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Topology optimization problems are typically non-convex, and as such, multiple local minima exist. Depending on the initial design, the type of optimization algorithm and the optimization parameters, gradient-based optimizers converge to one of those minima. Unfortunately, these minima can be highly suboptimal, particularly when the structural response is very non-linear or when multiple constraints are present. This issue is more pronounced in the topology optimization of geometric primitives, because the design representation is more compact and restricted than in free-form topology optimization. In this paper, we investigate the use of tunneling in topology optimization to move from a poor local minimum to a better one. The tunneling method used in this work is a gradient-based deterministic method that finds a better minimum than the previous one in a sequential manner. We demonstrate this approach via numerical examples and show that the coupling of the tunneling method with topology optimization leads to better designs.
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This content will become publicly available on January 1, 2026
A geometry projection method for topology optimization of frames with structural shapes
We present a topology optimization method based on the geometry projection technique for the design of frames made of structural shapes. An equivalent-section approach is formulated that represents the cross-section of the structural shapes as a homogeneous rectangular section. The accuracy of this approach is demonstrated by comparison to analyses performed using body-fitted meshes of the original sections for different loads and boundary conditions. A novel geometric representation is also introduced to represent the equivalent section as a cuboid. Like offset solids, this representation is endowed with an explicit expression for the computation of the signed distance to the boundary of the primitive and of its sensitivities, allowing for an efficient implementation. An overlap constraint is imposed via the formulation of auxiliary primitives associated to the structural members, which guarantees the resulting designs do not exhibit impractical intersections of primitives that would preclude their construction. The efficacy and efficiency of the method is demonstrated via 2D and 3D design examples. The examples demonstrate that the proposed method renders optimal designs and exhibits good convergence. They also illustrate the ability to design structures with far lower optimal volume fractions than those typically employed in continuum topology optimization techniques.
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- Award ID(s):
- 1751211
- PAR ID:
- 10562173
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Structural and Multidisciplinary Optimization
- Volume:
- 68
- Issue:
- 1
- ISSN:
- 1615-147X
- Subject(s) / Keyword(s):
- Feature mapping Structural shapes Structural profiles Ultralight frame structures Equivalent section
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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