GEO-E1050 - Finite Element Method in Geoengineering, Lecture, 3.9.2024-5.12.2024

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: 03.09.2024 - 05.12.2024

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. One resit of the tests during the course is always available, with an extra resit typically possible.

  The alternative, discussed during the first lecture, is a final exam instead of resits. The exam would consist of 2 parts, each must be passed. The exam would be not obligatory for those who passed the tests. Grades from tests do not carry to the exam. Other alternatives may be proposed by the students in the first lecture.

  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 complet

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

Study Material

• valid for whole curriculum period:

  The course will be supported by the provided materials and books in the library.

  Additional study materials are distributed during the course and available in MyCourses system. 

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

SDG: Sustainable Development Goals

9 Industry, Innovation and Infrastructure

11 Sustainable Cities and Communities

12 Responsible Production and Consumption

13 Climate Action