Structural Design Optimization

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This example shows how to apply our iterative mesh generator on structural design optimization problems. In [1] and [2], the level set method was used to track the interface during structural shape optimization. Here, we use the same technique for the interface, but solve the physical problem by updating an unstructured mesh and using the finite element method. Some of the advantages with this approach includes:

• The Neumann boundary conditions are easily implemented by using natural boundary conditions with the finite element method.
• Graded meshes allow for more efficient solvers (but the two examples below use uniform meshes).
• The finite element method is more developed for structural problems, allowing for example specialized elements and connection to existing software packages.

• Here we minimize the compliance for a structure that is loaded vertically at the right side, and we use a minimum-area constraint. The small hole in the initial configuration is required to obtain a correct topology.

  Initial	Final

  
  MSMpeg4 AVI (2.0MB)

• Again we minimize the compliance subject to a minimum-area constraint. Note that the level set method can merge holes to create different topologies, but as before we need an initial configuration with holes.

  Initial	Final

  
  MSMpeg4 AVI (1.7MB)

References

[1] Sethian, J., Wiegmann, A. Structural boundary design via level set and immersed interface methods. J. Comput. Phys., 163, 489-528, 2000.
[2] Allaire, G., Jouve, F., Toader, A.-M. Structural optimization using sensitivity analysis and a level-set method. J. Comput. Phys., 194, 363-393, 2004.