Column Optimization using a Direct Search Method

Transcription

1 Iteratoal Joural o Iovatos Egeerg ad Tehology (IJIET olum tmzato usg a ret Searh Method Jagr Sgh eartmet o vl Egeerg, GNE, Ludhaa, Pua, Ida Soa huta eartmet o vl Egeerg, AIET, Jaladhar, Pua, Ida Arat: olums are a mortat rutural omoet ay gve ramed ruture, ad otrute suatally towards ts total o. The dea o olum otmzato thereore lays a mortat role rgg dow the overall o o ruture. The udy resets oe o the dret searh methods - omlex Iteratve Method - or mmum o desg o reored orete olums. o o a R olum otutes the o o orete as well as eel, whh are uto o ts ross-setoal dmesos ad orresodg eel area. I the urret udy oly two deedet desg varales, amely rato o deth o eutral axs to deth o olum k ad eretage area o logtudal reoremet have ee osdered. Remag desg varales were made deedet o these two varales. omlex Iteratve Method, eg a gradet ree method was adoted to te ts eey. arous olums were osdered or desg wth eouragg results. The aer llurates alato o the method wth a examle rolem. Keywords: tmzato, omlex Iteratve Method, R olum I. INTRUTIN The am o devsg etter desg solutos whle satsyg saety ad erormae orats at lea o, s ot a ew oe. From tme mmemoral a egeer has vegated several alteratves ad hose the e amog these. A desg roess has always ee a roess o hoe whh the desger s tuto ad exeree layed a mortat role. But the o ad soal mortae o rutures ult owadays has reased so muh that t has eome mossle to rely exlusvely o the tuto ad exeree o egeers. The eed to reate oetve methods o eetve otmum desg has ee the rmary ause o the rad develomet o rutural otmzato tehques (Mad, Brgg otmzato tehques oely ad osetly to desg rate makes t ossle or a desger to rodue otmal rutures. olums are a mortat rutural omoet ay gve ramed ruture, ad otrute suatally towards ts total o. The oet o olum otmzato thus lays a sgat role redug the overall o o ruture. Ths aer resets a smle ad easy to aly tehque or otag otmum olum desg arameters. II. FRMULATIN F PTIMIZATIN PRBLEM The o o a reored orete olum oss o the o o orete ad eel. Ths a e otaed usg the ollowg relatosh: (1 where = total o o olum = o o eel er ut volume o eel = volume o eel the olum = o o orete (ludg ormwork er ut volume o orete = volume o orete the olum vdg Eq. 1 y, we get olume 5 Issue 1 Feruary ISSN:

2 Iteratoal Joural o Iovatos Egeerg ad Tehology (IJIET Puttg (2 G, where G = gross volume o olum Eq. 2 eomes ( G» 1 G (3 Takg oetve uto Z ad o rato, Eq. 3 eomes Se Z ( 1 G (4 s a oat arameter or a gve lae, the oetve uto Z reresets total o o olum whh we eed to mmze. Followg orats (IS 456: 2000 were osdered whle ormulatg the otmzato rolem: orats or axal load aaty ad momet aaty o the olum orats or mmum ad maxmum logtudal reoremet the olum orat or mmum umer o logtudal ars v orat or maxmum erheral dae etwee logtudal ars v orat or mmum ad maxmum wdth ad maxmum deth o olum Wthout volatg ay o the orats, olum otmzato rolem oss determato o deth, wdth, eretage area o logtudal reoremet ad lateral te sag s suh that the o o olum s mmzed. Mathematally, ths otmzato rolem a e ated as Mmze Z ( 1 G Suet to 0.36 k k ( s P (5 2 y 0.36 k k ( k ( s M k ( ( (8 d 300 (9 4 Max.( B1, B2, B3, B (10 (11 1 (12 1 III. METH F SLUTIN The otmzato rolem was solved usg omlex Iteratve Method. The method essetally osed evaluatg the oetve uto at r ( s+1, where s = umer o deedet desg varales easle vertes o olume 5 Issue 1 Feruary ISSN:

3 Iteratoal Joural o Iovatos Egeerg ad Tehology (IJIET a omlex (losed gure ad teratvely movg towards the otmum ot y suessve modatos. I eah e the vertex X L whh yelded the large value o oetve uto (wor vertex was relaed y a ew vertex X N alog the le og the wor vertex ad etrod o the remag vertes. It was mortatly assured that the ew vertex dd ot volate ay o the orats ad gave a smaller oetve uto value tha the wor vertex. The ew vertex was otaed as X N X (X X L (13 where β > 0 X = etrod o all vertes exet X L X = wor vertex L Whe the releted ot X N volated ay o the orats, t was moved hal way towards the etrod y redug β-value y hal, utl t eame easle. I ths way, the omlex was rolled over ad over towards the mmum, remag wth the easle sae. The roess was oed whe the devato o uto value at the vertes rom the etrod eame suetly small (β < A grahal reresetato o the method s show Fgure 1. I the reset udy, value o s (umer o deedet desg varales was take as two. Rato o deth o eutral axs to deth o olum k ad eretage area o logtudal reoremet were take as deedet desg varales. Remag desg varales lke ross-setoal dmesos ad were otaed rom these two values usg ther relatosh wth eah other (Eq. 5 ad Eq. 6. Numer o logtudal eel ars the olum was take as 16; equally dvded o our sdes. value k value Seres1 Seres2 Seres3 Seres4 Seres5 Seres6 Seres7 Seres8 Seres9 Seres10 Seres11 Seres12 Seres13 Seres14 Seres15 Seres16 Seres17 Seres18 Seres19 Seres20 Seres21 Seres22 Fgure 1. Grahal reresetato o omlex Iteratve Method as aled to olum otmzato I. SELETIN F INITIAL PINTS AN THER PARAMETERS The umer o vertes (r the omlex was take as 3,.e. equal to s+1 (s =2. Thus 3 easle artg desgs requred to tate the otmzato roess were seleted y osderg ovetoal olum desg orresodg olume 5 Issue 1 Feruary ISSN:

4 Iteratoal Joural o Iovatos Egeerg ad Tehology (IJIET to 3 deret values o eretage o logtudal eel, amely 2.1, 2.5 ad 3.0 (lyg wth the ermssle rage o 0.8 to 4.0. erta other arameters lke o rato (α, grades o orete ad eel ( k ad y, olum heght (h ad olum loads were gve at the egg.. EXAMPLE The gve set o loads or the olum was take as: Axal load = 1011 kn ad Momet = 137 kn-m. olum heght was 3.5 m. Grades o orete ad eel were take as M30 ad Fe415 resetvely. The o rato was take as 85. The otmum desg arameters vz. eretage o logtudal eel, ross-setoal dmesos ad sag o lateral tes, were determed ad are reseted Tale 1. Numer o teratve yles requred or otmzato has also ee dated the same tale. Peretage o logtudal eel dereased rom 2.0 % to 0.8 % ad oetve uto (Z redued rom to , datg a suatal otmzato level o 36.1 %. I. NLUSINS 1. The otmzato results otaed y the use o omlex Iteratve Method (ret Searh Method or desg o reored orete olums were very eouragg ad aordgly ts sutalty ads roved. 2 Although oth reduto eel area ad ross-setoal area o olum otrutes towards otmzato o reored orete olums, the reduto eel area lays a greater role otmzato as omared to reduto ross-setoal area o olums. Tale-1 omarso o ovetoal ad otmum desg values Parameter ovetoal desg tmum desg Logtudal eel ( 2. 0 % 0.8 % eth ( 480 mm 900 mm Wdth ( 310 mm 150 mm Te sag (8 mm da. ar 192 mm 150 mm etve uto (Z Numer o teratve yles - 48 II. LIST F SYMBLS A = area o reoremet the th row B, 1 B, 2 B, 3 B = wdth o our eams, amely B 4 1,B2,B3 adb4 that are attahed to the gve olum = wdth o olum = wdth o olum = wdth o olum 1, whh les mmedately eeath olum 1 d = maxmum erheral dae amog logtudal ars o the olum = deth o olum = deth o olum = deth o olum 1, whh les mmedately eeath olum 1 olume 5 Issue 1 Feruary ISSN:

5 Iteratoal Joural o Iovatos Egeerg ad Tehology (IJIET = ress orete at the level o th row o reoremet k = harater regth o orete s = ress the th row o reoremet, omresso eg ove ad teso eg egatve k = deth o eutral axs rom extreme omresso er M P y = atual value o edg momet as aled o the olum = umer o rows o reoremet = eretage area o logtudal reoremet 100 A = eretage area o eel the th row o reoremet = atual value o axal load as aled o the olum = dae o the th row o reoremet eel, measured rom the etrod o the seto. It s ove towards the hghly omressed edge ad egatve towards the lea omressed edge. = dameter o logtudal ar REFERENES [1] M. J. Box, A ew method o oraed otmzato ad omarso wth other methods, omut. J., 1965, ol 8, [2] A. M. Bradt, W. zeszewsk, S. Jedo, W. Marks, S. wzarek ad Z. Wasutysk, rtera ad methods o rutural otmzato, Polsh Set Pulshers, Warszawa, [3]. am, S. Pezeshk ad G. ao, tmzato o two dmesoal rutures, J o Strutural Egeerg ASE, 1998, 124(5, [4] IS Ida adard la ad reored orete ode o rate (ourth revso Bureau o Ida Stadards, New elh. [5] U. Krsh, Multlevel otmal desg o reored orete rutures, Egeerg tmzato, 1983, 6(4, [6] K. I. Mad, tmum desg o rutures, Newes-Butterworths, Lodo, [7] H. Moharram, ad. E. Grerso, omuter automated desg o reored orete rameworks, J o Strutural Egeerg ASE, 1993, 119(7, [8]. Lee, ad J. Ah, Flexural desg o reored orete rames y geet algorthm, Joural o Strutural Egeerg, ASE, 2003, 129(6, [9]. S. Reddy, Bas rutural aalyss, Tata MGraw Hll, New elh, [10] J. Sgh ad. R. Sharma, tmal eam desg usg omlex Method, Joural o Ituto o Egeers (Ida, 2009, ol 90, [11] E. I. Taak ad P. M. Wrght, tmalty rtera method or uldg rames, J o Strutural Egeerg ASE, 1981, 107(7, olume 5 Issue 1 Feruary ISSN: