Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
LEARNING OUTCOMES
After taking the course you should understand:
1. the direct (displacement based) derivation of Finite Element Method and can apply it in practice as well as know about the variational (general) derivation of Finite Element Method
2. how finite elements are derived and know about the finite element shape function, element families etc. Know the influence of chosen element on solution accuracy. Can practically check the accuracy of the Finite Element Solution
3. principles behind special finite elements like infinite elements and interface elements. Understand how automatic mesh refinement is performed.
4. how meshless methods and other numerical methods fit within the generalised framework of finite element method
5. how the finite element method can be applied to number of steady state problems described by differential equations and know about the link between variational formulation of FEM and the above problems.
6. Understand limitations of numerical methods, in particular the Finite Element Method.
You should also be able to:
A1. analyse simple problems and suggest proper (2D or 3D) Finite Element approach
A2. create a Finite Element model for given problem.
A3. analyse the created Finite Element Model, including the influence of the simplification made in the model on final solution
A4. analyse simple Finite Element solutions in order to identify errors and can rectify them.
Credits: 5
Schedule: 27.10.2020 - 03.12.2020
Teacher in charge (valid 01.08.2020-31.07.2022): Wojciech Solowski
Teacher in charge (applies in this implementation): Wojciech Solowski
Contact information for the course (applies in this implementation):
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
Valid 01.08.2020-31.07.2022:
Introductory subjects: tensor transformation, tensor calculus, coordinates transformation etc. Continuous vs discrete systems, geometrical nonlinearities etc. Direct formulation of Finite Element Method (displacement approach as a minimization of total potential energy). Generalized formulation of Finite Element Method;
Standard and hierarchical element shape functions, finite element families, numerical integration, special Finite Elements.
Plane stress, plane strain, axisymmetric stress analysis. Three dimensional stress analysis. Problems in linear elasticity and perfect plasticity. Introductions to steady state field problems: heat conduction, fluid flow.
Errors, error estimates, adaptive finite element refinement, typical errors in Finite Element solutions.
Other numerical methods: point based approximations; optionally partition of unity approximations, element-free Galerkin method.
Introduction to Finite Element Code written in Matlab, as well as to the commercial Finite Element Codes (e.g. Comsol, OptumG2 and similar)
Several introductiory simulations relevant for problems in geotechnics and rock mechanics
Applies in this implementation:
It seems that we will be having the course fully on-line this year, as the pandemic situation seems to becoming worse. That is unfortunate, and the course content and teaching methods will be somewhat adjusted to this situation. In any case, the core learning outcomes will stay the same.
Assessment Methods and Criteria
Valid 01.08.2020-31.07.2022:
To be decided during the first lecture / exercises in the course.
Initial proposal for discussion:
a) three tests during lectures The tests grade may be improved by activities during the lectures. (50% of total mark)
b) exercises - attendance, reports, homeworks (50% of the total mark)
No final exam.
Applies in this implementation:
The evaluation methods of the course will be discussed in the first lecture. However, most likely, we will stay without final exam. Unlike in the usual situation, the partial exams will allow to use all the materials. Most likely I will require hand written answers to the questions, at least partially, as means to confirm the identity. That would mean that you have to have means to scan or photograph the paper and send it, typically a phone is good enough. The alternative will be to turn on the camera during the exam - this way I can see you working and do not need any other proof.
The course will be using mainly Zoom for the lectures and and exercises. In case there is strong preference for MS Teams, they could be used instead, as currently the capabilities are very similar.
Workload
Valid 01.08.2020-31.07.2022:
5 credits, 135h total
Workload:
12 x 2h = 24h - attending lectures
12 x 2h = 24h - attending exercises
8 x 2h = 16h - preparation for lectures
11 x 4h = 44h - homeworks / finishing exercises
3 x 9h = 27 h - preparation for partial exam tests (partial exam tests held during lectures)
Small changes and adjustments in the workload are possible and discussed during the first lecture.
Applies in this implementation:
The workload of the course will remain at 135h.
However, as we will likely have it fully virtual, there will be less peer pressure and peer help. I will try to make group work / group help more available, similar to the course with a lot of contact teaching. However, for that to happen, I will need your help. It will be also essential to attend the classes when they happen, as otherwise it will be much more difficult to meet the peers, ask questions and get answers. My experience is that peer help is essential in this course, as you tend to struggle with different things. Me and my assistants will be available during exercises, and I will be available for questions during lectures, but - all in all - it would be best if you could call a friend at the time you are doing your homework and check why things are not working - or better still - have a time when a whole group is working on the homework, with discussions when things do not work. The homework will remain personal, so each of you will have to submit original homework, with own report - yet discussions and help about being unstuck is of great help.
To sum up, if you will properly ask for help from the teachers, assistants and fellow students, your workload will be likely much below 135h, and your grade will be rather good. On the other hand, if you choose to unstuck yourself on your own, each time you get stuck (and you will get stuck), the workload may be way beyond 135h...
DETAILS
Study Material
Valid 01.08.2020-31.07.2022:
The course will be supported by the available materials and books in the library.
Additional study materials will be distributed during the course and available in MyCourses system.
Applies in this implementation:
We will be preparing extra materials for the course, as it will be taught online. This may include extra videos, instructions and similar. However, the exercise materials and lectures slides likely will stay the most important materials. Lectures - and if you agree - exercises - will be recorded, so you can check on them later on when you have troubles. It is essential to communicate during the lectures and exercises - this way you can get a different explanation for an issue you don't understand. We do not get as much non-verbal feedback during virtual classes as normally (we barely get feedback at all sometimes), so we cannot know whether you do understand things well or whether we should explain again, perhaps differently. So, if you will not clearly tell us that you need another explanation, you will likely not get it. Thinking that I do not understand it now, perhaps I will understand it in the future, but I will not ask question, usually leads to you getting stuck and spending many hours trying to understand something that could be explained in minutes. So, communication during the lectures and exercises is essential and will significantly reduce your workload.
Prerequisites
Valid 01.08.2020-31.07.2022:
Knowledge of matrix calculus, basic tensor analysis, differential calculus and differential equations. Knowledge of concepts of stress, strain, elasticity and knowledge if basic constitutive models for materials.
For Aalto students a continuum mechanics course, bachelor level (KJR-2001) and Civil Engineering Construction Materials (Master level course) are the recommended pre-requisites.
SDG: Sustainable Development Goals
9 Industry, Innovation and Infrastructure
12 Responsible Production and Consumption
FURTHER INFORMATION
Details on the schedule
Applies in this implementation:
Please be ready to attend the course via Zoom. Instructions: https://www.aalto.fi/en/services/zoom-quick-guide Lectures and exercises in place are cancelled in favour of on-line teaching.
- Teacher: Adibaskoro Tito
- Teacher: Gupta Abhishek
- Teacher: Solowski Wojciech