Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
On the Topological Derivative in Shape Optimization
SIAM Journal on Control and Optimization
Structural boundary design via level set and immersed interface methods
Journal of Computational Physics
Journal of Computational Physics
Incorporating topological derivatives into level set methods
Journal of Computational Physics
Structural optimization using sensitivity analysis and a level-set method
Journal of Computational Physics
Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization
SIAM Journal on Control and Optimization
Generating smooth parting lines for mold design for meshes
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Incorporating topological derivatives into shape derivatives based level set methods
Journal of Computational Physics
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Parting direction is one of the main parameters that significantly affect mouldability and manufacturing costs of a cast part. In conventional optimal design of cast part, a parting direction is pre-selected by a designer and fixed throughout the optimization. However, when the optimization is performed with a different parting direction, the resulting design will also be different, and more importantly it will end up with different working performance. Therefore, we take the parting direction as a design variable in the optimization of a cast part so that the working performance can be optimized as much as possible. With these goals, a level set based method is proposed for the simultaneous optimization of cast part and parting direction. In each iteration, an optimal parting direction is first computed for the current structure, then the boundary of the current structure is updated by a design velocity that guarantees the design be moldable with the optimal parting direction. Therefore, although the parting direction may be changed during the optimization, the structure will always be moldable in the current parting direction. Numerical examples are provided in 3D.