Advanced Finite Element Methods

11M1140

Master

German

5.0

winter and summer term

1 semester

Simulation using Finite Element Analysis (FEA) is a widely used component of the digital twin in mechanical, plant and vehicle engineering. The method enables product properties to be calculated at the development stage and thus forms the basis for the evaluation of designs.  In order to meet the requirements of cost-effectiveness, use of resources and functionality at the same time, the design of the components should aim for the limit value. This requires the consideration of physical non-linearities and dynamic effects. Building on the FEA for linear problems, the essential phenomena of non-linear statics and linear dynamics and their implementation in the FEA are dealt with and illustrated using practical examples. Students learn to assess whether nonlinear phenomena must be taken into account in modeling and how they can implement them. They are able to recognize the possibilities and limitations of the method and transfer them to new situations.

1. introduction to FEA

2. nonlinear methods of the FEA

2.1 Nonlinear boundary conditions

2.2 Geometric nonlinearity

2.3 Material nonlinearity

2.4 Solution methods for nonlinear systems of equations

3 FEA in dynamics

3.1 Mechanical basics

3.2 Model structure in the FEA program

3.3 Practical examples

4. computer practical course

The total workload for the module is 150 hours (see also "ECTS credit points and grading").

• Portfolio exam

Prior knowledge in the following areas is recommended for successful participation in the module: Fundamentals of the finite element method, mathematics, mechanics, materials technology, design theory, CAD

Students will be able to describe the theoretical relationships of FEA. They are able to explain the influence of non-linearities and how dynamic effects are to be taken into account. They can define non-linear material behavior and model non-linear boundary conditions.

.Students are able to evaluate the influence of non-linear and dynamic phenomena and draw conclusions for modeling. They are able to select suitable solution algorithms for non-linear systems and demonstrate this in calculations. Students can work on a practical problem using their specialist knowledge, discuss calculation results against the background of component optimization and relate them to the mechanical principles. They can decide on the choice of solutions based on their specialist knowledge.

Students can assess the validity of complex FEA simulations, taking into account non-linearities and dynamic phenomena in relation to the task, taking into account aspects of good scientific practice and on the basis of their specialist knowledge.  

Students can carry out non-linear FEA analyses in a standard software package, taking into account material non-linearities, geometric non-linearities and non-linear boundary conditions. They can analyze and evaluate the natural vibration behavior of assemblies and derive theory-based optimization approaches.

Based on a technical problem of a product, students can formulate suitable research questions aimed at the technical causes of the problems and use the possibilities of FEA.

Students can analyze problems in small teams, develop solutions and communicate the results orally and in writing to other students and experts. They can obtain and evaluate information from external organizations and research literature and make it usable for their own work. Students can organize themselves as a small group with regard to project management, team organization and agile management.

• Forstmann, Jochen

• Schmehmann, Alexander
• Forstmann, Jochen
• Richter, Christoph Hermann