Course syllabus

Jump to today

Course-PM 

TME235 Mechanics of solids quarter 1, 2020, 7.5 hp

Course is offered by the department of Industrial and Materials Science

Contact details

Course purpose

The course provides an introduction to the mechanics of continuous media with particular focus on solids. An important part of the course is the derivation and understanding the general field equations in three dimensions. These equations provide a generic basis for solid mechanics, fluid mechanics and heat transport. To be able to formulate the equations in three dimensions Cartesian tensors and the index notation will be used. The role of constitutive equations in distinguishing different types of problem will be emphasized. In particular, linear elasticity is used for different structural elements such as beams, plates and shells. Energy methods are introduced to show important concepts and phenomena in linear elasticity such as superposition and reciprocity. The relation between energy methods and the finite element method is shown. A short introduction to the finite element method is given in terms of both running a commercial software and of own programming in Matlab.

 

Schedule

See Calender in Canvas. Calender in Canvas is used for both Mechanics of solids (TME235) and Mechanics of fluids (TME226).  First lecture on Monday August 31. Time 15:15-16:00 on Zoom. See link in Calender or Course Summary below.

Timeedit

A suggested planning for your studies (Continuum mechanics part) can be found under Modules. 

Teaching

All teaching will this year be possible to follow digitally via Zoom (or similar) or as pre-recorded videos. 

Lectures will be given digitally. Either via Zoom or pre-recorded videos.

Tutorial sessions will be given in lecture rooms. These sessions will also be possible to follow via Zoom (or similar, links will be sent out). The rule is that maximum 50% of the seats in the lecture room are allowed to be used (every second seat). Therefore, the class will be divided into two groups (group 1 and 2). Each group is allowed to follow the tutorial session physically once per week. When group 1 is allowed to be in the lecture room then group 2 is only allowed follow via Zoom. And vice versa. 

The  same planning goes for the computer classes. 

The reason for this year's special planning is that there are two constraints: maximum 50 persons are allowed in a room and maximum every second seat is allowed to be used. There are more than 50 students in the course.

Supervision for assignments, computer assignments will for all occasions also be available on Zoom (or similar).

To reduce the risk of the spread of infection, it is important that you 

  • Follow the classes from home if you are ill, even if the symptoms are mild
  • Keep a distance from other people
  • Wash your hands often / use hand sanitiser

If we feel that this year's planning does not work then we have to change during the course (or obviously if Chalmers or the Swedish government make new decisions). Please, help us by following the rules.  

We will divide the class into two groups via Canvas. Further information will be given during the first lecture (Monday 31 August, 15.15-16:00).

Course literature

Lecture notes (as pdf files on Canvas).

For further reading: An introduction to continuum mechanics with applications, J.N. Reddy, 2008. This book can be viewed electronically:
https://www.vlereader.com/Reader?ean=9780511475719

If you want to access the book when you are outside the campus: 
http://www.lib.chalmers.se/en/search/about-e-books/

Learning objectives and syllabus

Learning objectives (after completion of this course, the student should be able to):

  • Manipulate tensor expressions using index notation, and use the divergence theorem and the transport theorem.
  • Derive the equations of continuity, momentum and energy for a continuum.
  • Extract essential aspects of a given stress state, such as principal values, principal directions, hydrostatic stress, deviatoric stress, stress vector on a plane, etc.
  • Account for the role of a constitutive equation and determine its nature (e.g. solid/fluid, incompressible etc)
  • Formulate linear constitutive equations: Hookean solid, Newtonian fluid, Fourier s law
  • Formulate Hooke's law for general three dimensional stress-strain condition with specialization to plane stress and plane strain.
  • Formulate the boundary value problem for equilibrium of a continuum with boundary conditions.
  • Derive and utilize Clapeyron's theorem and reciprocity relations.
  • Derive the weak form (virtual work formulation) of linear momentum and show how it is used in the finite element method.
  • Establish the principle of minimum potential energy for linear elasticity and show the relation to the weak form.
  • Derive the plate equation together with proper boundary conditions and specialize to axisymmetry.
  • Derive the buckling loads for a rectangular plate.
  • Derive equilibrium equations for membrane condition of axisymmetric shells.
  • Formulate the kinematic assumption, equilibrium equations and the deflection of cylindrical shells subjected to membrane and bending condition.

More detailed learning outcomes are found on Canvas in separate pdf files.

Link to the syllabus on Studieportalen.

Study plan

Examination

To pass the course the student must pass the assignments and a written exam. The grade is determined by the written exam.

The hand-in assignments (denoted A1-A13) concerning continuum mechanics (first part of the course which is shared with Mechanics of fluids TME225) must be handed in no later than Friday 18 September 16.00. These assignments must be handed in individually and it is recommended that they are hand-written. Scan in solutions to pdf file/files (e.g. by using a document scanning app such as CamScanner or Genius Scan) and submit electronically to Canvas.

The assignments (denoted C1-C4) concerning the solid mechanics part of the course must be handed before their respective deadline. The deadline for C1 and 2 is 3rd of October while for C3 and 4 the deadline is 17th of October . You can choose to work individually or in a group of two (you choose your own co-worker). The reports should together with computer codes be uploaded on Canvas.

The written examination is planned to take place 29 October 14.00-18.00. Exactly how it will be conducted depends on what is decided by Chalmers vice-president for education. We have been told that a decision will be taken first half of September.

Matlab introductions

In the course Matlab will be used. If you are not familiar with Matlab the following links are recommended:
https://edge.edx.org/courses/course-v1:ChalmersX+ChT007x+yearly/about

http://se.mathworks.com/help/matlab/getting-started-with-matlab.html

 

 

Course summary:

Date Details Due