Topology Optimization subjected to Contact Constraints

Introduction and motivation

Due to major advances of 3D-printing technologies over the last two decades, new design approaches such as topology optimization have become more and more important. However, the great breakthrough has not yet been achieved because the numerical optimization is based on simulations, which in turn are based on model assumptions. And it is well known, that these assumptions impact the simulation and lead to differences between simulations and experiments. In particular, popular assumptions are ideal supports, such as bearings, linear material behavior or perfectly known loads. For this reason, this research project aims at the impact of different bearing models on the optimization and simulation of dynamic systems.

Therefore, the Solid Isotropic Material with Penalization (SIMP) approach [1] is applied and combined with contact formulations. These contact formulations allow a more accurate numerical discription of the supports, since the concepts of force and form closure can be used.

On this occasion, the optimization toolbox TOptiMuM is developed, which solves two and three dimensional problems. TOptiMuM is written in C++ and handles static and dynamic compliance optimization problems, which are subjected to contact constraints. Furthermore, the Portable, Extensible Toolkit for Scientific Computation (PETSc) [2,3,4] is used, which is developed by the Argonne National Laboratory.

This research project is part of the "SENSUS" research training centre at the interface between applied mathematics and computational engineering. Detailed information about the graduate school SENSUS can be foundhere.

Two dimensional Beam

The impact of three different support modelling techniques on the final design is visualized. All three optimizations start from the same initial density distribution and all optimizations are subjected to the same loads. One can see that the material destribution inside the flange is sensitive against the different bearing modells.

 

Student Theses

This topic offers a combination of mechanics and optimization and provides much space for student work. Please contact us, if you are interested to contribute to this topic within the scope of a project work or a Bachelor-/Masterthesis.

Literatur

  • [1] Bendsøe, M.P.; Sigmund, O.: Topology Optimization: Theory, Methods and Applications. Berlin, Heidelberg: Springer Science and Business Media, 2. Edn., 2013.
  • [2] Balay, S.; Gropp, W.D.; McInnes, L.C.; Smith, B.F.: Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries.
    In Modern Software Tools for Scientific Computing, pp. 163–202. Boston, MA: Birkh¨auser Boston, 1997.
  • [3] Balay, S.; Abhyankar, S.; Adams, M.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Dener, A.; Eijkhout, V.; Gropp, W.; Karpeyev, D.; Kaushik, D.; Knepley, M.; May, D.; McInnes, L.C.; Mills, R.T.; Munson, T.; Rupp, K.; Sanan, P.; Smith, B.; Zampini, S.; Zhang, H.; Zhang, H.: PETSc Web page. www.mcs.anl.gov/petsc, 2019.

  • [4] Balay, S.; Abhyankar, S.; Adams, M.; Brown, J.; Brune, P.; Buschelman, K.; Dalcin, L.; Dener, A.; Eijkhout, V.; Gropp, W.;
    Karpeyev, D.; Kaushik, D.; Knepley, M.; May, D.; McInnes, L.C.; Mills, R.T.; Munson, T.; Rupp, K.; Sanan, P.; Smith, B.; Zampini, S.;
    Zhang, H.; Zhang, H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 3.14, Argonne National Laboratory, 2020.