Journal ArticleDOI
Explicit level set and density methods for topology optimization with equivalent minimum length scale constraints
TLDR
A minimum length scale is imposed by adopting geometric constraints that have been recently proposed for density-based topology optimization with projections filters that provide a computationally inexpensive solution for the instabilities which often appear in level set XFEM topological optimization.Abstract:
The goal of this paper is to introduce local length scale control in an explicit level set method for topology optimization. The level set function is parametrized explicitly by filtering a set of nodal optimization variables. The extended finite element method (XFEM) is used to represent the non-conforming material interface on a fixed mesh of the design domain. In this framework, a minimum length scale is imposed by adopting geometric constraints that have been recently proposed for density-based topology optimization with projections filters. Besides providing local length scale control, the advantages of the modified constraints are twofold. First, the constraints provide a computationally inexpensive solution for the instabilities which often appear in level set XFEM topology optimization. Second, utilizing the same geometric constraints in both the density-based topology optimization and the level set optimization enables to perform a more unbiased comparison between both methods. These different features are illustrated in a number of well-known benchmark problems for topology optimization.read more
Citations
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Journal ArticleDOI
Analytical level set fabrication constraints for inverse design.
TL;DR: This work constructs a fabrication constraint penalty function for level set geometry representations of nanophotonic devices with arbitrary geometries that limits both the gap size and boundary curvature of a device.
Journal ArticleDOI
Level set topology and shape optimization by density methods using cut elements with length scale control
TL;DR: This paper employs, without significant modifications, many of the base ingredients from the density method to construct a crisp interface level set optimization approach using a simple cut element method, which provides an accurate tool to model arbitrary, crisp interfaces on a structured mesh based on the thresholding of a level set—or density—field.
Journal ArticleDOI
A hybrid density/level set formulation for topology optimization of functionally graded lattice structures
Miche Jansen,Olivier Pierard +1 more
TL;DR: A strategy for the design of additively manufactured structures that is able to simultaneously optimize the shape of the macroscale structure and the functionally graded lattices inside this design is presented.
Journal ArticleDOI
Adaptive level set topology optimization using hierarchical B-splines
TL;DR: Numerical studies employing static linear elastic material/void problems in 2D and 3D demonstrate the ability of the proposed method to start from a coarse mesh and converge to designs with complex geometries and fine features, reducing the overall computational cost.
Posted Content
Adaptive level set topology optimization using hierarchical B-splines.
TL;DR: In this article, an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines is presented, where both the level set function and the state variable fields are discretized by hierarchical Bsplines.
References
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