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: 02.11.2021 - 10.12.2021
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Wojciech Solowski
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
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
Assessment Methods and Criteria
valid for whole curriculum period:
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.
Workload
valid for whole curriculum period:
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.
DETAILS
Study Material
valid for whole curriculum period:
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.
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
SDG: Sustainable Development Goals
9 Industry, Innovation and Infrastructure
12 Responsible Production and Consumption
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Please refer to the course syllabus for more detailed information, lecture and exercises times and content. Detailed schedule and content of each lecture / exercises will be given in MyCourses
Teaching Period:
2020-2021 Autumn II
2021-2022 Autumn II
Course Homepage: https://mycourses.aalto.fi/course/search.php?search=GEO-E1050
Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.