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Integrated topology and packaging optimization using coupled material and component pseudo-densities

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This paper reviews a novel method for integrated topology and packaging optimization in lightweight systems design. Presented as the component-existence model, this approach introduces a new class of packaging design variable coupled with traditional material pseudo-densities in a standard topology workflow. This method adopts a modified interpolation scheme compatible with standard finite element mesh discretizations, and through development of so-called design fields and variable mapping functions, applies gradient-based optimization and analytical sensitivity expressions for driving design updates. The resulting framework can consider multiple overlapping components, enhances effective component mobility in the design domain, and features numerical efficiency comparable to standard topology-only problems. This method is demonstrated in six numerical case studies and compared against solutions from full factorial analysis, with resulting integrated designs approaching or exceeding benchmark configurations within ±5%.

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This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).

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Correspondence to Il Yong Kim.

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Replication of results

Sufficient information for replicating results is provided throughout the manuscript. Of importance are the inclusion of methodology details such as design field descriptions, priority schemes, and mapping functions. Also included are details for the numerical implementation and case studies, including phase-based settings and case study setup. Pseudocode is also provided in the Appendix for further clarification of the iTOPO workflow. Appropriate references are specified for aspects not immediately within the scope of this paper (e.g., standard checkerboard filtering).

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Responsible Editor: Jianbin Du

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Appendix. Pseudocode

Appendix. Pseudocode

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Roper, S.W.K., Kim, I.Y. Integrated topology and packaging optimization using coupled material and component pseudo-densities. Struct Multidisc Optim 64, 3345–3380 (2021).

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