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Semi-analytical gradient-based optimization of exact CAD models using intermediate field representations

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Abstract

This paper proposes an approach to bridge the gap between industrial applications of Computer Aided Design (CAD) and Topology Optimization (TO) by enabling fast and unintrusive gradient-based optimization in nearly any CAD modeling kernel. The proposed approach allows directly optimizing the parameters of a CAD feature tree, thus ensuring that the final optimized design is automatically a CAD model with human-interpretable and editable parameters. This is achieved by introducing an intermediate Signed Distance Field (SDF) representation in the mathematical formulation. This field acts as an interface between the high-level heterogeneous CAD parameters and density field upon which the design’s physical performance is evaluated. Derivatives are evaluated through a hybrid scheme of physical adjoint systems and geometrical finite differences, and then chained back to the CAD parameters. We directly optimize the input CAD model and avoid any time-consuming or error-prone shape reinterpretation post-process. The preservation of intentional features in the CAD construction enables designers to guarantee subsequent editing, manufacturing, or assembly interfaces of the optimized designs. We demonstrate the stability and efficiency of the approach through numerical experiments for a variety of 2D and 3D CAD parameterization strategies and optimization objectives.

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Acknowledgements

The authors would like to thank Shanglong Zhang for his help in testing the present method within industrial CAD and CAE workflows.

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Authors and Affiliations

  1. LMI, National Institute of Applied Sciences (INSA), 76000, Rouen, France

    Martin-Pierre Schmidt

  2. 76131, Karlsruhe, Germany

    Peter Clausen

  3. 22587, Hamburg, Germany

    Claus B. W. Pedersen

  4. 78140, Velizy, France

    Martin-Pierre Schmidt & Pascal Hebrard

Authors
  1. Martin-Pierre Schmidt
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  4. Pascal Hebrard
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Correspondence to Martin-Pierre Schmidt.

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Replication of Results

The method and all default settings are described in detail in Sect. 2. Any non-default settings applied in Sect. 3 are specified. All examples use a simple and transparent update scheme without hidden parameters. However, we remark that similar results and faster convergence are achieved using more advanced optimization schemes such as the Method of Moving Asymptotes. The method can be seen as an extension of density-based topology optimization where the density field is projected from a CAD model. Therefore, in order to implement the approach, the authors suggest starting from a well established topology optimization code such as the 88 lines code from Andreassen et al. (2011). A CAD modeling kernel or a simple CSG/sketch-based kernel with SDF capabilities should be added. Then the lengthscale filter on the design variables should be replaced by a smooth Heaviside projection of the SDF to create the physical densities considered in the analysis.

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Schmidt, MP., Clausen, P., Pedersen, C.B.W. et al. Semi-analytical gradient-based optimization of exact CAD models using intermediate field representations. Struct Multidisc Optim 66, 138 (2023). https://doi.org/10.1007/s00158-023-03595-9

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