Project Details
Projekt
Scaled boundary isogeometric analysis enhanced by machine learning
Applicant
Dr.-Ing. Margarita Chasapi
Subject Area
Applied Mechanics, Statics and Dynamics
Term
since 2024
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 495926269
Isogeometric methods enable an integrated workflow based on a common representation for both geometric design and numerical simulation, while aiming at high-quality computational meshes with low approximation error. The simulation of volumetric domains entails challenges in the context of isogeometric analysis. In particular for 3D problems in solid mechanics, only the surface representation is available from CAD and the interior discretization is missing. The isogeometric scaled boundary method allows the direct analysis of solids based on the original surface representation. In this way, polyhedral objects are discretized by decomposing the domain into sections that share a common point, the scaling center. Thus, the scaled boundary approach is restricted to star-shaped geometries. These aspects entail a manual meshing phase prior to the analysis comprising the choice of scaling center, the discretization of the volumetric interior and possibly the decomposition into star-shaped subdomains. Furthermore, the cost of numerical integration and analysis increases for higher-order splines and in particular when nonlinear, time-dependent problems come into play. This project aims to exploit the potential of machine learning techniques in view of automatizing the mesh generation procedure and accelerating the numerical analysis. The starting point comprises problems in solid mechanics discretized with the isogeometric scaled boundary method. In this project, artificial neural networks will be employed to automatize the discretization of the interior domain and obtain efficient quadrature rules. In particular, training procedures will be developed to predict the position of interior control points such as the scaling center, as well as the optimal choice of quadrature points for numerical integration. Classification strategies will be discussed for different types of geometries and for the recognition of star-shaped domains. The capabilities of the developed machine learning-driven analysis framework will be assessed on representative benchmarks for linear problems in solid mechanics. These topics will be addressed in interdisciplinary collaboration between the fields of geometrical modeling, computational mechanics and numerical mathematics, which is essential for the realization of optimal mesh design and efficient analysis.
DFG Programme
Research Units
