Fulfilled R&D projects

Finite element solution of topology optimization problems

Keywords Topology optimization, weight reduction, stiffness optimization
Programs in use Tosca, ANSYS

Nowadays using of finite element (FE) optimization tools allows to simplify designer's work. The goal of thу current project is the demonstration of FE tools for topological, shape and bead optimization. FE topological optimization software FE-DESIGN Tosca was chosen as the main instrument of analysis. Research presented was carried out in the frameworks of trial academic license provided by Mechanical Engineering Service Company.


FE topological algorithm Optimality Criterion and Tosca controller-based algorithm are adopted in FE-DESIGN Tosca software. It is announced by developers and illustrated in the current research, that with use of Tosca it's possible to use adaptive mesh refinement, groups of symmetry, member size control, filtration radius control, manufacturing and stamping restriction.

As illustration of algorithm working the test optimization problem - cantilever beam - was solved. The problem statement and process of solution are shown at Fig. 1-2.


 Topology Optimization Process

Figure. 1. Problem statement

Figure. 2. Topological optimization process

Demonstration of symmetry groups options was carried out on the same problem. Using of symmetry group could be helpful in large industrial problem: it could assist to reduce the number of DOF.



topology optimization

topology optimization

Figure 3. Cyclic symmetry

Figure 4. Line symmetry

topology optimization

topology optimization

Figure 5. Central point symmetry  

Figure 6. Symmetry of rotation

The problem of U-shape plate was solved for testing of member size control option.



Figure 7. Problem statement

Figure 8. Without member size control

Figure 9. Minimization of member size

 Figure 10. Maximization of member size

As the example of MIN-MAX problem the J-curved plate with 3 load cases was optimized.




Figure 11. Problem statement

 Figure 12. Topological optimization process

Topological Optimization of the high-pressure vessel “Crystal” used for artificial diamond manufacturing was taken as the example of large industrial problem.



 Figure 13. High-pressure vessel “Crystal”

Figure 14. Results of topological optimization            (with use of symmetry)

In order to get the suitable for designer result of optimization the possibility of Tosca.Smooth tool was used. This tool allows creation of CAD model based on optimization results.


 high-pressure vessel optimization  high pressure vessel optimization

Figure. 15. Topological optimization of the high-pressure vessel

Thus, in this example, it was shown how to decrease the constriction weight by using FE topological optimization tools.