Investigations of Topology and Shape of Multi-material Optimum Design of Structures

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1 Advanced Scence and Tecnology Letters Vol.141 (GST 2016), pp ttp://dx.do.org/ /astl Investgatons of Topology and Sape of Mult-materal Optmum Desgn of Structures Quoc Hoan Doan 1, Dongkyu Lee 2, Hyemn Km 3, Hyunjung Park 4, Soom Sn 5 1 Department of Arctectural Engneerng, Sejong Unversty, Seoul 05006, Korea. Emal address: doanquocoan048@gmal.com 2* Correspondng autor, Assstant Professor, Department of Arctectural Engneerng, Sejong Unversty, Seoul 05006, Korea. Emal address: dongkyulee@sejong.ac.kr 3 Department of Arctecture, Kyungnam College of Informaton & Tecnology, 4 Dvson of Arctecture, Slla Unversty 5 Researc Insttute of Industral Tecnology, Pusan Natonal Unversty Abstract. Ts study provdes an nvestgaton to evaluate te effectveness of te use of te mult constructonal materal n unt cell plate of steel grd structure. Tree dfferent steel plate types are used: SS400, SM570, and UL700. To assess te present metod, a steel grd confguraton s optmzed usng te soluton of automatc computaton of mult-materal topology optmzaton. Te dfferences between te use of combnatons of 2 materals and 3 materals n a gven steel grd plate are dscussed. Topology canges n te automatc dstrbuton of mult-materal are presented durng optmzaton procedures sowng a selectve possblty of structural desgn wen usng mult-materals. Numercal results are presented to verfy te effcency of procedure n desgnng unt cell plate of steel grd structure n partcular and arctectural engneerng n general. Keywords: nvestgaton; topology optmzaton; steel grd structure; multmateral. 1 Introducton In te case of buldng constructon, partal renforcement at basement lnked to te columns may be effcent on economc aspect and constructon perod. Te steel grd system presented n ts study s to renforce soft ground by partally resstng te load from above structure to te basement, one type of ground renforcement. It conssts of te plate members bonded on te top and bottom of te vertcal members and consttuted by te quantty of unt cells [1]. One-unt cell s produced by te combnaton of two orzontal plate members avng cross-lke sape and one vertcal column member. Tey are connected troug te jonts at te center of transverse plates. In ts study, te mult-materal topology optmzaton metod s presented to apply to unt cell orzontal plates. In te feld of topology optmzaton, mult-materal topology optmzaton s also an attractve part wc fnds te optmal dstrbuton of many dstnct materals n ISSN: ASTL Copyrgt 2016 SERSC

2 Advanced Scence and Tecnology Letters Vol.141(GST 2016) gven desgn doman. It as been takng attenton of researcers and desgners n many problems of materal scence researc and ndustral applcatons [2].In [3], a pase feld metod s descrbed for te mult-materal structural topology optmzaton wt a generalzed Can-Hllard model. Sgmund and Torquato [4] ntroduced te desgn of materals wt extreme termal expanson usng tree-pase topology optmzaton metod. In ts paper, mult-materal topology optmzaton metod based on alternatng actve pase algortm proposed by Tavakol and Mosen [5] s executed wt unt cell plates of steel grd structure. 2 Formulaton of Mult-materal Topology Optmzaton A mult-materal topology optmzaton problem could be expressed as below: mnmze : C (, U( )) A subject to : U( ) : K( ) u f mn T u Ku d V, ( 1,..., m) 0 1 ( 1,..., m) were C s general objectve functonal of topology optmzaton problem wc s an ntegral dependng on and U over desgn doman. Superscrpt descrbes te fnte dmensonal vector correspondng to eac topology feld. varables of relatve densty for pase t at te element level. mn (1) denotes desgn s te lower bound of desgn varables, e.g. = U denotes te soluton of partal dfferental equaton constrant wc s an element of every topology optmzaton problem. u and f are dsplacement vector and global load, respectvely. K s te global stffness matrx. In ts problem, A, te admssble desgn space. V s te volume fracton constrant for pase. mn 3 Defntons of Unt Module Plate of Steel Grd Structure Te steel grd structure sown n Fg. 1 [1] s consttuted by many unt cells. Te unt cell plate s analyzed usng mult-materal topology optmzaton n ts study. Its desgn doman as a square sape dvded n to fnte element mes as sown n Fg. 2. Te materal area occupes 19% of total desgn volume, and te oter s 81% of vod volume. Unty loads are put at te center pont of te plate. Ts study uses tree dfferent types of steel plate wt ascendng strengt wc are descrbed separately by color: green, blue, red s SS400, SM570, and UL700 respectvely. 242 Copyrgt 2016 SERSC

3 Advanced Scence and Tecnology Letters Vol.141 (GST 2016) Fg. 1. Steel grd structure Fg. 2. Desgn doman of plate 4 Numercal Applcatons Table 1. Materal volume of two materal test case Partcpatng materal amount (%) Test case SS400 SM570 UL700 #1 6% 13% - #2-6% 13% #3 13% - 6% Table 2. Materal volume of tree materal test case Partcpatng materal amount (%) Test case SS400 SM570 UL700 #1 11% 3% 5% #2 7% 9% 3% #3 3% 13% 3% Case #1 Case #2 Case #3 Copyrgt 2016 SERSC 243

4 Advanced Scence and Tecnology Letters Vol.141(GST 2016) SM400 SM570 UL700 Fg. 3. Optmal topologcal sape of two materal combnaton examples. Case #1 Case #2 Case #3 SM400 SM570 UL700 Fg. 4. Optmal topologcal sape of tree materal combnaton examples. Te nput parameters for two and tree materal case are sown n Table 1 and Table 2, respectvely. Te optmal topology sapes for dfferent volume of partcpatng materal of two materal and tree materal examples are sown n Fg. 3 and Fg 4, respectvely. 4 Conclusons By applyng te dfferent amount of requred materals, te dfferent topology dstrbuton of materals may be produced n te prescrbed desgn doman. Te results sow tat tere could be selectve structural desgn possblty of te use and combnaton of mult-materals wen desgners and engneers use more tan one materal for structures. Acknowledgements. Ts researc was supported by a grant (2013R1A1A ) from te Natonal Researc Foundaton of Korea (NRF) funded by te Korea government. and by Basc Scence Researc Program troug te Natonal Researc Foundaton of Korea(NRF) funded by te Mnstry of Educaton. (No. NRF- 2014R1A1A3A ) References 1. Lee, DK., Yun, HK., Km, JH., Sn, SM., Lee, DU.: Renforcement structure and metod for renforcng soft ground usng unt module of steel grd , Cerkaev, A.: Varatonal metod for optmal multmateral compostes and optmal desgn. Int J Eng Sc 2014; 83: do:ttp://dx.do.org/ /j.jengsc Copyrgt 2016 SERSC

5 Advanced Scence and Tecnology Letters Vol.141 (GST 2016) 3. Zou, S., Wang, MY.: Multmateral structural topology optmzaton wt a generalzed Can--Hllard model of multpase transton. Struct Multdscp Optm 2006;33: do: /s Sgmund, O., Torquato, S.: Desgn of materals wt extreme termal expanson usng a tree-pase topology optmzaton metod. J Mec Pys Solds 1997;45: do:ttp://dx.do.org/ /s (96) Tavakol, R., Mosen, SM.: Alternatng actve-pase algortm for multmateral topology optmzaton problems: a 115-lne MATLAB mplementaton. Struct Multdscp Optm 2014;49: do: /s Hyunda steel. Hyunda steel product gude. Korea: Group A. Albaba Group Copyrgt 2016 SERSC 245

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