Topology Optimization Method of Stamping Structures Based on the Directional Density Field
Abstract
:1. Introduction
2. Topology Optimization Method
2.1. The Directional Density Field and Definition of the Design Variables
2.2. The Finite Element Model
2.3. The Optimization Model
2.4. Uniform Thickness Control
3. Numerical Examples
3.1. Case 1
3.2. Case 2
4. Conclusions
- (1)
- The directional density field, realized by the multiple Heaviside projections, is effective in enabling directional material adding and removal. This type of material change ensures no interior void or undercut and, therefore, is very suited for designing stamping structures.
- (2)
- The polynomial-fitting-based surface offset provides the dynamic truncation threshold offsets that have proved more effective in uniform thickness control than keeping a constant truncation threshold offset because the surface normal vectors are not always aligned with the stamping direction.
- (3)
- The smoothing radius for the truncation threshold majorly affects the optimization result. A larger smoothing radius for leads to less variation in stamping depth and, therefore, a shallower V-shaped cross section, for which the bending deformation resistance is weakened. On the other hand, a larger radius leads to more column design variables participating the drawing depth averaging, resulting in a smaller drawing angle and, therefore, improved manufacturability due to the fewer plastic deformations.
- (4)
- Varying the target thickness of the thin-walled structure leads to major changes in the optimization result, but there is no deterministic rule for pre-defining the best target thickness, which varies case by case. Hence, simultaneously optimizing the shell topology and thickness would be a very interesting future topic.
- (5)
- The proposed topology optimization algorithm exhibits excellent convergence stability. Minor fluctuations have been observed which are reasonable given the continuously increasing strategy.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Yuan, Z.; Geng, L.; Wang, N.; Wu, T.; Qi, W.; Dai, Y.; Huang, J. Topology Optimization Method of Stamping Structures Based on the Directional Density Field. Materials 2024, 17, 656. https://doi.org/10.3390/ma17030656
Yuan Z, Geng L, Wang N, Wu T, Qi W, Dai Y, Huang J. Topology Optimization Method of Stamping Structures Based on the Directional Density Field. Materials. 2024; 17(3):656. https://doi.org/10.3390/ma17030656
Chicago/Turabian StyleYuan, Zhiling, Lei Geng, Ningning Wang, Tao Wu, Wei Qi, Yuhua Dai, and Jiaqi Huang. 2024. "Topology Optimization Method of Stamping Structures Based on the Directional Density Field" Materials 17, no. 3: 656. https://doi.org/10.3390/ma17030656