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. Basic Finite Difference Method and its use
4. 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. Limitations of numerical methods, in particular the Finite Element Method.
7. Basic principles of elasto-plasticity
8. Mohr-Coulomb model, both in associated and non-associated version.
You should also be able to:
A1. Analyse simple problems involving linear elasticity, Mohr-Coulomb model and water flow and suggest proper 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.
A5. Use Mohr-Coulomb model in simple Finite Element Method calculations
Credits: 5
Schedule: 25.10.2022 - 02.12.2022
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:
The course gives insights into Finite Element Method. Finite Element Method can be used for lean and innovative design. Its use can lead to reduction of amount of materials used in construction. It can also analyse problems involving new sustainable materials.
Course content:
Introductory subjects: tensor transformation, tensor calculus, coordinates transformation etc. Direct formulation of Finite Element Method (displacement approach as a minimization of total potential energy). Generalized formulation of Finite Element Method; Finite Element Method algorithm and calculations. Standard and hierarchical element shape functions, finite element families.
Plane strain simplification. Problems in linear elasticity and perfect plasticity. Introductions to steady state field problems: heat conduction, fluid flow.
Calculations in commercial Finite Element Codes (e.g. Comsol, OptumG2) and similar including several introductiory simulations relevant for problems in geotechnics and rock mechanics
Elasto-Plasticity and general Mohr-Coulomb model. Associated and non-associated plasticity.
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) two tests during lectures. (50% of total mark)
b) exercises - (attendance), assignments (50% of the total mark)
No final exam.
Participation in the exercises is highly recommended and proven to reduce the course workload significantly. However, in general, skipping exercise sessions is allowed, provided that the related assignements is completed in time. The attendance for the partial exams (or resits of them) is required for the course completion.
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 - lecture tests
3 x 2h + 9x4h = 42h - homework / finishing exercises
2 x 12h = 24 h - preparation for tests (tests held during lectures)
Small changes and adjustments in the workload are possible and discussed during the first lecture.
DETAILS
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:
Teaching Language : English
Teaching Period : 2022-2023 Autumn II
2023-2024 Autumn IIEnrollment :
Registration for the course will take place on Sisu (sisu.aalto.fi).