Tillförlitlig dimensionering mot utmattning UTMIS Vårmöte 2018 på Högskolan i Skövde

Transcription

1 Tillförlitlig dimnsionring mot utmattning UTMIS Vårmöt 2018 på Högskolan i Skövd Rami Mansour & Mårtn Olsson KTH Hållfasthtslära mart@kth.s ramimans@kth.s

2 Introduction Ovrviw of rliabl dsign Traditional safty factor and probability of failur Topology optimization with fatigu constraints and casting dfcts

3 Ovrviw of rliabl dsign Stp 1: Chas th rd spot Whr is it xpctd to hav fatigu failur for th givn dsign? Stp 5 Stp 2 Stp 3 Stp 4 Stp 1

4 Ovrviw of rliabl dsign Stp 2: Explor th dsign spac Whr is it xpctd to hav failur for diffrnt dsign choics dfind by variabls x 1 and x 2? Accurat surrogat modls Efficint sampling stratgis Stp 5 Stp 2 Stp 3 Stp 4 Stp 1

5 Ovrviw of rliabl dsign Stp 3: Optimization Choos x 1 and x 2 so that wight is minimizd whil avoiding failur Efficint optimization algorithms Global solutions mthods Stp 5 Stp 2 Stp 3 Stp 4 Stp 1

6 Ovrviw of rliabl dsign Stp 4: Probabilistic dsign: x - uncrtain If x 1 and x 2 ar uncrtain, a probability of failur P f is always prsnt. Computation of P f Stp 1 Stp 2 Stp 3 Stp 4 Stp 5

7 Ovrviw of rliabl dsign Stp 5: Rliability-basd dsign optimization (RBDO) Choos man valus of x 1 and x 2 so that wight is minimizd whil limiting th probability of failur P f Stp 1 Stp 2 Stp 3 Stp 4 Stp 5

8 Safty factor and probability of failur Th sprad in loads, matrial paramtrs and gomtrical dimnsions is not takn into account. Dimnsion th structur so that an objctiv, i.. wight, is minimizd with th constraint that th strss do not xcd an allowd valu. Dsign variabls: Cross sctional ara x i Rquirmnt: strss in ach bar < 200 Mpa. Safty factor =1!

9 Safty factor and probability of failur In rality variabls hav a crtain sprad. Th dtrministic solution givs for th activ constraints a probability of th strss xcding th allowd valu of 50 %. Man valus Random input Random output

10 Safty factor and probability of failur Rquirmnt: strss in ach bar < 200/1.1 Mpa Safty factor =1.1 Using a safty factor 1.1 yilds a probability of failur of 0.1% Highr cross sctional aras x Lowr strss

11 Safty factor and probability of failur Each safty factor corrsponds to a probability of failur in bar 8 Safty Factor Probability of failur i bar Goal: Dimnsion th structur so that an objctiv, i.. wight, is minimizd with th constraint that th probability of th strss xcding an allowd valu is limitd.

12 Safty factor and probability of failur 1) W nd approximat probability dnsity function of input. 2) Th program nd to b fast and convrg.

13 Safty factor and probability of failur g x x Strngth Strss, 1 2

14 Safty factor and probability of failur N = 10 5 FE-runs at 7 hours ach => 80 yars to comput P f g Strngth Strss x, x 1 2 Failur

15 Safty factor and probability of failur g Strngth Strss x, x 1 2 Failur Implicitly known, FE P f x, x dx dx f X1, X g x, x Explicitly known

16 Application to fatigu problms Failur Strss,, P P x x f x x dx dx 1 2 f f,fatigu 1 2 XX Implicitly known, FE Explicitly known

17 Application to fatigu problm HCF-prdiction for P f,fatigu Matrial paramtrs Componnt gomtry & loading FEcomputations HCF-modl Fatigu tsts Fatigu risk for givn dsign Courtsy of GKN W do: Modls and mthods to find th fatigu risk + rquirmnts on tsting and computations

18 Application to fatigu problm HCF-prdiction for P f,fatigu HCF-rsarch: Modls for fatigu that - ar fully FEM-adaptd - incud strss and volum - includ an ffctiv fatigu strss fild SV-plot

19 Application to fatigu problm HCF-prdiction for P f,fatigu Assumd dfcts in th matrial Wakst link: Proposd volum mthod: x y

20 Rliabl fatigu dsign - dfinition Comput total probability of fatigu failur Pf Pf,fatigu Strss x fx x dx Th conditional probability of fatigu for a known dsign and load Distribution of dsign variabls Goal: Constraint on P f and optimiz wight = RBDO, Rliability Basd Dsign Optimization (stp 5)

21 Topology optimization with fatigu constraints and casting considrations Ausfrritic AB -Intgrat fatigu constraints and casting considrations (porosity distribution) dirctly in th topology optimization. -Dvlopmnt of mthodology to b usd by industrial partnrs

22 Solution stratgy Topology optimization with fatigu constraints and casting considration Altair Solidthinking solution 1 - Topology Optimization with Inspir 2 - Fatigu Simulation with ncod DsignLif 3 - Casting Simulation with Click2Cast LighTrain solution Topology optimization with fatigu constraint and porosity distribution. If succssful, to b implmntd in commrcial softwar.

23 Topology optimization in commrcial softwar Applid xtrnal forcs on nods Nodal displacmnt Minimiz complianc of structur subjct to volum rquirmnt Dsign variabls min x min x f u x s.t V V x x x max rq Whr: u 1 K f Stiffnss matrix

24 Topology optimization in commrcial softwar min s.t x x N 1 0,1 f u x vx V rq Whr: N 1 u xk f 1 v x k Volum of lmnt Rlativ dnsity of lmnt Stiffnss matrix of lmnt Minimiz complianc of structur subjct to volum rquirmnt NOT POSSIBLE TO SOLVE

25 Topology optimization in commrcial softwar min s.t 0 x x N 1 1 f u x v x q V rq Whr: N 1 q u x k f 1 Pnalty paramtr Typically q= 3 v x k Volum of lmnt Rlativ dnsity of lmnt Stiffnss matrix of lmnt POSSIBLE TO SOLVE Minimiz complianc of structur subjct to volum rquirmnt

26 Topology optimization in commrcial softwar Minimiz mass subjct to strss constraint min x s.t N 1 max 0 x 1 Whr: T σ m x σ 1 N u xk f 1 rq m x mass of lmnt Strss in lmnt Rlativ dnsity of lmnt Cu x y xy NOT POSSIBLE TO SOLVE Matrial

27 Topology optimization in commrcial softwar Minimiz mass subjct to strss constraint min x N 1 1/ p s.t N p v 1 0 x 1 Whr: T mx σ σ 1 N u xk f 1 rq m x mass of lmnt Strss in lmnt Rlativ dnsity of lmnt Cu x y xy POSSIBLE TO SOLVE Matrial

28 Probability of fatigu failur: Wakst link modl Probability of failur: p f 1 1 xp V rf V u dv Dfin Equivalnt Strss: qu 1 V rf V dv 1 T σ p f qu 1 xp u, u Wibull scal and shap paramtrs

29 Topology optimization with fatigu constraint Finit lmnt discrtisation: N qu dv v V rf V V rf 1 Global strss in strss-constraind topology optimization: N 1 v p 1 p Th global strss in strss-constraind topology optimization is qual to th quivalnt strss (V rf = 1). Rquirmnt of fatigu failur: 1 ln 1 p f p f,rq qu u p f,rq

30 Topology optimization with fatigu constraint min x N 1 1/ 1 u p f,rq s.t N v 1 ln 1 0 x 1 Whr: T mx σ Minimiz mass subjct to strss constraint 1 N u xk f 1 σ Cu x y xy Matrial m x mass of lmnt Strss in lmnt Rlativ dnsity of lmnt

31 Solution stratgy Topology optimization with fatigu constraints and casting considration Altair Solidthinking solution 1 - Topology Optimization with Inspir 2 - Fatigu Simulation with ncod DsignLif 3 - Casting Simulation with Click2Cast LighTrain solution Topology optimization with fatigu constraint and porosity distribution. If succssful, to b implmntd in commrcial Softwar.

32 How to includ porosity distribution in fatigu constraints & topology optimization?

33 TACK!