{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T19:22:35Z","timestamp":1768677755126,"version":"3.49.0"},"reference-count":34,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2012,11,1]],"date-time":"2012-11-01T00:00:00Z","timestamp":1351728000000},"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":[[2012,11]]},"abstract":"<jats:p>In the design of buildings, structural analysis is traditionally performed after the aesthetic design has been determined and has little influence on the overall form. In contrast, this paper presents an approach to guide the form towards a shape that is more structurally sound. Our work is centered on the study of how variations of the geometry might improve structural stability. We define a new measure of structural soundness for masonry buildings as well as cables, and derive its closed-form derivative with respect to the displacement of all the vertices describing the geometry. We start with a gradient descent tool which displaces each vertex along the gradient. We then introduce displacement operators, imposing constraints such as the preservation of orientation or thickness; or setting additional objectives such as volume minimization.<\/jats:p>","DOI":"10.1145\/2366145.2366178","type":"journal-article","created":{"date-parts":[[2012,11,14]],"date-time":"2012-11-14T20:36:17Z","timestamp":1352925377000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":58,"title":["Structural optimization of 3D masonry buildings"],"prefix":"10.1145","volume":"31","author":[{"given":"Emily","family":"Whiting","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"Hijung","family":"Shin","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"Robert","family":"Wang","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"John","family":"Ochsendorf","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"Fr\u00e9do","family":"Durand","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]}],"member":"320","published-online":{"date-parts":[[2012,11]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.09.032"},{"key":"e_1_2_2_2_1","unstructured":"Allen E. and Zalewski W. 2009. Form and Forces: Designing Efficient Expressive Structures. Wiley.  Allen E. and Zalewski W. 2009. Form and Forces: Designing Efficient Expressive Structures . Wiley."},{"key":"e_1_2_2_3_1","volume-title":"Proc. CAAD Futures Conf., 231--244","author":"Attar R.","unstructured":"Attar , R. , Aish , R. , Stam , J. , Brinsmead , D. , Tessier , A. , Glueck , M. , and Khan , A . 2009. Physics-based generative design . In Proc. CAAD Futures Conf., 231--244 . Attar, R., Aish, R., Stam, J., Brinsmead, D., Tessier, A., Glueck, M., and Khan, A. 2009. Physics-based generative design. In Proc. CAAD Futures Conf., 231--244."},{"key":"e_1_2_2_4_1","first-page":"4","article-title":"Embedded rationality: A unified simulation framework for interactive form-finding","volume":"8","author":"Attar R.","year":"2010","unstructured":"Attar , R. , Aish , R. , Stam , J. , Brinsmead , D. , Tessier , A. , Glueck , M. , and Khan , A. 2010 . Embedded rationality: A unified simulation framework for interactive form-finding . Intl. Journal of Architectural Computing 8 , 4 (December), 399--418. Attar, R., Aish, R., Stam, J., Brinsmead, D., Tessier, A., Glueck, M., and Khan, A. 2010. Embedded rationality: A unified simulation framework for interactive form-finding. Intl. Journal of Architectural Computing 8, 4 (December), 399--418.","journal-title":"Journal of Architectural Computing"},{"key":"e_1_2_2_5_1","volume-title":"Nonlinear Programming","author":"Bertsekas D. P.","unstructured":"Bertsekas , D. P. 1995. Nonlinear Programming , second ed. Athena Scientific , ch. 2.1.1. Bertsekas, D. P. 1995. Nonlinear Programming, second ed. Athena Scientific, ch. 2.1.1."},{"key":"e_1_2_2_6_1","unstructured":"Bertsimas D. and Tsitsiklis J. N. 1997. Introduction to Linear Optimization. Athena Scientific.   Bertsimas D. and Tsitsiklis J. N. 1997. Introduction to Linear Optimization . Athena Scientific."},{"key":"e_1_2_2_7_1","first-page":"167","article-title":"Thrust network analysis: a new methodology for three-dimensional equilibrium","volume":"48","author":"Block P.","year":"2007","unstructured":"Block , P. , and Ochsendorf , J. 2007 . Thrust network analysis: a new methodology for three-dimensional equilibrium . Journal Intl. Assoc. for Shell and Spatial Structures 48 , 3, 167 -- 173 . Block, P., and Ochsendorf, J. 2007. Thrust network analysis: a new methodology for three-dimensional equilibrium. Journal Intl. Assoc. for Shell and Spatial Structures 48, 3, 167--173.","journal-title":"Journal Intl. Assoc. for Shell and Spatial Structures"},{"key":"e_1_2_2_8_1","volume-title":"-P","author":"Delfour M. C.","year":"2001","unstructured":"Delfour , M. C. , and Zol\u00e9sio , J . -P . 2001 . Shapes and Geometries: Analysis, Differential Calculus, and Optimization. SIAM. Delfour, M. C., and Zol\u00e9sio, J.-P. 2001. Shapes and Geometries: Analysis, Differential Calculus, and Optimization. SIAM."},{"key":"e_1_2_2_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778782"},{"key":"e_1_2_2_10_1","volume-title":"Practical methods of optimization","author":"Fletcher R.","unstructured":"Fletcher , R. 1987. Practical methods of optimization , second ed. John Wiley & Sons , New York . Fletcher, R. 1987. Practical methods of optimization, second ed. John Wiley & Sons, New York."},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531339"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/218380.218443"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00371-002-0189-4"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360674"},{"key":"e_1_2_2_15_1","volume-title":"Numerical Methods in Sensitivity Analysis and Shape Optimization","author":"Laporte E.","unstructured":"Laporte , E. , and Le Tallec , P. 2003. Numerical Methods in Sensitivity Analysis and Shape Optimization . Birkh\u00e4user . Laporte, E., and Le Tallec, P. 2003. Numerical Methods in Sensitivity Analysis and Shape Optimization. Birkh\u00e4user."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015719"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/1141911.1141941"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620121207"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00430042"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778776"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276458"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/1360612.1360675"},{"key":"e_1_2_2_23_1","doi-asserted-by":"crossref","unstructured":"Schiftner A. and Balzer J. 2010. Statics-sensitive layout of planar quadrilateral meshes. In Advances in Architectural Geometry Springer 221--236.  Schiftner A. and Balzer J. 2010. Statics-sensitive layout of planar quadrilateral meshes. In Advances in Architectural Geometry Springer 221--236.","DOI":"10.1007\/978-3-7091-0309-8_16"},{"key":"e_1_2_2_24_1","volume-title":"Proc. ACSA Technology Conference: The Intersection of Design and Technology, 87--92","author":"Shea K.","year":"2000","unstructured":"Shea , K. 2000 . EifForm: a generative structural design system . In Proc. ACSA Technology Conference: The Intersection of Design and Technology, 87--92 . Shea, K. 2000. EifForm: a generative structural design system. In Proc. ACSA Technology Conference: The Intersection of Design and Technology, 87--92."},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1276377.1276479"},{"key":"e_1_2_2_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566580"},{"key":"e_1_2_2_27_1","volume-title":"Proc. Eurographics Symposium on Geometry Processing, 109--116","author":"Sorkine O.","unstructured":"Sorkine , O. , and Alexa , M . 2007. As-rigid-as-possible surface modeling . In Proc. Eurographics Symposium on Geometry Processing, 109--116 . Sorkine, O., and Alexa, M. 2007. As-rigid-as-possible surface modeling. In Proc. Eurographics Symposium on Geometry Processing, 109--116."},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/378456.378522"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/37402.37427"},{"key":"e_1_2_2_30_1","doi-asserted-by":"crossref","unstructured":"Trefethen L. N. and Bau D. 1997. Numerical Linear Algebra. SIAM ch. 19.  Trefethen L. N. and Bau D. 1997. Numerical Linear Algebra . SIAM ch. 19.","DOI":"10.1137\/1.9780898719574"},{"key":"e_1_2_2_31_1","doi-asserted-by":"publisher","DOI":"10.1145\/2185520.2185583"},{"key":"e_1_2_2_32_1","doi-asserted-by":"publisher","DOI":"10.1145\/142920.134033"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1618452.1618458"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1145\/1531326.1531341"}],"container-title":["ACM Transactions on Graphics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2366145.2366178","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2366145.2366178","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T09:34:44Z","timestamp":1750239284000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2366145.2366178"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":34,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1145\/2366145.2366178"],"URL":"https:\/\/doi.org\/10.1145\/2366145.2366178","relation":{},"ISSN":["0730-0301","1557-7368"],"issn-type":[{"value":"0730-0301","type":"print"},{"value":"1557-7368","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]},"assertion":[{"value":"2012-11-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}