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. Upon successfull completion of the course students can:

• 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

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

Students must complete 3 homework examples during the semester (20 points each). Additionally, there will be a final written test at the end of the semester (40 points).

Pleas sign up for the course in TISS.