{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T16:26:52Z","timestamp":1764174412153,"version":"3.41.0"},"reference-count":39,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,7,20]],"date-time":"2017-07-20T00:00:00Z","timestamp":1500508800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2017,8,31]]},"abstract":"<jats:p>We introduce a lightweight structure optimization approach for problems in which there is uncertainty in the force locations. Such uncertainty may arise due to force contact locations that change during use or are simply unknown a priori. Given an input 3D model, regions on its boundary where arbitrary normal forces may make contact, and a total force-magnitude budget, our algorithm generates a minimum weight 3D structure that withstands any force configuration capped by the budget. Our approach works by repeatedly finding the most critical force configuration and altering the internal structure accordingly. A key issue, however, is that the critical force configuration changes as the structure evolves, resulting in a significant computational challenge. To address this, we propose an efficient critical instant analysis approach. Combined with a reduced order formulation, our method provides a practical solution to the structural optimization problem. We demonstrate our method on a variety of models and validate it with mechanical tests.<\/jats:p>","DOI":"10.1145\/3072959.3073626","type":"journal-article","created":{"date-parts":[[2017,7,21]],"date-time":"2017-07-21T12:24:07Z","timestamp":1500639847000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":24,"title":["Lightweight structure design under force location uncertainty"],"prefix":"10.1145","volume":"36","author":[{"given":"Erva","family":"Ulu","sequence":"first","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James","family":"Mccann","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Levent Burak","family":"Kara","sequence":"additional","affiliation":[{"name":"Carnegie Mellon University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,7,20]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601157"},{"volume-title":"Introduction to optimization of structures","author":"Banichuk Nikolai Vladimirovich","key":"e_1_2_2_2_1"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01650949"},{"volume-title":"Bends\u00f8e and Ole Sigmund","year":"2003","author":"Martin","key":"e_1_2_2_4_1"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778800"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461994"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00373-5"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.09.021"},{"volume-title":"Geodesics in Heat: A New Approach to Computing Distance Based on Heat Flow. ACM Trans. Graph. 32","year":"2013","author":"Crane Keenan","key":"e_1_2_2_9_1"},{"key":"e_1_2_2_10_1","unstructured":"Ga\u00cbl Guennebaud Beno\u00eet Jacob and others. 2010. Eigen v3. http:\/\/eigen.tuxfamily.org. (2010).  Ga\u00cbl Guennebaud Beno\u00eet Jacob and others. 2010. Eigen v3. http:\/\/eigen.tuxfamily.org. (2010)."},{"volume-title":"Hibbeler and Tan Kiang","year":"2015","author":"Russell","key":"e_1_2_2_11_1"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruc.2004.09.005"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01836562"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/2980179.2982436"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-012-0780-x"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719628"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601168"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-015-1109-8"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766955"},{"volume-title":"Wright","year":"2006","author":"Nocedal Jorge","key":"e_1_2_2_20_1"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766937"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2010.03.010"},{"key":"e_1_2_2_23_1","unstructured":"PolyJet2017. PolyJet Materials Data Sheet. (2017). http:\/\/www.stratasys.com\/materials.  PolyJet2017. PolyJet Materials Data Sheet. (2017). http:\/\/www.stratasys.com\/materials."},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461957"},{"volume-title":"Convex Analysis","author":"Rockafellar R. Tyrell","key":"e_1_2_2_25_1","doi-asserted-by":"crossref","DOI":"10.1515\/9781400873173"},{"volume-title":"Eighteenth Annual Solid Freeform Fabrication Symposium. 402--415","year":"2007","author":"Rosen David W","key":"e_1_2_2_26_1"},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/2766926"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461979"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566580"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185544"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7403(68)90021-0"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.4030998"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/2542355.2542361"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/2508363.2508382"},{"key":"e_1_2_2_35_1","doi-asserted-by":"publisher","DOI":"10.1145\/2699648"},{"key":"e_1_2_2_36_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2010.01655.x"},{"key":"e_1_2_2_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2015.03.012"},{"key":"e_1_2_2_38_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073219"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461967"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073626","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3072959.3073626","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:37:23Z","timestamp":1750217843000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3072959.3073626"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7,20]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,8,31]]}},"alternative-id":["10.1145\/3072959.3073626"],"URL":"https:\/\/doi.org\/10.1145\/3072959.3073626","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"type":"print","value":"0730-0301"},{"type":"electronic","value":"1557-7368"}],"subject":[],"published":{"date-parts":[[2017,7,20]]},"assertion":[{"value":"2017-07-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}