Course syllabus

Welcome to TME235 Mechanics of solids, 2024!

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

• examiner: Martin Fagerström (martin.fagerstrom@chalmers.se, 031-7721300)
  
• lecturers: Martin Fagerström; Magnus Ekh (magnus.ekh@chalmers.se); Lars Davidson (lada@chalmers.se, 031-7721404)
• lab teachers: Lei Liu (lei.liu@chalmers.se); Nasrin Talebi (nasrin.talebi@chalmers.se); Andhika Pratama (andhikap@chalmers.se);  Gaetano Sardina (sardina@chalmers.se)

Course purpose

The course provides an introduction to the mechanics of continuous media with a particular focus on solids. An important part of the course is the derivation and understanding of 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 problems 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

Schedule can be found on TimeEdit.

Teaching will be given in class rooms on campus. Lectures with details about theory and derivations are available as pre-recorded videos.  Quizzes are available for training. Summarizing lectures/workshops are given on campus (see TimeEdit).

First lecture will take place on Monday 2 September . Time 15:15-17:00 in room EA (given by Magnus Ekh). 

Tutorial sessions and computer classes will be given on Campus in the rooms shown on TimeEdit. 

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://r2.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/

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 final exam. The grade is determined by the final exam.

The hand-in assignments (denoted A1-A13) concern continuum mechanics (first part of the course which is shared with Mechanics of fluids TME226) must be handed in no later than Friday 20 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) concern the solid mechanics part of the course must be handed in before their respective deadline. The deadline for C1 and 2 is ( October at 8 am, while for C3 and 4 the deadline is 21 October at 8 am. 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 31 October 14.00-18.00 at campus Lindholmen. The exam is planned to be in Computer rooms. On the exam the allowable aids are: formula sheet as well as the computers with Matlab and Python installed (no connection to internet).  

Questions and discussion platform

Yata (direct access from Canvas) 

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