 |
|
Piecewise Constant Level Set Method | |
|
The conventional level set method is a powerful scheme for representing the moving boundary. Under this level set framework, the boundary models can be easily changed without specification of the topology of the structure during the optimization process. In the this level set framework usually several level set functions are used to define multi-phase problems, for example for 4 phases problem 2 level set functions are used. With this scheme, n level set functions will be used to express 2n different regions. One problem of this scheme is that if the number of different phases is not exactly equal to 2n, some regions must be empty since the total number of the phased is over estimated. Other than the conventional level set model, here we propose to use only one level set function which is a piecewise constant value function to represent the different phases in a whole design domain for structural topology optimization problems. The piecewise constant level set (PCLS) method was first proposed by Lie-Lysaker-Tai (Lie, 2006) in the interface problem fields such as image segmentation or denoising problems. Comparing with the conventional discrete level set method, the piecewise constant level set method is free of the Hamilton-Jacobi equation because of the smoothness of the functional and the constraints in this approach. | |
 |
|
| Subdomains represented with a piecewise level set function. | |
 |
|
| Characteristic function in each subdomain. | |
| In two-phase problem, the value of the level set function is predefined as 1 or 2 to specify the different areas of the two phases, and then the iso-surface value k is set as 1.5. | |
|
|
|
| The iso-surface in PCLS method. | |
|
Example: Minimum mean compliance design problem of a short cantilever beam. |
|
|
|
|
 |
 |
| Step 1 | |
 |
 |
| Step 25 | |
 |
 |
|
Step 45 |
|
 |
 |
|
Step 300 |
|
| Our research currently also focuses on the following | |
| |
| Supported by: | |
| |
