---
_id: '7117'
abstract:
- lang: eng
  text: We propose a novel generic shape optimization method for CAD models based
    on the eXtended Finite Element Method (XFEM). Our method works directly on the
    intersection between the model and a regular simulation grid, without the need
    to mesh or remesh, thus removing a bottleneck of classical shape optimization
    strategies. This is made possible by a novel hierarchical integration scheme that
    accurately integrates finite element quantities with sub-element precision. For
    optimization, we efficiently compute analytical shape derivatives of the entire
    framework, from model intersection to integration rule generation and XFEM simulation.
    Moreover, we describe a differentiable projection of shape parameters onto a constraint
    manifold spanned by user-specified shape preservation, consistency, and manufacturability
    constraints. We demonstrate the utility of our approach by optimizing mass distribution,
    strength-to-weight ratio, and inverse elastic shape design objectives directly
    on parameterized 3D CAD models.
article_number: '157'
article_processing_charge: No
article_type: original
author:
- first_name: Christian
  full_name: Hafner, Christian
  id: 400429CC-F248-11E8-B48F-1D18A9856A87
  last_name: Hafner
- first_name: Christian
  full_name: Schumacher, Christian
  last_name: Schumacher
- first_name: Espen
  full_name: Knoop, Espen
  last_name: Knoop
- first_name: Thomas
  full_name: Auzinger, Thomas
  id: 4718F954-F248-11E8-B48F-1D18A9856A87
  last_name: Auzinger
  orcid: 0000-0002-1546-3265
- first_name: Bernd
  full_name: Bickel, Bernd
  id: 49876194-F248-11E8-B48F-1D18A9856A87
  last_name: Bickel
  orcid: 0000-0001-6511-9385
- first_name: Moritz
  full_name: Bächer, Moritz
  last_name: Bächer
citation:
  ama: 'Hafner C, Schumacher C, Knoop E, Auzinger T, Bickel B, Bächer M. X-CAD: Optimizing
    CAD Models with Extended Finite Elements. <i>ACM Transactions on Graphics</i>.
    2019;38(6). doi:<a href="https://doi.org/10.1145/3355089.3356576">10.1145/3355089.3356576</a>'
  apa: 'Hafner, C., Schumacher, C., Knoop, E., Auzinger, T., Bickel, B., &#38; Bächer,
    M. (2019). X-CAD: Optimizing CAD Models with Extended Finite Elements. <i>ACM
    Transactions on Graphics</i>. ACM. <a href="https://doi.org/10.1145/3355089.3356576">https://doi.org/10.1145/3355089.3356576</a>'
  chicago: 'Hafner, Christian, Christian Schumacher, Espen Knoop, Thomas Auzinger,
    Bernd Bickel, and Moritz Bächer. “X-CAD: Optimizing CAD Models with Extended Finite
    Elements.” <i>ACM Transactions on Graphics</i>. ACM, 2019. <a href="https://doi.org/10.1145/3355089.3356576">https://doi.org/10.1145/3355089.3356576</a>.'
  ieee: 'C. Hafner, C. Schumacher, E. Knoop, T. Auzinger, B. Bickel, and M. Bächer,
    “X-CAD: Optimizing CAD Models with Extended Finite Elements,” <i>ACM Transactions
    on Graphics</i>, vol. 38, no. 6. ACM, 2019.'
  ista: 'Hafner C, Schumacher C, Knoop E, Auzinger T, Bickel B, Bächer M. 2019. X-CAD:
    Optimizing CAD Models with Extended Finite Elements. ACM Transactions on Graphics.
    38(6), 157.'
  mla: 'Hafner, Christian, et al. “X-CAD: Optimizing CAD Models with Extended Finite
    Elements.” <i>ACM Transactions on Graphics</i>, vol. 38, no. 6, 157, ACM, 2019,
    doi:<a href="https://doi.org/10.1145/3355089.3356576">10.1145/3355089.3356576</a>.'
  short: C. Hafner, C. Schumacher, E. Knoop, T. Auzinger, B. Bickel, M. Bächer, ACM
    Transactions on Graphics 38 (2019).
date_created: 2019-11-26T14:22:09Z
date_published: 2019-11-06T00:00:00Z
date_updated: 2026-07-19T22:30:05Z
day: '06'
ddc:
- '000'
department:
- _id: BeBi
doi: 10.1145/3355089.3356576
ec_funded: 1
external_id:
  isi:
  - '000498397300007'
file:
- access_level: open_access
  checksum: 56a2fb019adcb556d2b022f5e5acb68c
  content_type: application/pdf
  creator: bbickel
  date_created: 2019-11-26T14:24:26Z
  date_updated: 2020-07-14T12:47:49Z
  file_id: '7119'
  file_name: xcad_sup_mat_siga19.pdf
  file_size: 1673176
  relation: supplementary_material
  title: X-CAD Supplemental Material
- access_level: open_access
  checksum: 5f29d76aceb5102e766cbab9b17d776e
  content_type: application/pdf
  creator: bbickel
  date_created: 2019-11-26T14:24:27Z
  date_updated: 2020-07-14T12:47:49Z
  description: This is the author's version of the work.
  file_id: '7120'
  file_name: XCAD_authors_version.pdf
  file_size: 14563618
  relation: main_file
  title: 'X-CAD: Optimizing CAD Models with Extended Finite Elements'
- access_level: open_access
  checksum: 0d31e123286cbec9e28b2001c2bb0d55
  content_type: video/mp4
  creator: bbickel
  date_created: 2019-11-26T14:27:37Z
  date_updated: 2020-07-14T12:47:49Z
  file_id: '7121'
  file_name: XCAD_video.mp4
  file_size: 259979129
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file_date_updated: 2020-07-14T12:47:49Z
has_accepted_license: '1'
intvolume: '        38'
isi: 1
issue: '6'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Submitted Version
project:
- _id: 24F9549A-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '715767'
  name: 'MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and
    Modeling'
publication: ACM Transactions on Graphics
publication_identifier:
  issn:
  - 0730-0301
publication_status: published
publisher: ACM
quality_controlled: '1'
related_material:
  record:
  - id: '12897'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: 'X-CAD: Optimizing CAD Models with Extended Finite Elements'
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 38
year: '2019'
...