This course delivers the skillset in linear or structural modeling that is required to solve structural problems from which you can develop finite element (FE) models for practical applications. It also teaches how results can be correctly interpreted. The course introduces you to the theory behind FE software and offers you practical experience in using FE software. The course uses a commercially available FE package (access provided for the duration of the course ) in a series of weekly practical sessions where models are constructed for sample problems and results are verified against simplified analytical models or open literature.
The majority of professionals in many branches of mechanical engineering will benefit from adding finite element method (FEM) to their skills array. The ability to develop modeling skills, based on a solid theoretical foundation, under supervision in a non-critical environment will allow you to acquire new skills and techniques in a logical and progressive manner.
The main topics of this course:
- finite element method
- linear static analysis
- finite element type formulation
- finite element model setup using commercial software
- plane stress/strain
In this course you will gain:
- Strong theoretical understanding of FEM
- Application of FEM to practical engineering problems
- Efficient modeling techniques
- Understanding the importance of verification and validation
Practicals and assignments are done using Abaqus (for which you will obtain a student license for the duration of the course). Note that TU Delft can offer you only a student license of Abaqus, which is sufficient to complete the course.
After finishing this course, or if you have sufficient experience with stress/structural analysis, you may choose to take the second course non-linear modeling.
Computational methods in structural analysis are of prime importance in industry as tools to assess the efficiency and performance of structures in the field of aerospace, mechanical, civil and biomedical engineering. A combination of theoretical and practical knowledge in finite element (FE) analysis are valuable skills needed to address such problems in industry. To efficiently model a real life engineering problem using finite element analysis and predict its future behavior, an engineer must possess a strong theoretical understanding of the finite element method (FEM) along with an understanding of the importance of verification and validation of such computational models.
Each week consists of 1 lecture and 1 practical. Only week 1 consists of 2 lectures to provide a solid foundation in FEM before switching to using commercial software.
Week 1: Information about the course; An introduction to the finite element method; Finite element formulation using the bar element with the direct stiffness approach.
Lecture 2: Stiffness matrix formulation by inspection; Minimum total potential energy approach applied to the finite element formulation; Weighted residual approach and its use to formulate a finite element equilibrium equation; Shape functions; connectivity matrix.
Week 2: Truss element in a 2D plane; Transformations between co-ordinate systems; discretisation.
Practical: A first view of the software you chose to use; The example dealt with in the classroom lectures of week 1 is worked out in the software for verification; A peek into the input files; Extra: a look at scripting.
Week 3: Euler-Bernoulli Beam Theory; Pure beam bending element formulation; Frame element formulation; Modified transformation matrix.
Practical: number of elements; Different types of elements; what is a good mesh?
Week 4: Higher order approximation functions; Lagrange polynomials; Natural Coordinate systems; Isoparametric element definition.
Practical: Post-processing results and errors; Convergence studies and errors; An example problem with convergence check.
Week 5: 2D triangular elements under in-plane loads and bending loads; Basic theory behind plate bending; Shape functions, stiffness matrix, transformation matrix and force vector of membrane elements; Polynomial function for the plate bending element.
Practical: Boundary conditions, load types and other constraints; Work together on special symmetry conditions; Model size reduction.
Week 6: 2D rectangular elements under in-plane loads; Shape functions in standard and natural co-ordinates; Stiffness matrix formulation of isoparamteric elements; Key features of quadrilateral elements; Extra: gauss quadrature (video).
Practical: Recap on material properties and definition; Offsets in shells and beams; Plane-stress and plane strain conditions; Example problems with both cases.
Week 7: lecture time kept open for discussion and remaining questions
Practical: Matching and non-matching meshes in multi-part models; How to overcome non-matching meshes; Applying special constraints and methods to do so; An exercise using multiple parts in one model.
Multiple assignments are provided, both theoretical and practical.
Homework submissions throughout the course, which will require theoretical understanding, practical use of commercial software and programming own pieces of FE code.
For this course you will be provided with a license for ABAQUS software (student version). You are also free to use another program, but for those TU Delft does not provide a license and they should be obtained by the learner.
If you successfully complete your online course you will be awarded with a TU Delft certificate.
This certificate will state that you were registered as a non-degree-seeking student at TU Delft and successfully completed the course. The certificate will also indicate the number of ECTS credits this course is equal to (3 ECTS) when this course is taken as part of a degree program at the university.
If you decide that you would like to apply to the full Master's program in Aerospace Engineering, you will need to go through the admission process as a regular MSc student. If you are admitted, you can then request an exemption for this course that you completed as a non-degree-seeking student. The Board of Examiners will evaluate your request and will decide whether or not you are exempted.
General admission to this course
Required prior knowledge
- A relevant BEng or BSc degree in a subject closely related to the content of the course or specialized program in question, such as aerospace engineering, aeronautical engineering, mechanical engineering, civil engineering or (applied) physics.
- If you do not meet these requirements because you do not have a relevant Bachelor's degree but you have a Bachelor's degree from a reputable institution and you think you have sufficient knowledge and experience to complete the course, you are welcome to apply, stating your motivation and reasons for admission. The faculty of aerospace engineering will decide whether you will be admitted based on the information you have provided. Appeal against this decision is not possible.
Expected prior knowledge
In addition to the entry requirements mentioned above, prior knowledge of the topic is necessary in order to complete this course. For admission purposes, TU Delft will not ask you for proof of this prior knowledge, but it is your responsibility to ensure that you have the sufficient knowledge, obtained through relevant work experience or prior education.
To view the essential background knowledge, please check your knowledge against the learning objectives of these comparable TU Delft courses:
- Basic Structural Mechanics
- Structural Analysis & Buckling
- Differential Equations and Linear Algebra
- Programming experience (either Python or Matlab)
Expected Level of English
English is the language of instruction for this online course. If your working language is not English or you have not participated in an educational program in English in the past, please ensure that your level of proficiency is sufficient to follow the course. TU Delft recommends an English level equivalent to one of the following certificates (given as an indication only; the actual certificates are not required for the admission process):
- TOEFL score 90+ (this is an internet-based test)
- IELTS (academic version) overall Band score of at least 6.5
- University of Cambridge: "Certificate of Proficiency in English" or "Certificate in Advanced English"
In order to complete your admission process you will be asked to upload the following documents:
- a CV which describes your educational and professional background (in English)
- a copy of your passport or ID card
- a copy of relevant transcripts and diplomas
If you have any questions about this course or the TU Delft online learning environment, please visit our Help & Support page.