Finite Element Based Structural Optimization by GENESIS
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1 Finie Elemen Based Srucural Opimizaion by GENESIS
2 Ouline! Design approach! Numerical Opimizaion " Advanages " Limiaions! Srucural opimizaion in GENESIS! Examples " Composie panel design opimizaion subjec o crack propagaion consrain " High Speed Civil Transpor Wing Problem! Opimizaion Errors 2
3 Design Approach! Defined design goal " Minimum weigh design: Given load, required srengh! Analyze proposed design, for accepabiliy! Change one or more design variables o see if any design improvemen can be obained.! OK, when he design is a funcion of only a few variables! More sysemaic approach needed: Numerical opimizaion 3
4 Numerical Opimizaion Advanages (Vanderplaas)! A major advanage is he reducion in design ime his is especially rue when he same compuer program can be applied o many design projecs.! Opimizaion provides a sysemaic design procedure.! We can deal wih a wide variey of design variables and consrains which are difficul o visualize using graphical or abular mehods.! Opimizaion requires a minimal amoun of humanmachine ineracion. 4
5 Numerical Opimizaion Limiaions (Vanderplaas)! Compuaional ime increases as he number of design variables increases. If one wishes o consider all possible design variables, he cos of auomaed design is ofen prohibiive.! I can seldom be guaraneed ha he opimizaion algorihm will obain he global opimum design. Therefore, i may be desirable o resar he opimizaion process from several differen poins o provide reasonable assurance of obaining he global opimum.! Because many analysis programs were no wrien wih auomaed design in mind, adapaion of hese programs o an opimizaion code may require significan reprogramming of he analysis rouines. 5
6 Srucural Opimizaion in Genesis! FEA for he iniial proposed design! Design cycle sars " Sensiiviy analysis (gradien compuaions) for he responses included in he objecive funcion and he consrains " High qualiy approximaion for he original problem and opimizaion of he approximaed problem " FEA for he new design " Convergence check, sar new design cycle if necessary! Improved Design/Opimum 6
7 Srucural Opimizaion in Genesis! DOBJ: defines objecive funcion! DCONS: defines consrains! DOPT: defines opimizaion parameers! DEQUAT: o implemen equaions in GENESIS! DTABLE: o assign values for parameers in equaions 7
8 Composie panel design opimizaion subjec o crack propagaion consrain P N y z x y 0 5" 20" P N y 2 a 20" (45/-45/90/0) s skin siffener in. Srucural design variables 8
9 Low Fideliy (LF) Model K 0 = σ 0 LF f π a Sress inensiy facor in he 0 ply Far-field sress in he 0 ply K K 0 LF 0 Q 1.0 LF Direc Opimizaion Implemened in GENESIS via is equaion uiliy 9
10 LF opimizaion 2a= 4.0 in., h= 2.5 in., N y =2500 lb./in. 45 skin blade skin blade 90 0 skin blade 0 Cycle 0 Cycle W= lb W= lb K=64,642 psi in K=105,927 psi in Cycle 2 Cycle W= lb K=101,000psi in W= lb K=99,986 psi in 10
11 High Fideliy (HF) Model K K 0 HF 0 Q 1.0 HF Direc Opimizaion Implemened in GENESIS via is equaion uiliy a σ y σ y1 σ y2 σ y3 σ ynb elemens σ n r. 125a b r 125 a y = r K 2πr 11
12 HF opimizaion 2a= 4.0 in., h= 2.5 in., N y =2500 lb./in. 45 skin blade skin blade 90 0 skin blade 0 Cycle 0 Cycle W= lb W= lb K=61,935 psi in K=104,643 psi in Cycle 2 Cycle W= lb K=101,440psi in W= lb K=99,982 psi in 12
13 High Speed Civil Transpor Wing Problem! 250-passenger! 5500 nmi. Range! Cruise Mach speed of 2.4 y Configuraion variables x! Roo chord lengh cv 3! Tip chord lengh z Leading edge radius (fixed)! In-board sweep angle cv 1 cv 4 + x! Thickness o chord raio Locaion of maximum hickness (fixed) Ouboard LE sweep (fixed) cv 2 Nacelle locaions (fixed) Wing semispan (fixed) 13
14 Alernaive o empirical weigh equaions Srucural Opimizaion! Srucural design variables " 26 skin panel hickness-plae " 12 spar cap areas-rod " 2 rib cap areas-rod! Objecive Funcion " Srucural weigh! Consrains " Sress allowable " Buckling Wing skin panel Spar caps Shear webs Rib caps 14
15 DESIGN CYCLE HISTORY! DESIGN OBJECTIVE MAXIMUM CONSTRAINT! CYCLE FUNCTION VIOLATION! %! %! %! %! %! % 15
16 Opimizaion Errors! Modeling! Trapped in a local opimum " Iniial design " Round-off errors! Convergence parameers 16
17 Opimizaion Error Srucural Opimizaions: GENESIS PC WBMW (lb.) Alpha saion WBMW (lb.) PC WBMW (lb.) Alpha saion WBMW (lb.) Config Config Perurbed iniial values differen opimizaion mehod lbs. Repairable Numerical Noise lbs. 17
18 Opimizaion Errors objecive funcion Wb E %(PC-UNIX)/PC configuraion 18
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