Finite element solution of topology optimization problems
Area of expertise:


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 FEDESIGN 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 controllerbased algorithm are adopted in FEDESIGN 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. 12.


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.
Figure 3. Cyclic symmetry 
Figure 4. Line symmetry 
Figure 5. Central point symmetry 
Figure 6. Symmetry of rotation 
The problem of Ushape 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 MINMAX problem the Jcurved plate with 3 load cases was optimized.
Figure 11. Problem statement 
Figure 12. Topological optimization process 
Topological Optimization of the highpressure vessel “Crystal” used for artificial diamond manufacturing was taken as the example of large industrial problem.
Figure 13. Highpressure 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.
Figure. 15. Topological optimization of the highpressure vessel
Thus, in this example, it was shown how to decrease the constriction weight by using FE topological optimization tools.