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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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A Heat Method for Generalized Signed Distance
We introduce a method for approximating the signed distance function (SDF) of geometry corrupted by holes, noise, or self-intersections. The method implicitly defines a completed version of the shape, rather than explicitly repairing the given input. Our starting point is a modified version of theheat methodfor geodesic distance, which diffuses normal vectors rather than a scalar distribution. This formulation provides robustness akin togeneralized winding numbers (GWN), but provides distance function rather than just an inside/outside classification. Our formulation also offers several features not common to classic distance algorithms, such as the ability to simultaneously fit multiple level sets, a notion of distance for geometry that does not topologically bound any region, and the ability to mix and match signed and unsigned distance. The method can be applied in any dimension and to any spatial discretization, including triangle meshes, tet meshes, point clouds, polygonal meshes, voxelized surfaces, and regular grids. We evaluate the method on several challenging examples, implementing normal offsets and other morphological operations directly on imperfect curve and surface data. In many cases we also obtain an inside/outside classification dramatically more robust than the one obtained provided by GWN.
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- Award ID(s):
- 2212290
- PAR ID:
- 10607519
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- ACM Transactions on Graphics
- Volume:
- 43
- Issue:
- 4
- ISSN:
- 0730-0301
- Format(s):
- Medium: X Size: p. 1-19
- Size(s):
- p. 1-19
- Sponsoring Org:
- National Science Foundation
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