[{"publisher":"Wiley","department":[{"_id":"DEP3000"},{"_id":"DEP3020"}],"conference":{"name":"93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2023","location":"Dresden","start_date":"2023-05-30","end_date":"2023-06-02"},"abstract":[{"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.","lang":"eng"}],"issue":"3","publication_status":"published","series_title":"  Proceedings in applied mathematics and mechanics : PAMM","_id":"12643","doi":"https://doi.org/10.1002/pamm.202300177","user_id":"83781","intvolume":"        23","type":"conference_speech","status":"public","author":[{"first_name":"Jan","full_name":"Liedmann, Jan","last_name":"Liedmann"},{"first_name":"Franz-Joseph","full_name":"Barthold, Franz-Joseph","last_name":"Barthold"},{"last_name":"Gerzen","first_name":"Nikolai","full_name":"Gerzen, Nikolai","id":"76704"}],"year":"2023","citation":{"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","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>, .","short":"J. Liedmann, F.-J. Barthold, N. Gerzen, Gradient-Based Determination of Principal Design Influences on Composite Structures, Wiley, 2023.","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>.","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>","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).","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.","havard":"J. Liedmann, F.-J. Barthold, N. Gerzen, Gradient-based determination of principal design influences on composite structures, Wiley, 2023.","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>.","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).","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>.","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>"},"volume":23,"title":"Gradient-based determination of principal design influences on composite structures","language":[{"iso":"eng"}],"date_updated":"2025-06-12T13:36:04Z","publication":"93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2023","publication_identifier":{"eissn":["1617-7061"]},"date_created":"2025-03-03T07:50:35Z"},{"publication_status":"published","isi":"1","publisher":"Springer Science and Business Media LLC","issue":"5","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"DEP3020"}],"intvolume":"        65","user_id":"83781","type":"scientific_journal_article","article_number":"160","doi":"10.1007/s00158-022-03252-7","_id":"12801","place":"Berlin","citation":{"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","short":"N. Gerzen, T. Mertins, C.B.W. Pedersen, Structural and Multidisciplinary Optimization 65 (2022).","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>.","havard":"N. Gerzen, T. Mertins, C.B.W. Pedersen, Geometric dimensionality control of structural components in topology optimization, Structural and Multidisciplinary Optimization. 65 (2022).","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>.","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).","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>.","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>","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>","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>."},"volume":65,"title":"Geometric dimensionality control of structural components in topology optimization","status":"public","external_id":{"isi":["000796069200001"]},"year":"2022","author":[{"first_name":"Nikolai","last_name":"Gerzen","id":"76704","full_name":"Gerzen, Nikolai"},{"full_name":"Mertins, Thorsten","first_name":"Thorsten","last_name":"Mertins"},{"last_name":"Pedersen","full_name":"Pedersen, Claus B. W.","first_name":"Claus B. W."}],"date_updated":"2025-06-26T13:39:04Z","date_created":"2025-04-16T05:58:58Z","publication_identifier":{"issn":["1615-1488"],"eissn":["1615-147X"]},"publication":"Structural and Multidisciplinary Optimization","language":[{"iso":"eng"}],"keyword":["Manufacturing constraints","Topology optimization","Geometric constraints","Gradient based structural optimization","Lattice designing","Additive manufacturing"]},{"user_id":"61906","related_material":{"link":[{"relation":"confirmation","url":"https://broschuerenservice.nrw.de/default/shop/digitalisierung-im-bauwesen-ausbildungsinhalte-nordrhein-westfalischer-hochschulen-lehre|1555"}]},"date_updated":"2025-02-28T12:57:20Z","corporate_editor":["Ministerium für Heimat, Kommunales,  Bau und Gleichstellung   des Landes Nordrhein-Westfalen"],"publication":"Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer Hochschulen","type":"book_chapter","date_created":"2025-02-28T12:17:36Z","place":"Düsseldorf","language":[{"iso":"ger"}],"_id":"12615","oa":"1","citation":{"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.","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.","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.","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.","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.","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.","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.","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).","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.","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","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.","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."},"publication_status":"published","title":"Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik","status":"public","page":"84-85","author":[{"first_name":"Daniel","full_name":"Materna, Daniel","id":"61906","last_name":"Materna"},{"first_name":"Nikolai","last_name":"Gerzen","id":"76704","full_name":"Gerzen, Nikolai"}],"year":"2021","main_file_link":[{"url":"https://broschuerenservice.nrw.de/aimeos/default/files?download_page=0&product_id=1556&files=5/6/56f2588e0c724f8e59c70138d169bae3.pdf","open_access":"1"}],"department":[{"_id":"DEP3020"}]},{"page":"73-74","status":"public","department":[{"_id":"DEP3020"}],"author":[{"id":"61906","last_name":"Materna","first_name":"Daniel","full_name":"Materna, Daniel"},{"last_name":"Gerzen","id":"76704","full_name":"Gerzen, Nikolai","first_name":"Nikolai"}],"year":"2021","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.","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.","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.","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.","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.","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.","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.","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).","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.","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.","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","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."},"title":"Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik","language":[{"iso":"eng"}],"place":"Düsseldorf","_id":"12616","date_updated":"2025-02-28T12:57:49Z","related_material":{"link":[{"relation":"confirmation","url":"https://broschuerenservice.nrw.de/default/shop/digitalisierung-im-bauwesen-forschungsinhalte-nordrhein-westfalischer-hochschulen-forschung|1556"}]},"user_id":"61906","corporate_editor":["Ministerium für Heimat, Kommunales, Bau und Gleichstellung des Landes Nordrhein-Westfalen"],"date_created":"2025-02-28T12:23:21Z","type":"book_chapter","publication":"Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer Hochschule"},{"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.","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.","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.","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","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.","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.","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.","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.","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.","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.","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.","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."},"publication_status":"published","title":"Efficient Variational Design Sensitivity Analysis","status":"public","page":"229-257","publisher":"Springer-Verlag","year":2016,"author":[{"first_name":"Franz-Joseph","full_name":"Barthold, Franz-Joseph","last_name":"Barthold"},{"last_name":"Gerzen","first_name":"Nikolai","id":"76704","full_name":"Gerzen, Nikolai"},{"last_name":"Kijanski","first_name":"Wojciech","full_name":"Kijanski, Wojciech"},{"id":"61906","first_name":"Daniel","full_name":"Materna, Daniel","last_name":"Materna"}],"department":[{"_id":"DEP3020"}],"user_id":"74004","date_updated":"2023-03-15T13:49:39Z","editor":[{"first_name":"Pekka","full_name":"Neittaanmäki, Pekka","last_name":"Neittaanmäki"},{"last_name":"Repin","first_name":"Sergey","full_name":"Repin, Sergey"},{"full_name":"Tuovinen, Tero","first_name":"Tero","last_name":"Tuovinen"}],"publication":"Mathematical Modeling and Optimization of Complex Structures","publication_identifier":{"isbn":["978-3-319-23563-9"],"eisbn":["978-3-319-23564-6"]},"type":"book_chapter","date_created":"2020-05-15T07:26:12Z","language":[{"iso":"eng"}],"_id":"2282"},{"date_created":"2020-05-15T07:51:49Z","type":"journal_article","publication":"International Journal for Numerical Methods in Engineering","intvolume":"        96","date_updated":"2023-03-15T13:49:39Z","user_id":"74004","doi":"10.1002/nme.4545","_id":"2315","language":[{"iso":"eng"}],"extern":"1","title":"Variational sensitivity analysis of a non-linear solid shell element","publication_status":"published","volume":96,"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>","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.","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.","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>.","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.","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.","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.","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>.","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>","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","short":"N. Gerzen, F.-J. Barthold, S. Klinkel, W. Wagner, D. Materna, International Journal for Numerical Methods in Engineering 96 (2013) 29–42."},"issue":"1","department":[{"_id":"DEP3020"}],"author":[{"full_name":"Gerzen, Nikolai","first_name":"Nikolai","last_name":"Gerzen","id":"76704"},{"first_name":"Franz-Joseph","last_name":"Barthold","full_name":"Barthold, Franz-Joseph"},{"last_name":"Klinkel","first_name":"S.","full_name":"Klinkel, S."},{"full_name":"Wagner, W.","last_name":"Wagner","first_name":"W."},{"last_name":"Materna","id":"61906","full_name":"Materna, Daniel","first_name":"Daniel"}],"year":2013,"main_file_link":[{"url":"https://onlinelibrary.wiley.com/doi/full/10.1002/nme.4545"}],"page":"29-42","status":"public"},{"issue":"3","author":[{"last_name":"Gerzen","id":"76704","full_name":"Gerzen, Nikolai","first_name":"Nikolai"},{"id":"61906","last_name":"Materna","full_name":"Materna, Daniel","first_name":"Daniel"},{"first_name":"Franz-Joseph","last_name":"Barthold","full_name":"Barthold, Franz-Joseph"}],"year":2012,"main_file_link":[{"url":"https://link.springer.com/article/10.1007%2Fs00466-011-0648-8"}],"department":[{"_id":"DEP3020"}],"status":"public","page":"379-396","title":"The inner structure of sensitivities in nodal based shape optimisation","extern":"1","citation":{"short":"N. Gerzen, D. Materna, F.-J. Barthold, Computational Mechanics 49 (2012) 379–396.","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","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.","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.","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.","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.","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.","havard":"N. Gerzen, D. Materna, F.-J. Barthold, The inner structure of sensitivities in nodal based shape optimisation, 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.","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.","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."},"volume":49,"publication_status":"published","_id":"2316","language":[{"iso":"eng"}],"publication":"Computational Mechanics","date_created":"2020-05-15T07:51:51Z","type":"journal_article","intvolume":"        49","user_id":"74004","date_updated":"2023-03-15T13:49:39Z"}]