Course syllabus

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TME235 Mechanics of solids lp1 HT19 (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

TimeEdit

Course literature

Lecture notes that will be uploaded on Canvas.

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

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

 

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 separted 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-A14) concerning continuum mechanics (first part of the course which is shared with Mechanics of fluids TME225) must be handed in no later than Wednesday 18 September 16.00. These assignments must be handed in individually and it is recommended that they are hand-written.

The assignments (denoted C1-C5) concerning the solid mechanics part of the course must be handed in in no later than Friday 18 October 23.59. They are preferable solved in groups of two and must be submitted electronically via Canvas.

 

The written examination takes place 31 October 14.00-18.00.

Allowed aids at the written examination are a sheet of Formulas (will be distributed), Mathematical handbooks (such as Beta), basic calculator (“typgodkänd” with the first part of the designation:  Casio FX82…, TexasTI30…, Sharp ELW531… Not capable of drawing graphs), English dictionaries. Note that no own notes are allowed in the allowed aids.

Grading:

  • 0-9.5p: fail
  • 10-14.5p: grade 3
  • 15-19.5p: grade 4
  • 20-25p-: 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

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

 

 

Course summary:

Date Details Due