{"607620":{"#nid":"607620","#data":{"type":"event","title":"PhD Defense by Xiaojia Shelly Zhang","body":[{"value":"\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EPh.D. Thesis Defense Announcement\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETopology Optimization with Multiple Materials, Multiple Constraints, and Multiple Load Cases\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EBy\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EXiaojia Shelly Zhang\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EAdvisor:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Glaucio H. Paulino (CEE)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ECommittee Members:\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Eric de Sturler (Math, Virginia Tech), Dr. Alexander Shapiro (ISYE), Dr. Yang Wang (CEE),\u003C\/p\u003E\r\n\r\n\u003Cp\u003EDr. Alok Sutradhar, (MAE, Ohio State), Dr. Lucia Mirabella (Corporate Technology, Siemens Corporation)\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EDate \u0026amp; Time:\u003C\/strong\u003E Monday, July 30, 2018, 1:30PM\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003ELocation:\u003C\/strong\u003E Sustainable Education Building 122\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u003Cstrong\u003EABSTRACT\u003C\/strong\u003E\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETopology optimization is a practical tool that allows for improved structural designs. This thesis focuses\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eon developing both theoretical foundations and computational frameworks for topology optimization to\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eeffectively and efficiently handle many materials, many constraints, and many load cases. Most work in\u003C\/p\u003E\r\n\r\n\u003Cp\u003Etopology optimization has been restricted to linear material with limited constraint settings for multiple\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ematerials. To address these issues, we propose a general multi-material topology optimization formulation\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ewith material nonlinearity. This formulation handles an arbitrary number of materials with flexible material\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eproperties, features freely specified material layers, and includes a generalized volume constraint setting.\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETo efficiently handle such arbitrary constraints, we derive an update scheme that performs robust updates\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eof design variables associated with each constraint independently. The derivation is based on the\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eseparable feature of the dual problem of the convex approximated primal subproblem with respect to the\u003C\/p\u003E\r\n\r\n\u003Cp\u003ELagrange multipliers, and thus the update of design variables in each constraint only depends on the\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ecorresponding Lagrange multiplier. This thesis also presents an efficient filtering scheme, with\u003C\/p\u003E\r\n\r\n\u003Cp\u003Ereduced-order modeling, and demonstrates its application to 2D and 3D topology optimization of truss\u003C\/p\u003E\r\n\r\n\u003Cp\u003Enetworks. The proposed filtering scheme extracts valid structures, yields the displacement field without\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eartificial stiffness, and improve convergence, leading to drastically improved computational performance.\u003C\/p\u003E\r\n\r\n\u003Cp\u003ETo obtain designs under many load cases, we present a randomized approach that efficiently optimizes\u003C\/p\u003E\r\n\r\n\u003Cp\u003Estructures under hundreds of load cases. This approach only uses 5 or 6 stochastic sample load cases,\u003C\/p\u003E\r\n\r\n\u003Cp\u003Einstead of hundreds, to obtain similar optimized designs (for both continuum and truss approaches).\u003C\/p\u003E\r\n\r\n\u003Cp\u003EThrough examples using Ogden-based, bilinear, and linear materials, we demonstrate that proposed\u003C\/p\u003E\r\n\r\n\u003Cp\u003Etopology optimization frameworks with the new multi-material formulation, update scheme, and discrete\u003C\/p\u003E\r\n\r\n\u003Cp\u003Efiltering lead to a design tool that not only finds the optimal topology but also selects the proper type and\u003C\/p\u003E\r\n\r\n\u003Cp\u003Eamount of material with drastically reduced computational cost.\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n\r\n\u003Cp\u003E\u0026nbsp;\u003C\/p\u003E\r\n","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":"","field_summary_sentence":[{"value":"Topology Optimization with Multiple Materials, Multiple Constraints, and Multiple Load Cases"}],"uid":"27707","created_gmt":"2018-07-10 19:35:11","changed_gmt":"2018-07-10 19:35:11","author":"Tatianna Richardson","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2018-07-30T14:30:00-04:00","event_time_end":"2018-07-30T16:30:00-04:00","event_time_end_last":"2018-07-30T16:30:00-04:00","gmt_time_start":"2018-07-30 18:30:00","gmt_time_end":"2018-07-30 20:30:00","gmt_time_end_last":"2018-07-30 20:30:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"221981","name":"Graduate Studies"}],"categories":[],"keywords":[{"id":"100811","name":"Phd Defense"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1788","name":"Other\/Miscellaneous"}],"invited_audience":[{"id":"78771","name":"Public"},{"id":"174045","name":"Graduate students"},{"id":"78751","name":"Undergraduate students"}],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[],"email":[],"slides":[],"orientation":[],"userdata":""}}}