Regularization Effect

Initial

Final

Evolution

2D MBB Beam Example

2D Michell-Type Structure Example

3D Cantilever MBB Beam Example

Design Domain and Boundary Conditions

(Fixed Constraint in Yellow Area)

Representative publications:

Conference:

Long Jiang, Shikui Chen, and Xiangmin Jiao, “Parametric Shape & Topology Optimization: A New Level Set Approach Using Cardinal Kernel Functions”, ASME Proceedings of IDETC/CIE, August 6-9, 2017, Cleveland, Ohio, USA.

Journal:

Long Jiang, Shikui Chen and Xiangmin Jiao, “Parametric Shape & Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions”, International Journal for Numerical Methods in Engineering, accepted, 2017.

 

 

 

 

 

Zero-Lever  Set Evolution

Design Domain and Boundary Conditions

Level Set Function Evolution

Zero Level Set Evolution

Parametric Shape & Topology Optimization: A New Level Set Approach Based on Cardinal Kernel Functions

The parametric level set method is an extension of the conventional level set methods for topology optimization. By parameterizing the level set function, levels let methods can be directly coupled with mathematical programming to achieve better numerical robustness and computational efficiency. Moreover, the parametric level set scheme can not only inherit the primary advantages of the conventional level set methods, such as clear boundary representation and the flexibility in handling topological changes, but also alleviate some undesired features from the conventional level set methods, such as the need for re-initialization. However, in the existing RBF-based parametric level set method, it is difficult to find out the range of the design variables. Besides, the parametric level set function often suffers large fluctuations during the optimization process. These issues cause difficulties both in numerical stability control and in material property mapping. In this research, a unique Cardinal Basis Function (CBF) is constructed based on the Radial Basis Function (RBF) partition of unity collocation method, which is employed to parameterize the level set surface. The benefit of CBF is that the range of the design variables can now be precisely specified as the value of the current level set function. We also introduce a distance regularization energy functional to maintain a desired distance regularized level set function during the evolution. With this desired feature, the level set evolution is stabilized against large fluctuations. In addition, the material property mapping from the level set function to the finite element model can be more accurate.

Lever Set Function Evolution

Design Domain and Boundary Conditions

 

Radial Basis Function

Cardinal  Basis Function

Design Evolution (Start from No-hole Initial Design)

Design Evolution (Start from Multi-holes Initial Design)