Finite Element Method – 2
Prerequisites
- Basic programming skills in FreeFEM++
- Finite element theoretical knowledge
This course follows the Finite element method – 1 course.
Course summary
The course focuses on the resolution of linear and non-linear elasticity problem in the FreeFEM++ framework. The course combines theoretical foundations with practical programming exercises throughout.
The theoretical component of the course focuses on the weak formulation of mechanical problems and establishes the mathematical foundations of their finite element approximation. Beginning with linear elasticity under the small-strain assumption, the course progressively extends the framework to nonlinear elasticity and finite-strain formulations. Particular attention is given to geometric nonlinearities and to the Newton–Raphson solution procedure commonly used for the numerical treatment of nonlinear problems.
The practical implementation and solution of these problems are then carried out within the FreeFEM++ framework. Appropriate function spaces and weak formulations are chosen and implemented for both linear and nonlinear applications. Various techniques for enforcing boundary conditions are also presented, highlighting the impact of numerical modeling choices on the quality and robustness of the results. Finally, a series of advanced case studies is considered to illustrate the treatment of phenomena such as buckling, loss of stability, and material nonlinearities. Some examples are illustrated below.
