Online Course: Linear Modeling

TU Delft Open & Online Education

Programme Description

Online Course: Linear Modeling

TU Delft Open & Online Education

This course delivers the skillset in linear or structural modelling 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 uses an open source FE package in a series of weekly practical sessions where models are constructed for sample problems and results are validated against simplified analytical models or open literature.

The majority of professionals in many branches of mechanical engineering will benefit from adding FEM to their skills array. The ability to develop modelling skills under supervision in a non-critical environment means that skills and techniques can be acquired in a logical, 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 modelling techniques
  • Understanding the importance of verification and validation

Practicals and assignments are done using either Abaqus or Patran/Nastran (based on your preference). After finishing this course, or if you have sufficient experience with stress/structural analysis, you may choose to take the second-course non-linear modelling.


Computational methods in structural analysis are of prime importance in the 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 the 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.

Course Syllabus

  • 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.
    Practical: A first view of the software you chose to use; The example dealt with in the classroom lectures worked out in the software for verification; A sneak peek into the input files; Extra: a look at scripting.
  • Week 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.
    Practical: Boundary conditions, load types and other constraints; Work together on special symmetry conditions; Model size reduction.
  • Week 3: Truss element in a 2D plane; Transformations between coordinate systems.
    Practical: Discretisation or meshing; Different types of elements.
  • Week 4: Euler-Bernoulli Beam Theory; Pure beam bending element formulation; Frame element formulation; Modified transformation matrix.
    Practical: Post-processing results and errors; Convergence studies and errors; An example problem with convergence check.
  • Week 5: Higher order approximation functions; Lagrange polynomials; Natural Coordinate systems; Isoparametric element definition.
    Practical: Recap on material properties and definition; Offsets in shells and beams; Plane-stress and plane strain conditions; Example problems with both cases.
  • Week 6: 2D triangular elements under in-plane loads and bending loads; the Basic theory behind plate bending; Shape functions, stiffness matrix, transformation matrix and force vector of membrane elements; the Polynomial function for the plate bending element.
    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.
  • Week 7: 2D rectangular elements under in-plane loads; Shape functions in standard and natural co-ordinates; Stiffness matrix formulation of isoparametric elements; Key features of quadrilateral elements; Extra: gauss quadrature (video).
    Practical: Practical space will be kept open for discussion.


Multiple assignments are provided, both theoretical and practical. Assignments may be altered to particular needs to develop competencies you are looking for.


Homework and practical submissions.

This school offers programs in:
  • English

Last updated September 18, 2018
Duration & Price
This course is Online
Start Date
Start date
Part time
750 EUR