Parametric Structural Shape & Topology Optimization with a Variational Distance Regularized Level Set Methods

The signed-distance function (SDF) gives the shortest distance from a given point to the boundary and indicates whether the point is inside or outside the boundary with the sign. SDF is highly preferred in classical level set methods in order to maintain the numerical stability during the topology optimization process and also to provide a metric for the distance-based interpolation of material properties. A common way of achieving the signed-distance function is to periodically implement the so called re-initialization scheme by solving an additional Hamilton-Jacobi partial differential equation. But in classical level set methods, such re-initialization is implemented outside the optimization loop with the optimization process suspended, which might shift the design and cause convergence issues. In this paper, a double-well potential functional is employed for distance regularization within the structural topology optimization loop, which can ensure the signed-distance property of the level set function within a narrow band along the structural boundaries while keeping the level set function flat in the rest area of the computational domain. The Radial Basis Function (RBF) based parameterization techniques is combined with mathematical programming to improve the performance of the proposed method in handling topology optimization problems with non-convex objective functions and multiple constraints. The flatness of the level set function in the material region also enables easier creation of new holes in the topology optimization process.  Both 2D and 3D benchmark examples on minimum compliance optimization are provided to demonstrate the validity of the proposed method.

2D Cantilever Beam Example

2D MBB Beam Example

Representative publications:

Conference:

Long Jiang and Shikui Chen, “Parametric Structural Shape & Topology Optimization With A Variational Distance-Regularized Level Set Method”, ASME Proceedings of IDETC/CIE, August 21-24, 2016, Charlotte, North Carolina, USA.

Journal:

Long Jiang and Shikui Chen, “Parametric Structural Shape & Topology Optimization with a Variational Distance-Regularized Level Set Method”, Computer Methods in Applied Mechanics and Engineering, 321,(2017): 316-336.