under supervision.

New/postponed exam:

In the event of a postponed examination in this course, the exam may be held as an oral exam. The results in oral exams cannot be appealed.

None

Graded scale A-F

One internal examiner. External examiner is used periodically.