Computational Homogenization and Multi-Scale Modelling Employing an Image-Based Approach for the Structural Analysis of Shells
This project focusses on the in-silico design of thin, curved carbon-fibre reinforced concrete shell structures using the finite element method (FEM). With respect to efficiency, especially shell elements are suitable. In the scope of this project a numerical multi-scale model is to be developed. By homogenization of a representative volume element, which is able to incorporate shell kinematics (SRVE), the modelling of the carbon-fibre reinforcement and the use of 3D material laws is possible. To allow for geometrical and physical nonlinearities a coupled multi-scale method is used for calculation (FE2-method).
To reduce the numerical cost a new formulation based on the scaled-boundary finite element method (SBFEM) is used. The geometry is described using NURBS-based shape functions. This results in an isogeometric analysis for scaled boundaries (SBIGA).
Imaging techniques are used to create and validate the model. Using Level-Set or Marching-Cubes algorithms the surface description of the carbon-fibre rovings and the concrete are extracted from CT data. Using the above-mentioned element formulation, a numerical model of the structure is obtained.