Course syllabus

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Welcome to TME235 Mechanics of solids, 2021!

Below follow a preliminary syllabus. Some minor adjustments might be done until the course starts. 

Note that during the first 3 weeks TME226 Mechanics of fluids and TME235 Mechanics of solids are running together. 

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. Nonlinear kinematics and different strain measures are introduced. Nonlinear hyperelastic modelling is explored. 

 

Schedule and Teaching

See Calender in Canvas. Calender in Canvas is used for both Mechanics of solids (TME235) and Mechanics of fluids (TME226). Schedule can also be found on Timeedit (link) but here it should be noted that not all lectures will take place. Therefore, please follow the Canvas Calender.

All teaching will be possible to follow digitally via Zoom or Teams or as pre-recorded videos.  But a significant amount of the teaching will also be possible to follow in class rooms on campus. 

First lecture will take place on Monday August 31. Time 15:15-16:00 on Zoom. See link in Calender and https://chalmers.zoom.us/j/9411316874
Password: Mechanics

The "standard"  lectures are pre-recorded and can be found on Canvas. Quizzes are available for training. To complement the pre-recorded videos, about one "live-session" per week is offered. The live-session is a mixture of summary and workshop. The purpose of the workshop is to open up for questions and discussions. These live-sessions are either possible to follow only via Zoom or, in most cases, on Zoom and on Campus. See Calender. The reason for these alternative ways is that we need to follow the Covid-19 rules from Chalmers. For joining Zoom-sessions always use: https://chalmers.zoom.us/j/9411316874 with
Password: Mechanics

Tutorial sessions and computer classes will be given on Campus in the rooms shown in the Calender (and in Timeedit). It will also be possible to follow these as well as asking questions online via Teams. For entering the course room on Teams, you need to join the "team" Mechanics of Solids. You can use the following course code for joining directly: iwqnufv. Please join the Team as soon as possible and send an email to Kim (kim.auth@chalmers.se) or Carolyn (carolyn.oddy@chalmers.se) if you encounter any problems. There are more instructions on how to join in a document that you can also find in the Modules section on Canvas. The document also gives you some information on how to participate during the digital tutorial sessions. We strive for supplying equal support in the classroom and online!

 

Covid-19

To reduce the risk of spreading the 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

The rules from Chalmers that we need to follow are:

  • The teaching should be conducted in a hybrid format.
  • Classrooms with capacity up to 50 people may be used to their capacity.
  • Classrooms with a capacity of 51-100 people may be used for up to 50 people.
  • Classrooms with a capacity of more than 100 people may be used to maximum 50% of its capacity.

There are more than 50 students in the course, therefore we need to adapt the way the lectures are conducted. For the workshops in room EA and EE (week 4-8) we need to restrict the number of students in the rooms to max 50. In case this would be a problem then we will need to find a procedure. 

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:
 (Links to an external site.)https://www.vlereader.com/Reader?ean=9780511475719 (Links to an external site.)

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

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

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 for axisymmetry.
  • Establish large deformation kinematics with polar decomposition.
  • Use hyperelasticity for modelling of mechanical response of e.g. rubber material.
  • 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 (Link to an external site.)

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 17 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 exam is planned to take place 28 October 14.00-18.00. The exam is planned to be in Computer rooms at Chalmers.  All aids are allowed. However, it is not permitted to cooperate with or take help from another person. As a calculator you can use the computer with Matlab, Python, Mathematica, ... 

First part of the exam will be a quiz on Canvas. If you obtain >80% correct then you will be approved (if you also are approved on the hand-in assignments and computer assignments) on the course. If you get <80% then you have failed the exam. The time for this part is 2h, i.e. 14:00-16:00. The questions will be of similar type as those that you have on Canvas (for checking your understanding after watching the video lectures). The number of questions you will get is 20. The questions will be chosen such that they cover most parts of the course. Good training to prepare for this part of the exam is the quiz questions that you have on Canvas. (Together with all other learning of the course lectures, tutorial sessions, lecture notes, assignments, problems etc.)

As soon as you are finished with the quiz you can start to work with the next part of the exam (already before 16:00). This part will contain three problems to solve. The problems will be of similar type as those (not the questions regarding theory/derivations) you can find on old exams and the assignments. Since you have all possible aids this time (earlier years it has only been a formula sheet and a basic calculator) the questions are expanded a bit by asking you to motivate and explain your solution procedure more carefully. You can now also use your computer as a calculator (Matlab, Python, ...). You will be able to get 15 points totally on this part (preliminary 5 points per problem). If you are approved on the quiz (and assignments) then 0-5 points Grade 3; 6-10 points Grade 4 and 11-15 points Grade 5. 

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 (Links to an external site.)

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

Course summary:

Date Details Due