Two-scale topology optimization with microstructures

Zhu, Bo; Skouras, Mélina; Chen, Desai; Matusik, Wojciech

doi:10.1145/3072959.3126835

Cited by 32 publications

(32 citation statements)

References 65 publications

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“…Different from two-scale structural optimizations (e.g. [11], [1]) which assume axis-aligned microstructures, our method optimizes the orientation of microstructures, in particular, to align it with spatially-varying stress directions. We restrict our design method to lightweight microstructures that are composed of struts, i.e.…”

Section: Structural Optimization For 3d Printingmentioning

confidence: 99%

“…The design of lightweight structures by optimization is a classical and still active topic in engineering. Stimulated by the increasingly high flexibility and resolution offered by 3D printing, there has been a growing interest in optimizing structures that are composed of delicate microstructures [1], [2]. These approaches assume that the microstructures are aligned with a prescribed regular grid.…”

Section: Introductionmentioning

confidence: 99%

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Design and Optimization of Conforming Lattice Structures

Wang

Gao

2021

IEEE Trans. Visual. Comput. Graphics

123

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Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under applicationspecific external loads; the second takes the optimized configuration (i.e. locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method. His research is focused on computational design and digital fabrication, with an emphasis on topology optimization.Dr. Weiming Wang is a Marie Curie postdoc fellow at the

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Section: Structural Optimization For 3d Printingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design and Optimization of Conforming Lattice Structures

Wang

Gao

2021

IEEE Trans. Visual. Comput. Graphics

123

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“…And based on these two, (3) how do we search for a good design? Challenges in answering these questions include high-dimensional or ill-defined design spaces such as for topologies [10,11], material microstructures [12,13,14], or complex geometries [15,16], expensive evaluations of designs and their sensitivities, e.g., due to model nonlinearity [17,18], coupled materials or physics [19,20,21], or subjective goodness measures [22,23], or search inefficiency due to the absence of sensitivities [24,25,26] or the existence of random variables [27].…”

Section: Related Workmentioning

confidence: 99%

One-shot generation of near-optimal topology through theory-driven machine learning

Cang

Yao

Ren

2019

Computer-Aided Design

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We introduce a theory-driven mechanism for learning a neural network model that performs generative topology design in one shot given a problem setting, circumventing the conventional iterative process that computational design tasks usually entail. The proposed mechanism can lead to machines that quickly response to new design requirements based on its knowledge accumulated through past experiences of design generation. Achieving such a mechanism through supervised learning would require an impractically large amount of problem-solution pairs for training, due to the known limitation of deep neural networks in knowledge generalization. To this end, we introduce an interaction between a student (the neural network) and a teacher (the optimality conditions underlying topology optimization): The student learns from existing data and is tested on unseen problems. Deviation of the student's solutions from the optimality conditions is quantified, and used for choosing new data points to learn from. We call this learning mechanism "theory-driven", as it explicitly uses domain-specific theories to guide the learning, thus distinguishing itself from purely data-driven supervised learning. We show through a compliance minimization problem that the proposed learning mechanism leads to topology generation with near-optimal structural compliance, much improved from standard supervised learning under the same computational budget. example, the design of vehicle body-in-white is often done by experienced structure engineers, since topology optimization (TO) on full-scale crash simulation is not yet fast enough to respond to requests from higher-level design tasks, e.g., geometry design with style and aerodynamic considerations, and thus may slow down the entire design process 1 .Research exists in developing deep neural network models that learn to create structured solutions in a one-shot fashion, circumventing the need of iterations (e.g., in solving systems of equations [1], simulating dynamical systems [2], or searching for optimal solutions [3,4,5]). Learning of such models through data, however, is often criticized to have limited generalization capability, especially when highly nonlinear input-output relations or highdimensional output spaces exist [6,7,8]. In the context of TO, this means that the network may create structures with unreasonably poor physical properties when it responds to new problem settings. More concretely, consider a topology with a tiny crack in one of its trusses. This design would be far from optimal if the goal is to lower compliance, yet standard datadriven learning mechanisms do not prevent this from happening, i.e., they don't know that they don't know (physics).Our goal is to create a learning mechanism that knows what it does not know, and thus can self-improve in an effective way. Specifically, we are curious about how physicsbased knowledge, e.g., in the forms of dynamical models, theoretical bounds, and optimality conditions, can be directly injected into the learning of networks that ...

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“…Design for fabrication A large body of work has investigated optimization techniques offering design aids to create shapes that meet the prescribed structural objectives and fabrication constraints [LEM*17]. Recent examples include designing for deformation behavior [BBO*10; STC*13; PZM*15; MZL*17], meta‐materials [ZKBT17; MHSL18; IFW*16; ZSCM17], and lightweighting [Ben89; LSZ*14; WLQ*17]. Broader methods that can handle variety of requirements have also been investigated in [CLD*13; CBN*15; MHR*16; SXZ*17].…”

Section: Related Workmentioning

confidence: 99%

Structural Design Using Laplacian Shells

Ulu

McCann

Kara

2019

Computer Graphics Forum

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We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally‐sound minimum weight shell object. Our approach works by altering the local shell thickness repeatedly based on the stresses that develop inside the object. A key issue in shell design is that large thickness values might result in self‐intersections on the inner boundary creating a significant computational challenge during optimization. To address this, we propose a shape parametrization based on the solution to the Laplace's equation that guarantees smooth and intersection‐free shell boundaries. Combined with our gradient‐free optimization algorithm, our method provides a practical solution to the structural design of hollow objects with a single inner cavity. We demonstrate our method on a variety of problems with arbitrary 3D models under complex force configurations and validate its performance with physical experiments.

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Two-scale topology optimization with microstructures

Cited by 32 publications

References 65 publications

Design and Optimization of Conforming Lattice Structures

Design and Optimization of Conforming Lattice Structures

One-shot generation of near-optimal topology through theory-driven machine learning

Structural Design Using Laplacian Shells

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