After successful completion of the course, students are able to

• explain the modelling assumptions necessary in the derivation of the governing partial differential equations (PDE)
• discuss the different coupling types and corresponding PDEs
• derive the coupled finite element equations via the weak form of the governing PDEs
• conduct simple simulations and critically assess the results

The general procedure to solve coupled muli-field problems with the finite element method is explained. Different, simple couplings like forward coupling (e.g. heat conduction to solid mechanics), direct volume coupling (e.g. piezoelectricity) and interface coupling (e.g. solid mechanics and acoustics) are introduced.

Starting from the governing partial differential equations (PDEs) we explain how to derive a coupled finite element formulation via their weak formulation. The following coupling types are treated

• forward coupling between the temperature field (from heat conduction) to the mechanic field in which it causes thermal stresses
• direct volume coupling between electrostatic and mechanic field via the piezoelectric effect
• interface coupling between sold mechanics and acoustics

• Interactive lectures give an overview of the subject and highlight essential connections between topics,
• hands-on demonstrations of the software introduce the necessary tools to solve the illustrativ application examples
• pracitcal exercises increase the software skills and deepen the understaning of the covered physics
• regualr questions & answers sessions provide the opportunity to discuss problems with other students and teachers

3 homework assignments, final test, and active participation during the course

Pleas sign up for the course in TISS.

The courses "Fundamentals of Finite Element Methods" can also be taken in parallel to this course in the same term.