Introduction to Finite Element Method

In the module the main concepts and fundamentals of the finite element method are taught:

• Direct Stiffness Method,
• finite element modelling,
• variational formulation of the Finite Element Method,
• finite Elements for plates in membrane action, -isoparametric element concept,
• convergence behavior of finite element calculations / Convergence requirements,
• introduction onto locking and finite element technology,
• implementation aspects,
• finite elements for structural dynamics.

At the end of the module the students have understood the basics of the finite element method. They are able to apply the finite element method to linear problems in structural mechanics. Furthermore, at the end of the course, students are able to develop simple finite element programs by themselves and have the capability to extend the range of applications to more complex problems concerning the finite element method using specialist literature.

The final examination of this module is held as a written test (duration 90 min.). The exam consists of a combination of general questions and calculation assignments. Handling the general questions, the students are supposed to show that they have understood the fundamentals of the finite element method. Dealing with calculation assignments the students should also show that they have the ability to develop parts of a finite element code by themselves. Additionally, it is to be demonstrated that the finite element method can be applied to linear problems in structural mechanics.

The auxiliary means for the exam can be found at the bulletin at the chair or on the chair’s homepage (www.st.bgu.tum.de).

Firm knowledge in higher mathematics and numerical methods as well as good basic knowledge in mechanics and structural analysis.

• - Felippa ,C. A., "Introduction to Finite Element Methods" , University of Colorado at Boulder - Hughes, T.J.R., "The Finite Element Method", 2000, Dover Publications Inc. - Onate, E., "Structural Analysis with the Finite Element Method. Linear Statics", 2009, Springer

The module consists of a lecture and an exercise. The lecture contains classical presentations with script and notes. For consolidation of the content, exercises containing hand calculations and computer algebra are conducted. For further intensification of the contents additional exercise sheets (“Check your knowledge”) are provided.