Course syllabus for Finite element method - basics

Course syllabus adopted 2021-02-16 by Head of Programme (or corresponding).

Overview

  • Swedish nameFinita elementmetoden - grunder
  • CodeVSM167
  • Credits7.5 Credits
  • OwnerMPSEB
  • Education cycleSecond-cycle
  • Main field of studyArchitecture and Engineering, Civil and Environmental Engineering
  • DepartmentINDUSTRIAL AND MATERIALS SCIENCE
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 22117
  • Block schedule
  • Open for exchange studentsYes

Credit distribution

0107 Examination 7.5 c
Grading: TH		 7.5 c
  • 11 Jan 2024 am J_DATA
  • 05 Apr 2024 am J_DATA
  • 26 Aug 2024 pm J_DATA

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Mathematics courses in linear algebra and calculus in several dimensions. Furthermore, basic experience in programming with MATLAB is strongly recommended. Assignments using MATLAB programming is a part of the examination.

Aim

The aim of the course is to provide the theoretical foundation and understanding of the finite element method (FEM), which is the predominant numerical method used for analysis and design in the structural, mechanical, rock, energy and environmental engineering areas. The course gives necessary prerequisites for the courses Finite element method - structures (TME245), Timber engineering (VSM196), Structural concrete (VBB072), Steel structures (VSM191) and Concrete structures (VBB048).

Learning outcomes (after completion of the course the student should be able to)

  • Define the basic constituents defining a boundary value problem, in terms of a differential equation, data and boundary conditions, e.g. equilibrium for a structure with loads and supports,
  • Identify and separate the physical modeling (balance laws, material properties, loads and boundary conditions) as compared to the discretization (numerical solution, e.g. FEM),
  • From the boundary value problem on strong form (the partial differential equation and boundary conditions), derive the corresponding weak formulation for heat flow and elasticity problems. 
  • From the weak form, derive the corresponding finite element form.
  • Derive the weak and finite element form of transient problems (applied to heat flow problems)
  • Apply the basic theory of the finite element method as a numerical method to solve (partial) differential equations, involving the derivation of element contributions (element stiffness matrix and load vector) and the construction of suitable approximating functions (incluing isoparametric element formulation and numerical integration),
  • Apply the finite element method to problems of stationary and transient heat flow and linear static elasticity in one, two and three spatial dimensions.
  • Formulate the finite element method as a computational algorithm and implement simple finite element programs in MATLAB or Python for one and two dimensional problems. Judge and assess simulation results, and based on these results draw conclusions of whether the design meet the relevant design criteria or not.
  • Analyse the robustness and reliability of the simulation results with respect to uncertainty in input data, and to reflect on the validity of conclusions drawn from these results.

Content

  • Basic theory of the finite element method (FEM) applied to one- and two- dimensional heat flow and elasticity problems.
  • Strong and weak formulations of the governing equations.
  • Element approximations, isoparametric finite elements, numerical integration.
  • The global FE-formulation including assembling elements and solving systems of linear equations. 
  • Identification of boundary conditions

Organisation

The course is organized into approximately 30 h of lectures and 32 h of tutorials (mostly computer classes). The main theory is presented in the lectures. The main part of the computer classes are dedicated to group work with the computer assignments, although a few small size problems are solved by the instructors, exemplifying the theory.

Literature

  • N. Ottosen and H. Petersson: Introduction to the finite element method, Prentice Hall, New York 1992
  • K-G Olsson: Introduction to the finite element method. PROBLEMS, Division of Structural Mechanics, Lund 2004.  (relevant excerpts are made available on the course homepage)
  • CALFEM manual, A finite element toolbox to MATLAB (electronic version available)

Examination including compulsory elements

The final grade is determined based on the total credit points obtained both from computer assignments and a written final exam (aids allowed at the exam are a type-approved pocket calculator and a pre-defined formula sheet). Credits points from both computer assignments and the final exam are needed for a pasing grade, including a minimum of 33% on the final exam.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.