---
_id: '12643'
abstract:
- lang: eng
  text: Optimization of fiber-reinforced composite structures with nonlinear load-bearing
    behavior is a complex task that is becoming increasingly relevant in practice.
    Therefore, it is desirable to automatically determine essential influences on the
    structural behavior of fiber composite shells and stability-relevant objective
    functions and constraints in the context of structural optimization. This work
    deals with a variational approach for the derivation and computation of design
    sensitivities of elastic solid shell structures, as described in [1], and the
    extension to anisotropic layered composite structures. Design sensitivities concerning
    fiber angles and layer thicknesses are derived and quantitatively determined in
    the context of the finite ele-ment method (FEM). The anisotropic analysis model
    is founded on [2], in which a sophisti-cated solid-shell formulation based on
    reduced integration, as described in [3], is extended to discretize the composite
    with only one element over the whole thickness by means of mul-tiple integration
    points. This can be understood as a special case of equivalent-single-layer theories
    (ESLT). Examination of global stiffness and sensitivity matrices using methods
    from principal component analysis (PCA), such as singular value decomposition
    (SVD), are used to identify crucial design changes corresponding to major changes
    in the structural behavior of the composite. Results are discussed by referecne
    to a chosen numerical example.
author:
- first_name: Jan
  full_name: Liedmann, Jan
  last_name: Liedmann
- first_name: Franz-Joseph
  full_name: Barthold, Franz-Joseph
  last_name: Barthold
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
citation:
  ama: Liedmann J, Barthold FJ, Gerzen N. <i>Gradient-Based Determination of Principal
    Design Influences on Composite Structures</i>. Vol 23. Wiley; 2023. doi:<a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>
  apa: Liedmann, J., Barthold, F.-J., &#38; Gerzen, N. (2023). Gradient-based determination
    of principal design influences on composite structures. In <i>93rd Annual Meeting
    of the International Association of Applied Mathematics and Mechanics, GAMM 2023</i>
    (Vol. 23, Issue 3). Wiley. <a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>
  bjps: <b>Liedmann J, Barthold F-J and Gerzen N</b> (2023) <i>Gradient-Based Determination
    of Principal Design Influences on Composite Structures</i>. Wiley.
  chicago: 'Liedmann, Jan, Franz-Joseph Barthold, and Nikolai Gerzen. <i>Gradient-Based
    Determination of Principal Design Influences on Composite Structures</i>. <i>93rd
    Annual Meeting of the International Association of Applied Mathematics and Mechanics,
    GAMM 2023</i>. Vol. 23.   Proceedings in Applied Mathematics and Mechanics : PAMM.
    Wiley, 2023. <a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>.'
  chicago-de: 'Liedmann, Jan, Franz-Joseph Barthold und Nikolai Gerzen. 2023. <i>Gradient-based
    determination of principal design influences on composite structures</i>. <i>93rd
    Annual Meeting of the International Association of Applied Mathematics and Mechanics,
    GAMM 2023</i>. Bd. 23.   Proceedings in applied mathematics and mechanics : PAMM.
    Wiley. doi:<a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>,
    .'
  din1505-2-1: '<span style="font-variant:small-caps;">Liedmann, Jan</span> ; <span
    style="font-variant:small-caps;">Barthold, Franz-Joseph</span> ; <span style="font-variant:small-caps;">Gerzen,
    Nikolai</span>: <i>Gradient-based determination of principal design influences
    on composite structures</i>, <i>  Proceedings in applied mathematics and mechanics :
    PAMM</i>. Bd. 23 : Wiley, 2023'
  havard: J. Liedmann, F.-J. Barthold, N. Gerzen, Gradient-based determination of
    principal design influences on composite structures, Wiley, 2023.
  ieee: 'J. Liedmann, F.-J. Barthold, and N. Gerzen, <i>Gradient-based determination
    of principal design influences on composite structures</i>, vol. 23, no. 3. Wiley,
    2023. doi: <a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>.'
  mla: Liedmann, Jan, et al. “Gradient-Based Determination of Principal Design Influences
    on Composite Structures.” <i>93rd Annual Meeting of the International Association
    of Applied Mathematics and Mechanics, GAMM 2023</i>, vol. 23, no. 3, Wiley, 2023,
    <a href="https://doi.org/10.1002/pamm.202300177">https://doi.org/10.1002/pamm.202300177</a>.
  short: J. Liedmann, F.-J. Barthold, N. Gerzen, Gradient-Based Determination of Principal
    Design Influences on Composite Structures, Wiley, 2023.
  ufg: '<b>Liedmann, Jan/Barthold, Franz-Joseph/Gerzen, Nikolai</b>: Gradient-based
    determination of principal design influences on composite structures, Bd. 23, o. O.
    2023 (  Proceedings in applied mathematics and mechanics : PAMM).'
  van: 'Liedmann J, Barthold FJ, Gerzen N. Gradient-based determination of principal
    design influences on composite structures. 93rd Annual Meeting of the International
    Association of Applied Mathematics and Mechanics, GAMM 2023. Wiley; 2023. (  Proceedings
    in applied mathematics and mechanics : PAMM; vol. 23).'
conference:
  end_date: 2023-06-02
  location: Dresden
  name: 93rd Annual Meeting of the International Association of Applied Mathematics
    and Mechanics, GAMM 2023
  start_date: 2023-05-30
date_created: 2025-03-03T07:50:35Z
date_updated: 2025-06-12T13:36:04Z
department:
- _id: DEP3000
- _id: DEP3020
doi: https://doi.org/10.1002/pamm.202300177
intvolume: '        23'
issue: '3'
language:
- iso: eng
publication: 93rd Annual Meeting of the International Association of Applied Mathematics
  and Mechanics, GAMM 2023
publication_identifier:
  eissn:
  - 1617-7061
publication_status: published
publisher: Wiley
series_title: '  Proceedings in applied mathematics and mechanics : PAMM'
status: public
title: Gradient-based determination of principal design influences on composite structures
type: conference_speech
user_id: '83781'
volume: 23
year: '2023'
...
---
_id: '12801'
abstract:
- lang: eng
  text: The present contribution derives a theoretical framework for constructing
    novel geometrical constraints in the context of density-based topology optimization.
    Principally, the predefined geometrical dimensionality is enforced locally on
    the components of the optimized structures. These constraints are defined using
    the principal values (singular values) from a singular value decomposition of
    points clouds represented by elemental centroids and the corresponding relative
    density design variables. The proposed approach is numerically implemented for
    demonstrating the designing of lattice or membrane-like structures. Several numerical
    examples confirm the validity of the derived theoretical framework for geometric
    dimensionality control.
article_number: '160'
author:
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
- first_name: Thorsten
  full_name: Mertins, Thorsten
  last_name: Mertins
- first_name: Claus B. W.
  full_name: Pedersen, Claus B. W.
  last_name: Pedersen
citation:
  ama: Gerzen N, Mertins T, Pedersen CBW. Geometric dimensionality control of structural
    components in topology optimization. <i>Structural and Multidisciplinary Optimization</i>.
    2022;65(5). doi:<a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>
  apa: Gerzen, N., Mertins, T., &#38; Pedersen, C. B. W. (2022). Geometric dimensionality
    control of structural components in topology optimization. <i>Structural and Multidisciplinary
    Optimization</i>, <i>65</i>(5), Article 160. <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>
  bjps: <b>Gerzen N, Mertins T and Pedersen CBW</b> (2022) Geometric Dimensionality
    Control of Structural Components in Topology Optimization. <i>Structural and Multidisciplinary
    Optimization</i> <b>65</b>.
  chicago: Gerzen, Nikolai, Thorsten Mertins, and Claus B. W. Pedersen. “Geometric
    Dimensionality Control of Structural Components in Topology Optimization.” <i>Structural
    and Multidisciplinary Optimization</i> 65, no. 5 (2022). <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>.
  chicago-de: Gerzen, Nikolai, Thorsten Mertins und Claus B. W. Pedersen. 2022. Geometric
    dimensionality control of structural components in topology optimization. <i>Structural
    and Multidisciplinary Optimization</i> 65, Nr. 5. doi:<a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>,
    .
  din1505-2-1: '<span style="font-variant:small-caps;">Gerzen, Nikolai</span> ; <span
    style="font-variant:small-caps;">Mertins, Thorsten</span> ; <span style="font-variant:small-caps;">Pedersen,
    Claus B. W.</span>: Geometric dimensionality control of structural components
    in topology optimization. In: <i>Structural and Multidisciplinary Optimization</i>
    Bd. 65. Berlin, Springer Science and Business Media LLC (2022), Nr. 5'
  havard: N. Gerzen, T. Mertins, C.B.W. Pedersen, Geometric dimensionality control
    of structural components in topology optimization, Structural and Multidisciplinary
    Optimization. 65 (2022).
  ieee: 'N. Gerzen, T. Mertins, and C. B. W. Pedersen, “Geometric dimensionality control
    of structural components in topology optimization,” <i>Structural and Multidisciplinary
    Optimization</i>, vol. 65, no. 5, Art. no. 160, 2022, doi: <a href="https://doi.org/10.1007/s00158-022-03252-7">10.1007/s00158-022-03252-7</a>.'
  mla: Gerzen, Nikolai, et al. “Geometric Dimensionality Control of Structural Components
    in Topology Optimization.” <i>Structural and Multidisciplinary Optimization</i>,
    vol. 65, no. 5, 160, 2022, <a href="https://doi.org/10.1007/s00158-022-03252-7">https://doi.org/10.1007/s00158-022-03252-7</a>.
  short: N. Gerzen, T. Mertins, C.B.W. Pedersen, Structural and Multidisciplinary
    Optimization 65 (2022).
  ufg: '<b>Gerzen, Nikolai/Mertins, Thorsten/Pedersen, Claus B.W.</b>: Geometric dimensionality
    control of structural components in topology optimization, in: <i>Structural and
    Multidisciplinary Optimization</i> 65 (2022), H. 5.'
  van: Gerzen N, Mertins T, Pedersen CBW. Geometric dimensionality control of structural
    components in topology optimization. Structural and Multidisciplinary Optimization.
    2022;65(5).
date_created: 2025-04-16T05:58:58Z
date_updated: 2025-06-26T13:39:04Z
department:
- _id: DEP3020
doi: 10.1007/s00158-022-03252-7
external_id:
  isi:
  - '000796069200001'
intvolume: '        65'
isi: '1'
issue: '5'
keyword:
- Manufacturing constraints
- Topology optimization
- Geometric constraints
- Gradient based structural optimization
- Lattice designing
- Additive manufacturing
language:
- iso: eng
place: Berlin
publication: Structural and Multidisciplinary Optimization
publication_identifier:
  eissn:
  - 1615-147X
  issn:
  - 1615-1488
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Geometric dimensionality control of structural components in topology optimization
type: scientific_journal_article
user_id: '83781'
volume: 65
year: '2022'
...
---
_id: '12615'
author:
- first_name: Daniel
  full_name: Materna, Daniel
  id: '61906'
  last_name: Materna
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
citation:
  ama: 'Materna D, Gerzen N. Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik.
    In: Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des Landes Nordrhein-Westfalen,
    ed. <i>Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer
    Hochschulen</i>. ; 2021:84-85.'
  apa: 'Materna, D., &#38; Gerzen, N. (2021). Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik. In Ministerium für Heimat, Kommunales,  Bau und
    Gleichstellung   des Landes Nordrhein-Westfalen (Ed.), <i>Digitalisierung im Bauwesen
    - Ausbildungsinhalte nordrhein-westfälischer Hochschulen</i> (pp. 84–85).'
  bjps: '<b>Materna D and Gerzen N</b> (2021) Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik. In Ministerium für Heimat, Kommunales,  Bau und
    Gleichstellung   des Landes Nordrhein-Westfalen (ed.), <i>Digitalisierung im Bauwesen
    - Ausbildungsinhalte nordrhein-westfälischer Hochschulen</i>. Düsseldorf, pp.
    84–85.'
  chicago: 'Materna, Daniel, and Nikolai Gerzen. “Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik.” In <i>Digitalisierung im Bauwesen - Ausbildungsinhalte
    nordrhein-westfälischer Hochschulen</i>, edited by Ministerium für Heimat, Kommunales, 
    Bau und Gleichstellung   des Landes Nordrhein-Westfalen, 84–85. Düsseldorf, 2021.'
  chicago-de: 'Materna, Daniel und Nikolai Gerzen. 2021. Bauingenieurwesen: Digitales
    Bauen, Mathematik und Bauinformatik. In: <i>Digitalisierung im Bauwesen - Ausbildungsinhalte
    nordrhein-westfälischer Hochschulen</i>, hg. von Ministerium für Heimat, Kommunales, 
    Bau und Gleichstellung   des Landes Nordrhein-Westfalen, 84–85. Düsseldorf.'
  din1505-2-1: '<span style="font-variant:small-caps;">Materna, Daniel</span> ; <span
    style="font-variant:small-caps;">Gerzen, Nikolai</span>: Bauingenieurwesen: Digitales
    Bauen, Mathematik und Bauinformatik. In: <span style="font-variant:small-caps;">Ministerium
    für Heimat, Kommunales,  Bau und Gleichstellung   des Landes Nordrhein-Westfalen</span>
    (Hrsg.): <i>Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer
    Hochschulen</i>. Düsseldorf, 2021, S. 84–85'
  havard: 'D. Materna, N. Gerzen, Bauingenieurwesen: Digitales Bauen, Mathematik und
    Bauinformatik, in: Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des
    Landes Nordrhein-Westfalen (Ed.), Digitalisierung im Bauwesen - Ausbildungsinhalte
    nordrhein-westfälischer Hochschulen, Düsseldorf, 2021: pp. 84–85.'
  ieee: 'D. Materna and N. Gerzen, “Bauingenieurwesen: Digitales Bauen, Mathematik
    und Bauinformatik,” in <i>Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer
    Hochschulen</i>, Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des
    Landes Nordrhein-Westfalen, Ed. Düsseldorf, 2021, pp. 84–85.'
  mla: 'Materna, Daniel, and Nikolai Gerzen. “Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik.” <i>Digitalisierung im Bauwesen - Ausbildungsinhalte
    nordrhein-westfälischer Hochschulen</i>, edited by Ministerium für Heimat, Kommunales, 
    Bau und Gleichstellung   des Landes Nordrhein-Westfalen, 2021, pp. 84–85.'
  short: 'D. Materna, N. Gerzen, in: Ministerium für Heimat, Kommunales,  Bau und
    Gleichstellung   des Landes Nordrhein-Westfalen (Ed.), Digitalisierung im Bauwesen
    - Ausbildungsinhalte nordrhein-westfälischer Hochschulen, Düsseldorf, 2021, pp.
    84–85.'
  ufg: '<b>Materna, Daniel/Gerzen, Nikolai</b>: Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik, in: <i>Ministerium für Heimat, Kommunales,  Bau
    und Gleichstellung   des Landes Nordrhein-Westfalen (Hg.)</i>: Digitalisierung
    im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer Hochschulen, Düsseldorf
    2021,  S. 84–85.'
  van: 'Materna D, Gerzen N. Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik.
    In: Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des Landes Nordrhein-Westfalen,
    editor. Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer
    Hochschulen. Düsseldorf; 2021. p. 84–5.'
corporate_editor:
- Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des Landes Nordrhein-Westfalen
date_created: 2025-02-28T12:17:36Z
date_updated: 2025-02-28T12:57:20Z
department:
- _id: DEP3020
language:
- iso: ger
main_file_link:
- open_access: '1'
  url: https://broschuerenservice.nrw.de/aimeos/default/files?download_page=0&product_id=1556&files=5/6/56f2588e0c724f8e59c70138d169bae3.pdf
oa: '1'
page: 84-85
place: Düsseldorf
publication: Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer
  Hochschulen
publication_status: published
related_material:
  link:
  - relation: confirmation
    url: https://broschuerenservice.nrw.de/default/shop/digitalisierung-im-bauwesen-ausbildungsinhalte-nordrhein-westfalischer-hochschulen-lehre|1555
status: public
title: 'Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik'
type: book_chapter
user_id: '61906'
year: '2021'
...
---
_id: '12616'
author:
- first_name: Daniel
  full_name: Materna, Daniel
  id: '61906'
  last_name: Materna
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
citation:
  ama: 'Materna D, Gerzen N. Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik.
    In: Ministerium für Heimat, Kommunales, Bau und Gleichstellung des Landes Nordrhein-Westfalen,
    ed. <i>Digitalisierung Im Bauwesen - Forschungsinhalte Nordrhein-Westfälischer
    Hochschule</i>. ; 2021:73-74.'
  apa: 'Materna, D., &#38; Gerzen, N. (2021). Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik. In Ministerium für Heimat, Kommunales, Bau und Gleichstellung
    des Landes Nordrhein-Westfalen (Ed.), <i>Digitalisierung im Bauwesen - Forschungsinhalte
    nordrhein-westfälischer Hochschule</i> (pp. 73–74).'
  bjps: '<b>Materna D and Gerzen N</b> (2021) Bauingenieurwesen: Digitales Bauen,
    Mathematik Und Bauinformatik. In Ministerium für Heimat, Kommunales, Bau und Gleichstellung
    des Landes Nordrhein-Westfalen (ed.), <i>Digitalisierung Im Bauwesen - Forschungsinhalte
    Nordrhein-Westfälischer Hochschule</i>. Düsseldorf, pp. 73–74.'
  chicago: 'Materna, Daniel, and Nikolai Gerzen. “Bauingenieurwesen: Digitales Bauen,
    Mathematik Und Bauinformatik.” In <i>Digitalisierung Im Bauwesen - Forschungsinhalte
    Nordrhein-Westfälischer Hochschule</i>, edited by Ministerium für Heimat, Kommunales,
    Bau und Gleichstellung des Landes Nordrhein-Westfalen, 73–74. Düsseldorf, 2021.'
  chicago-de: 'Materna, Daniel und Nikolai Gerzen. 2021. Bauingenieurwesen: Digitales
    Bauen, Mathematik und Bauinformatik. In: <i>Digitalisierung im Bauwesen - Forschungsinhalte
    nordrhein-westfälischer Hochschule</i>, hg. von Ministerium für Heimat, Kommunales,
    Bau und Gleichstellung des Landes Nordrhein-Westfalen, 73–74. Düsseldorf.'
  din1505-2-1: '<span style="font-variant:small-caps;">Materna, Daniel</span> ; <span
    style="font-variant:small-caps;">Gerzen, Nikolai</span>: Bauingenieurwesen: Digitales
    Bauen, Mathematik und Bauinformatik. In: <span style="font-variant:small-caps;">Ministerium
    für Heimat, Kommunales, Bau und Gleichstellung des Landes Nordrhein-Westfalen</span>
    (Hrsg.): <i>Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer
    Hochschule</i>. Düsseldorf, 2021, S. 73–74'
  havard: 'D. Materna, N. Gerzen, Bauingenieurwesen: Digitales Bauen, Mathematik und
    Bauinformatik, in: Ministerium für Heimat, Kommunales, Bau und Gleichstellung
    des Landes Nordrhein-Westfalen (Ed.), Digitalisierung Im Bauwesen - Forschungsinhalte
    Nordrhein-Westfälischer Hochschule, Düsseldorf, 2021: pp. 73–74.'
  ieee: 'D. Materna and N. Gerzen, “Bauingenieurwesen: Digitales Bauen, Mathematik
    und Bauinformatik,” in <i>Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer
    Hochschule</i>, Ministerium für Heimat, Kommunales, Bau und Gleichstellung des
    Landes Nordrhein-Westfalen, Ed. Düsseldorf, 2021, pp. 73–74.'
  mla: 'Materna, Daniel, and Nikolai Gerzen. “Bauingenieurwesen: Digitales Bauen,
    Mathematik Und Bauinformatik.” <i>Digitalisierung Im Bauwesen - Forschungsinhalte
    Nordrhein-Westfälischer Hochschule</i>, edited by Ministerium für Heimat, Kommunales,
    Bau und Gleichstellung des Landes Nordrhein-Westfalen, 2021, pp. 73–74.'
  short: 'D. Materna, N. Gerzen, in: Ministerium für Heimat, Kommunales, Bau und Gleichstellung
    des Landes Nordrhein-Westfalen (Ed.), Digitalisierung Im Bauwesen - Forschungsinhalte
    Nordrhein-Westfälischer Hochschule, Düsseldorf, 2021, pp. 73–74.'
  ufg: '<b>Materna, Daniel/Gerzen, Nikolai</b>: Bauingenieurwesen: Digitales Bauen,
    Mathematik und Bauinformatik, in: <i>Ministerium für Heimat, Kommunales, Bau und
    Gleichstellung des Landes Nordrhein-Westfalen (Hg.)</i>: Digitalisierung im Bauwesen
    - Forschungsinhalte nordrhein-westfälischer Hochschule, Düsseldorf 2021,  S. 73–74.'
  van: 'Materna D, Gerzen N. Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik.
    In: Ministerium für Heimat, Kommunales, Bau und Gleichstellung des Landes Nordrhein-Westfalen,
    editor. Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer
    Hochschule. Düsseldorf; 2021. p. 73–4.'
corporate_editor:
- Ministerium für Heimat, Kommunales, Bau und Gleichstellung des Landes Nordrhein-Westfalen
date_created: 2025-02-28T12:23:21Z
date_updated: 2025-02-28T12:57:49Z
department:
- _id: DEP3020
language:
- iso: eng
page: 73-74
place: Düsseldorf
publication: Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer
  Hochschule
related_material:
  link:
  - relation: confirmation
    url: https://broschuerenservice.nrw.de/default/shop/digitalisierung-im-bauwesen-forschungsinhalte-nordrhein-westfalischer-hochschulen-forschung|1556
status: public
title: 'Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik'
type: book_chapter
user_id: '61906'
year: '2021'
...
---
_id: '2282'
author:
- first_name: Franz-Joseph
  full_name: Barthold, Franz-Joseph
  last_name: Barthold
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
- first_name: Wojciech
  full_name: Kijanski, Wojciech
  last_name: Kijanski
- first_name: Daniel
  full_name: Materna, Daniel
  id: '61906'
  last_name: Materna
citation:
  ama: 'Barthold F-J, Gerzen N, Kijanski W, Materna D. Efficient Variational Design
    Sensitivity Analysis. In: Neittaanmäki P, Repin S, Tuovinen T, eds. <i>Mathematical
    Modeling and Optimization of Complex Structures</i>. Springer-Verlag; 2016:229-257.'
  apa: Barthold, F.-J., Gerzen, N., Kijanski, W., &#38; Materna, D. (2016). Efficient
    Variational Design Sensitivity Analysis. In P. Neittaanmäki, S. Repin, &#38; T.
    Tuovinen (Eds.), <i>Mathematical Modeling and Optimization of Complex Structures</i>
    (pp. 229–257). Springer-Verlag.
  bjps: <b>Barthold F-J <i>et al.</i></b> (2016) Efficient Variational Design Sensitivity
    Analysis. In Neittaanmäki P, Repin S and Tuovinen T (eds), <i>Mathematical Modeling
    and Optimization of Complex Structures</i>. Springer-Verlag, pp. 229–257.
  chicago: Barthold, Franz-Joseph, Nikolai Gerzen, Wojciech Kijanski, and Daniel Materna.
    “Efficient Variational Design Sensitivity Analysis.” In <i>Mathematical Modeling
    and Optimization of Complex Structures</i>, edited by Pekka Neittaanmäki, Sergey
    Repin, and Tero Tuovinen, 229–57. Springer-Verlag, 2016.
  chicago-de: 'Barthold, Franz-Joseph, Nikolai Gerzen, Wojciech Kijanski und Daniel
    Materna. 2016. Efficient Variational Design Sensitivity Analysis. In: <i>Mathematical
    Modeling and Optimization of Complex Structures</i>, hg. von Pekka Neittaanmäki,
    Sergey Repin, und Tero Tuovinen, 229–257. Springer-Verlag.'
  din1505-2-1: '<span style="font-variant:small-caps;">Barthold, Franz-Joseph</span>
    ; <span style="font-variant:small-caps;">Gerzen, Nikolai</span> ; <span style="font-variant:small-caps;">Kijanski,
    Wojciech</span> ; <span style="font-variant:small-caps;">Materna, Daniel</span>:
    Efficient Variational Design Sensitivity Analysis. In: <span style="font-variant:small-caps;">Neittaanmäki,
    P.</span> ; <span style="font-variant:small-caps;">Repin, S.</span> ; <span style="font-variant:small-caps;">Tuovinen,
    T.</span> (Hrsg.): <i>Mathematical Modeling and Optimization of Complex Structures</i> :
    Springer-Verlag, 2016, S. 229–257'
  havard: 'F.-J. Barthold, N. Gerzen, W. Kijanski, D. Materna, Efficient Variational
    Design Sensitivity Analysis, in: P. Neittaanmäki, S. Repin, T. Tuovinen (Eds.),
    Mathematical Modeling and Optimization of Complex Structures, Springer-Verlag,
    2016: pp. 229–257.'
  ieee: F.-J. Barthold, N. Gerzen, W. Kijanski, and D. Materna, “Efficient Variational
    Design Sensitivity Analysis,” in <i>Mathematical Modeling and Optimization of
    Complex Structures</i>, P. Neittaanmäki, S. Repin, and T. Tuovinen, Eds. Springer-Verlag,
    2016, pp. 229–257.
  mla: Barthold, Franz-Joseph, et al. “Efficient Variational Design Sensitivity Analysis.”
    <i>Mathematical Modeling and Optimization of Complex Structures</i>, edited by
    Pekka Neittaanmäki et al., Springer-Verlag, 2016, pp. 229–57.
  short: 'F.-J. Barthold, N. Gerzen, W. Kijanski, D. Materna, in: P. Neittaanmäki,
    S. Repin, T. Tuovinen (Eds.), Mathematical Modeling and Optimization of Complex
    Structures, Springer-Verlag, 2016, pp. 229–257.'
  ufg: '<b>Barthold, Franz-Joseph et. al. (2016)</b>: Efficient Variational Design
    Sensitivity Analysis, in: Pekka Neittaanmäki et. al. (Hgg.): <i>Mathematical Modeling
    and Optimization of Complex Structures</i>, S. 229–257.'
  van: 'Barthold F-J, Gerzen N, Kijanski W, Materna D. Efficient Variational Design
    Sensitivity Analysis. In: Neittaanmäki P, Repin S, Tuovinen T, editors. Mathematical
    Modeling and Optimization of Complex Structures. Springer-Verlag; 2016. p. 229–57.'
date_created: 2020-05-15T07:26:12Z
date_updated: 2023-03-15T13:49:39Z
department:
- _id: DEP3020
editor:
- first_name: Pekka
  full_name: Neittaanmäki, Pekka
  last_name: Neittaanmäki
- first_name: Sergey
  full_name: Repin, Sergey
  last_name: Repin
- first_name: Tero
  full_name: Tuovinen, Tero
  last_name: Tuovinen
language:
- iso: eng
page: 229-257
publication: Mathematical Modeling and Optimization of Complex Structures
publication_identifier:
  eisbn:
  - 978-3-319-23564-6
  isbn:
  - 978-3-319-23563-9
publication_status: published
publisher: Springer-Verlag
status: public
title: Efficient Variational Design Sensitivity Analysis
type: book_chapter
user_id: '74004'
year: 2016
...
---
_id: '2315'
author:
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
- first_name: Franz-Joseph
  full_name: Barthold, Franz-Joseph
  last_name: Barthold
- first_name: S.
  full_name: Klinkel, S.
  last_name: Klinkel
- first_name: W.
  full_name: Wagner, W.
  last_name: Wagner
- first_name: Daniel
  full_name: Materna, Daniel
  id: '61906'
  last_name: Materna
citation:
  ama: Gerzen N, Barthold F-J, Klinkel S, Wagner W, Materna D. Variational sensitivity
    analysis of a non-linear solid shell element. <i>International Journal for Numerical
    Methods in Engineering</i>. 2013;96(1):29-42. doi:<a href="https://doi.org/10.1002/nme.4545">10.1002/nme.4545</a>
  apa: Gerzen, N., Barthold, F.-J., Klinkel, S., Wagner, W., &#38; Materna, D. (2013).
    Variational sensitivity analysis of a non-linear solid shell element. <i>International
    Journal for Numerical Methods in Engineering</i>, <i>96</i>(1), 29–42. <a href="https://doi.org/10.1002/nme.4545">https://doi.org/10.1002/nme.4545</a>
  bjps: <b>Gerzen N <i>et al.</i></b> (2013) Variational Sensitivity Analysis of a
    Non-Linear Solid Shell Element. <i>International Journal for Numerical Methods
    in Engineering</i> <b>96</b>, 29–42.
  chicago: 'Gerzen, Nikolai, Franz-Joseph Barthold, S. Klinkel, W. Wagner, and Daniel
    Materna. “Variational Sensitivity Analysis of a Non-Linear Solid Shell Element.”
    <i>International Journal for Numerical Methods in Engineering</i> 96, no. 1 (2013):
    29–42. <a href="https://doi.org/10.1002/nme.4545">https://doi.org/10.1002/nme.4545</a>.'
  chicago-de: 'Gerzen, Nikolai, Franz-Joseph Barthold, S. Klinkel, W. Wagner und Daniel
    Materna. 2013. Variational sensitivity analysis of a non-linear solid shell element.
    <i>International Journal for Numerical Methods in Engineering</i> 96, Nr. 1: 29–42.
    doi:<a href="https://doi.org/10.1002/nme.4545,">10.1002/nme.4545,</a> .'
  din1505-2-1: '<span style="font-variant:small-caps;">Gerzen, Nikolai</span> ; <span
    style="font-variant:small-caps;">Barthold, Franz-Joseph</span> ; <span style="font-variant:small-caps;">Klinkel,
    S.</span> ; <span style="font-variant:small-caps;">Wagner, W.</span> ; <span style="font-variant:small-caps;">Materna,
    Daniel</span>: Variational sensitivity analysis of a non-linear solid shell element.
    In: <i>International Journal for Numerical Methods in Engineering</i> Bd. 96 (2013),
    Nr. 1, S. 29–42'
  havard: N. Gerzen, F.-J. Barthold, S. Klinkel, W. Wagner, D. Materna, Variational
    sensitivity analysis of a non-linear solid shell element, International Journal
    for Numerical Methods in Engineering. 96 (2013) 29–42.
  ieee: N. Gerzen, F.-J. Barthold, S. Klinkel, W. Wagner, and D. Materna, “Variational
    sensitivity analysis of a non-linear solid shell element,” <i>International Journal
    for Numerical Methods in Engineering</i>, vol. 96, no. 1, pp. 29–42, 2013.
  mla: Gerzen, Nikolai, et al. “Variational Sensitivity Analysis of a Non-Linear Solid
    Shell Element.” <i>International Journal for Numerical Methods in Engineering</i>,
    vol. 96, no. 1, 2013, pp. 29–42, doi:<a href="https://doi.org/10.1002/nme.4545">10.1002/nme.4545</a>.
  short: N. Gerzen, F.-J. Barthold, S. Klinkel, W. Wagner, D. Materna, International
    Journal for Numerical Methods in Engineering 96 (2013) 29–42.
  ufg: '<b>Gerzen, Nikolai et. al. (2013)</b>: Variational sensitivity analysis of
    a non-linear solid shell element, in: <i>International Journal for Numerical Methods
    in Engineering</i> <i>96</i> (<i>1</i>), S. 29–42.'
  van: Gerzen N, Barthold F-J, Klinkel S, Wagner W, Materna D. Variational sensitivity
    analysis of a non-linear solid shell element. International Journal for Numerical
    Methods in Engineering. 2013;96(1):29–42.
date_created: 2020-05-15T07:51:49Z
date_updated: 2023-03-15T13:49:39Z
department:
- _id: DEP3020
doi: 10.1002/nme.4545
extern: '1'
intvolume: '        96'
issue: '1'
language:
- iso: eng
main_file_link:
- url: https://onlinelibrary.wiley.com/doi/full/10.1002/nme.4545
page: 29-42
publication: International Journal for Numerical Methods in Engineering
publication_status: published
status: public
title: Variational sensitivity analysis of a non-linear solid shell element
type: journal_article
user_id: '74004'
volume: 96
year: 2013
...
---
_id: '2316'
author:
- first_name: Nikolai
  full_name: Gerzen, Nikolai
  id: '76704'
  last_name: Gerzen
- first_name: Daniel
  full_name: Materna, Daniel
  id: '61906'
  last_name: Materna
- first_name: Franz-Joseph
  full_name: Barthold, Franz-Joseph
  last_name: Barthold
citation:
  ama: Gerzen N, Materna D, Barthold F-J. The inner structure of sensitivities in
    nodal based shape optimisation. <i>Computational Mechanics</i>. 2012;49(3):379-396.
  apa: Gerzen, N., Materna, D., &#38; Barthold, F.-J. (2012). The inner structure
    of sensitivities in nodal based shape optimisation. <i>Computational Mechanics</i>,
    <i>49</i>(3), 379–396.
  bjps: <b>Gerzen N, Materna D and Barthold F-J</b> (2012) The Inner Structure of
    Sensitivities in Nodal Based Shape Optimisation. <i>Computational Mechanics</i>
    <b>49</b>, 379–396.
  chicago: 'Gerzen, Nikolai, Daniel Materna, and Franz-Joseph Barthold. “The Inner
    Structure of Sensitivities in Nodal Based Shape Optimisation.” <i>Computational
    Mechanics</i> 49, no. 3 (2012): 379–96.'
  chicago-de: 'Gerzen, Nikolai, Daniel Materna und Franz-Joseph Barthold. 2012. The
    inner structure of sensitivities in nodal based shape optimisation. <i>Computational
    Mechanics</i> 49, Nr. 3: 379–396.'
  din1505-2-1: '<span style="font-variant:small-caps;">Gerzen, Nikolai</span> ; <span
    style="font-variant:small-caps;">Materna, Daniel</span> ; <span style="font-variant:small-caps;">Barthold,
    Franz-Joseph</span>: The inner structure of sensitivities in nodal based shape
    optimisation. In: <i>Computational Mechanics</i> Bd. 49 (2012), Nr. 3, S. 379–396'
  havard: N. Gerzen, D. Materna, F.-J. Barthold, The inner structure of sensitivities
    in nodal based shape optimisation, Computational Mechanics. 49 (2012) 379–396.
  ieee: N. Gerzen, D. Materna, and F.-J. Barthold, “The inner structure of sensitivities
    in nodal based shape optimisation,” <i>Computational Mechanics</i>, vol. 49, no.
    3, pp. 379–396, 2012.
  mla: Gerzen, Nikolai, et al. “The Inner Structure of Sensitivities in Nodal Based
    Shape Optimisation.” <i>Computational Mechanics</i>, vol. 49, no. 3, 2012, pp.
    379–96.
  short: N. Gerzen, D. Materna, F.-J. Barthold, Computational Mechanics 49 (2012)
    379–396.
  ufg: '<b>Gerzen, Nikolai et. al. (2012)</b>: The inner structure of sensitivities
    in nodal based shape optimisation, in: <i>Computational Mechanics</i> <i>49</i>
    (<i>3</i>), S. 379–396.'
  van: Gerzen N, Materna D, Barthold F-J. The inner structure of sensitivities in
    nodal based shape optimisation. Computational Mechanics. 2012;49(3):379–96.
date_created: 2020-05-15T07:51:51Z
date_updated: 2023-03-15T13:49:39Z
department:
- _id: DEP3020
extern: '1'
intvolume: '        49'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/article/10.1007%2Fs00466-011-0648-8
page: 379-396
publication: Computational Mechanics
publication_status: published
status: public
title: The inner structure of sensitivities in nodal based shape optimisation
type: journal_article
user_id: '74004'
volume: 49
year: 2012
...