{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,23]],"date-time":"2026-04-23T23:55:49Z","timestamp":1776988549292,"version":"3.51.4"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,10,12]],"date-time":"2020-10-12T00:00:00Z","timestamp":1602460800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper investigates the possibility of producing an equivalent structural behaviour of two components each consisting of a different material. This is achieved through the implementation of structural optimizations. It is assumed that the initial structure is produced by conventional injection moulding and the structure to be optimized is 3D printed. For comparison, two material pairings currently used in both processes are considered. As a structural optimization method, thickness optimizations are performed in order to change the resulting cross-section of the prototype. At the beginning, the mechanical problem is formulated analytically and methods for structural optimization are evaluated. With finite element analysis, two methods are presented, which introduce the generation of a variable thickness distribution in rib structures. The first method represents a state-of-the art optimization. Ribs are directly optimized by approximating cross-section forces and moments of the prototype rib and the initial rib. The second method represents a new approach to the optimization of thin-walled structures. Local stress distributions and resulting triaxiality states, which are approximated in an intermediate step, are analysed. A newly developed finite element structure is presented, with which it is possible to generate discrete triaxiality fields and determine the necessary local thickening. This method can be used in order to produce functional prototypes in early design stage. The substituted plastic parts are usually produced by injection moulding, which initially requires a high expenditure of time and money for tool construction. Additive manufacturing represents a solution here to accelerate the development process. However, these 3D-printed prototypes are, regarding the material properties and resulting mechanical behaviour, different to the injection-moulded ones.<\/jats:p>","DOI":"10.1093\/jcde\/qwaa069","type":"journal-article","created":{"date-parts":[[2020,9,17]],"date-time":"2020-09-17T12:38:40Z","timestamp":1600346320000},"page":"170-188","source":"Crossref","is-referenced-by-count":5,"title":["Size optimization methods to approximate equivalent mechanical behaviour in thermoplastics"],"prefix":"10.1093","volume":"8","author":[{"given":"Florian","family":"Althammer","sequence":"first","affiliation":[{"name":"Mercedes-Benz AG, Benz-Str., 71063 Sindelfingen, Germany"},{"name":"Institute for Aircraft Design, Pfaffenwaldring 31, 70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Ruf","sequence":"additional","affiliation":[{"name":"Mercedes-Benz AG, Benz-Str., 71063 Sindelfingen, Germany"},{"name":"Faculty of Mathematics and Economics, Ulm University, Helmholtzstra\u00dfe 18, 89081 Ulm, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Middendorf","sequence":"additional","affiliation":[{"name":"Institute for Aircraft Design, Pfaffenwaldring 31, 70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,10,12]]},"reference":[{"key":"2021012506512413800_bib1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-57504-8","volume-title":"Kontinuumsmechanik","author":"Altenbach","year":"2018"},{"key":"2021012506512413800_bib2","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.compstruct.2017.02.095","article-title":"Structural efficiency metrics for integrated selection of layup, material, and cross-section shape in laminated composite structures","volume":"170","author":"An","year":"2017","journal-title":"Composite Structures"},{"issue":"1","key":"2021012506512413800_bib3","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S1359-6454(99)00304-3","article-title":"Multi-objective optimization in material design and selection","volume":"48","author":"Ashby","year":"2000","journal-title":"Acta Materialia"},{"key":"2021012506512413800_bib4","volume-title":"Topology optimization: Theory, methods, and applications","author":"Bends\u00f8e","year":"2011","edition":"2nd"},{"key":"2021012506512413800_bib5","doi-asserted-by":"crossref","DOI":"10.3139\/9783446417502","volume-title":"Konstruieren mit Kunststoffen","author":"Erhard","year":"2008","edition":"4th"},{"key":"2021012506512413800_bib6","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.finel.2019.07.001","article-title":"A novel deep learning based method for the computational material design of flexoelectric nanostructures with topology optimization","volume":"165","author":"Hamdia","year":"2019","journal-title":"Finite Elements in Analysis and Design"},{"key":"2021012506512413800_bib7","article-title":"Theoretical and numerical analysis on material-stiffness characteristics for thin-walled beams on vehicles","author":"Han","year":"2011","journal-title":"Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference"},{"key":"2021012506512413800_bib8","doi-asserted-by":"crossref","first-page":"107341","DOI":"10.1016\/j.compositesb.2019.107341","article-title":"Comparison of physical and mechanical properties of PLA, ABS and nylon 6 fabricated using fused deposition modeling and injection molding","volume":"176","author":"Lay","year":"2019","journal-title":"Composites Part B: Engineering"},{"key":"2021012506512413800_bib10","doi-asserted-by":"crossref","first-page":"112477","DOI":"10.1016\/j.compstruct.2020.112477","article-title":"Robust topology optimization of thermoelastic metamaterials considering hybrid uncertainties of material property","volume":"248","author":"Li","year":"2020","journal-title":"Composite Structures"},{"key":"2021012506512413800_bib9","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/j.cma.2019.07.020","article-title":"A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets","volume":"356","author":"Li","year":"2019","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"1","key":"2021012506512413800_bib11","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0378-3758(94)90115-5","article-title":"Optimal latin-hypercube designs for computer experiments","volume":"39","author":"Park","year":"1994","journal-title":"Journal of Statistical Planning and Inference"},{"key":"2021012506512413800_bib12","volume-title":"A new theory for modelling the mass-efficiency of material, shape and form","author":"Pasini","year":"2002"},{"issue":"7","key":"2021012506512413800_bib13","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1016\/j.matdes.2006.05.028","article-title":"Shape transformers for material and shape selection of lightweight beams","volume":"28","author":"Pasini","year":"2007","journal-title":"Materials & Design"},{"issue":"4","key":"2021012506512413800_bib14","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1016\/j.tws.2003.08.001","article-title":"Causes of weight reduction effects of material substitution on constant stiffness components","volume":"42","author":"Patton","year":"2004","journal-title":"Thin-Walled Structures"},{"key":"2021012506512413800_bib15","doi-asserted-by":"crossref","first-page":"112790","DOI":"10.1016\/j.cma.2019.112790","article-title":"An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications","volume":"362","author":"Samaniego","year":"2020","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"issue":"5","key":"2021012506512413800_bib16","doi-asserted-by":"crossref","first-page":"2909","DOI":"10.1016\/j.matdes.2010.11.076","article-title":"Integrated shape and material selection for single and multi-performance criteria","volume":"32","author":"Singh","year":"2011","journal-title":"Materials & Design"},{"key":"2021012506512413800_bib17","article-title":"LS-OPT user\u2019s manual version 6","author":"Stander","year":"2019"},{"key":"2021012506512413800_bib18","volume-title":"Steifigkeit und Verformung von Kastenquerschnitten mit Verrippungen, Wanddurchbrechungen und bei Behinderung der Querschnittsverw\u00f6lbung","author":"Thum","year":"1941"},{"key":"2021012506512413800_bib19","volume-title":"Werkzeugmaschinen 2: Konstruktion und Berechnung","author":"Weck","year":"2013","edition":"8th"},{"key":"2021012506512413800_bib20","volume-title":"Leichtbau: Elemente und Konstruktion","author":"Wiedemann","year":"2007","edition":"3rd"}],"container-title":["Journal of Computational Design and Engineering"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/8\/1\/170\/36097675\/qwaa069.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/jcde\/article-pdf\/8\/1\/170\/36097675\/qwaa069.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,26]],"date-time":"2021-01-26T01:13:06Z","timestamp":1611623586000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jcde\/article\/8\/1\/170\/5920923"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,12]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,10,12]]},"published-print":{"date-parts":[[2021,1,25]]}},"URL":"https:\/\/doi.org\/10.1093\/jcde\/qwaa069","relation":{},"ISSN":["2288-5048"],"issn-type":[{"value":"2288-5048","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2021,2]]},"published":{"date-parts":[[2020,10,12]]}}}