SHAPE DESIGN SENSITIVITY ANALYSIS OF CONTACT PROBLEM WITH FRICTION

Transcription

1 SHAPE DESIGN SENSIIIY ANALYSIS OF ONA PROBLEM WIH FRIION 7 h AIAA/NASA/USAF/ISSMO Symposium o Mulidisipliay Aalysis ad Opimiaio K.K. hoi Nam H. Kim You H. Pak ad J.S. h fo ompu-aidd Dsi Dpam of Mhaial Eii oll of Eii h Uivsiy of Iowa Iowa iy IA 54 h Uivsiy of Floida oll of Eii

2 APPROAH Aalysis Rpodui Kl Pail Mhod RKPM oa Polm - aiaioal Iqualiy Paly Mhod fo Fiioal oa DSA of aiaioal Iqualiy Maial Divaiv of oa aiaioal Foms Shap Dsi Ssiiviy Aalysis Numial Exampls of Shap Dsi Opimiaio Doo Sal Polm Widshild Blad Polm h Uivsiy of Floida oll of Eii

3 REPRODUING KERNEL PARILE MEHOD RKPM Rpodud Displam Fuio R x x; y x φ y xy dy Ω a R x x as a Dia Dla Masu oio Fuio x; y x qx Hy x Hy x [y xy x q x [qxqx q x] y x ] h Uivsiy of Floida oll of Eii N-h Od omplss Rquim Rpodui odiio R x Ω m x; y x φ xx a y xy dy! m d x x dx m x mk x k...

4 Rpodui odiio RKPM o. M x qx H H [...] Mx m m x m x. x m x m m. x x m m m. x x x x; y x H Mx H y x R x H Mx Hy x φa y xy dy Ω R x NP x; x I x φa x I xi x I I I NP Φ I xd I h Uivsiy of Floida oll of Eii

5 RKPM o. Shap Fuio Φ I x I Dpds o u oodia Whas FEA Shap Fuios Dpd o oodia of h Rf Gomy Dos No Saisfy Kok Dla Popy: Φ I x J δ IJ Laa Mulipli Mhod fo Essial B.. Π U λ ζ d D Fis-od vaiaio is Π U D λ d D λ ζ d Fo oa Polm a Di asfomaio Mhod Is Usd h al.-996 h Uivsiy of Floida oll of Eii

6 ONA PROBLEM aiaioal Iqualiy a w l w w Soluio is oaid usi a pojio P v F wh { w H Ω : w o ad w a.. o } a w: Nolia sai y fom lw: Load li fom fo osvaiv load D Equival osaid Miimiaio Polm a l mi a w w l w w h Uivsiy of Floida oll of Eii

7 PENALY MEHOD FOR FRIIONAL ONA Impaio odiio Ω x x x x x x x Ω aial Slip Fuio oa osisy odiio ϕ x x oa Paly Fuio P ω d ω d wh iaio is pfomd oly o h io wh < o h Uivsiy of Floida oll of Eii

8 PENALY MEHOD o. -µω ω oa aiaioal Fom P ω d ω d h Uivsiy of Floida oll of Eii

9 ONA ARIAIONAL FORMS Sik odiio: ω µω ω Slip odiio : ω > µω wh ω ω µω d [ ν / ] s d d [ ν / ] α x β x γ x d α ν h Uivsiy of Floida oll of Eii

10 DSA OF ARIAIONAL INEQUALIY oa Is a aiaioal Iqualiy I Polm Paly Mhod Wis al.-99 ad Kikuhi & Od-988 a B Usd fo a Appoxima Soluio of I Shap Dsi Ssiiviy of I Has B Oaid y Sokolowski ad Zolsio 99 fo Lia Polm Dsi Ssiiviy Equaio is Aoh I Fo Lia Polms Appliaio of h Paly Mhod o Solv h Ssiiviy Equaio I Yilds h Sam Rsul As h Ssiiviy Equaio Oaid Fom h Paly Equaio h Uivsiy of Floida oll of Eii

11 h Uivsiy of Floida oll of Eii Maial Divaiv of Suual Poi Maial Divaiv of oa Poi Maial Divaiv of Naual oodia a oa DSA FORMULAION FOR ONA PROBLEM d d Ω Ω x x x x x d d x x x x

12 h Uivsiy of Floida oll of Eii MAERIAL DERIAIE OF ONA ARIAIONAL FORMS Nomal oa Fiiious Load Fom fo DSA [ ] ; * d d Liaid oa aiaioal Fom ; ; ; * * N * N κ ω ω ω ω α ω ω d d d d d d N

13 h Uivsiy of Floida oll of Eii MAERIAL DERIAIE OF ONA ARIAIONAL FORMS o. aial Sik Fiiious Load Fom fo DSA [ ] { } ν κ ω β ω β ω ω β ω β ν ω ω d d d d d d d ; *

14 h Uivsiy of Floida oll of Eii MAERIAL DERIAIE OF ONA ARIAIONAL FORMS o. aial Slip Fiiious Load Fom fo DSA [ ] [ ] [ ] [ ] [ ] ν κ ω β ω β ω ω β ω β ν ω ω d d d d d d d ; *

15 h Uivsiy of Floida oll of Eii aiaioal Equaio fo Mixd Fomulaio of Hyplasi Solid Liaid Imal Equaio wh liaid sai y fom is NONLINEAR ONA ANALYSIS [ ] Ω Ω λ λ Ω Ω D D d d d K p : J p d : p J : : ; a 3 3 * E E S E E E E Z a l ] p [ λ a ; ; a k k k k * k k * l

16 h Uivsiy of Floida oll of Eii aiaioal Equaio fo Pud Shap Dsi Shap Ssiiviy Equaio - s Od aiaio wh fiiious load foms fo DSA a SHAPE DESIGN SENSIIIY ANALYSIS Ω Ω Z a l [ ] Ω ζ λ λ κ Ω D D d d d div : : : : a E S E S E E a ; ; a * * Ω l

17 SHAPE DESIGN SENSIIIY ANALYSIS o. l Rmaks Ω [ ] B B f f div [ κ ] f f dω d oal fom of ssiiviy quaio No iaio is quid Fiioal oa is pah-dpd DSA ds o aid ou a ah ovd load sp - Di Diffiaio Mhod is usd Maial divaivs of displam a oa ods a usd fo DSA a x im sp h Uivsiy of Floida oll of Eii

18 DOOR SEAL ONA MODEL Riid Wall Ru Sal Maial osa D 8 KPa D KPa Bulk Modulus K 8 MPa Fiioal offii µ.5 Ru Sal 74 Pail Pois Riid Wall 3 Piwis Lia Mas Sms Load Sps fo Aalysis wih Displam Div Podu Moui h Uivsiy of Floida oll of Eii

19 MESHLESS ANALYSIS OF DOOR SEAL Fiiolss oa Fiioal oa Gap Opi h Uivsiy of Floida oll of Eii

20 DOOR SEAL ONA DESIGN u 8 u u u 4 u 6 u 7 u 4 u 9 u u 3 u 6 u u 3 u 5 u 5 u u 9 u u 7 u 5 u 6 u u u 8 u 3 u 4 6 Shap Dsi Paams Mi s.. Aa9 σ σ σ σ σ σ σ u Opimi: DO-SQP Iiial Dsi is Ifasil i i 6 h Uivsiy of Floida oll of Eii

21 AURAY OF SHAPE DSA RESULS Aalysis: 968 S Ssiiviy: 84 S fo 6 D 4.7 S Ψ Ψ FDM Ψ PROPOSED Ψ / Ψ Ψ Ψ FDM Ψ PROPOSED Ψ / Ψ u σ E E-6. Aa E E-5. σ 4.435E E-5. σ E E-6. σ E E-7.4 σ E E-5. Σ -.34E E-9. σ E E u 4 σ E E-6. Aa -.353E E-5. σ E E-6.9 σ E E-4. Σ E E-8. σ E E-4. u σ 44.64E-5.65E-5. Aa.63894E E-5. σ E E-5. σ E E-6. σ E E σ E E-5. Σ -.38E E-8. σ 44.96E-4.969E-4. u 5 σ 4.637E-4.637E-4. Aa E E-5. σ E E σ E E-5. Σ.36E-7.36E-7. σ E E-5. u 3 σ 44.64E-5.65E-5. Aa E E-5. σ E E-5. σ E E-7. σ 3.664E E σ E E-5. Σ E E-9. h Uivsiy of Floida oll of Eii

22 SHAPE OPIMIZAION HISORY OS.6E-.4E-.E-.E- 8.E- OS FUNION HISORY OS ONSRAINS ONSRAINS HISORY AREA vm75 vm86 vm44 vm4 vm3 vm38 vm5 6.E- 4.E-.E-.E IER IER h Uivsiy of Floida oll of Eii

23 OPIMIZED DOOR SEAL Opimum Shap Aalysis of Opimum Dsi h Uivsiy of Floida oll of Eii

24 SHAPE OPIMIZAION HISORY FDM OS FUNION HISORY OS 8 ONSRAIN FUNION HIS ORY AREA vm75 vm86 vm44 vm4 vm3 vm38 vm IER IER h Uivsiy of Floida oll of Eii

25 h Uivsiy of Floida oll of Eii OPIMIZED DOOR SEAL FDM

26 WINDSHIELD BLADE MODEL Muli-ody oa Flxil-iid Body oa Maial osa D 8 Kpa Bulk Modulus K 8 MPa D Kpa Fiioal offii µ.5 Widshild Blad 8 Pail Pois Riid Wall 6 Piwis Lia Mas Sms Load Sps fo Aalysis wih Displam Div Podu h Uivsiy of Floida oll of Eii

27 SHAPE DESIGN PARAMEERS OF BLADE u 7 u u 4 u u 8 u 5 u 6 u 3 u 9 Mi s.. Aa39 σ σ σ σ F y u u u u i i i i i i i i h Uivsiy of Floida oll of Eii

28 AURAY OF SHAPE DSA RESULS Aalysis: 633 S Ssiiviy: 33 S fo 6 D. S Ψ Ψ FDM Ψ PROPOSED Ψ / Ψ Ψ Ψ FDM Ψ PROPOSED Ψ / Ψ D D 3 Aa.8463E E-5. Aa.68668E E-5. σ E-4.847E σ E E σ E E-3. σ E E-4. σ E E σ E E σ E-4.37E σ E E-4. F x E E F x E E-5. F y8.74e-5.769e F y8.67e-4.673e-4. D D 4 Aa.E-5.E-5. Aa -.5E-5 -.5E-5. σ E E-5. σ E E-5.5 σ E E σ E E-5. σ E E σ E E-4. σ E E σ E E-4. F x8 -.8E-6 -.8E F x8.8e-5.8e-5. F y e e F y E E-5. h Uivsiy of Floida oll of Eii

29 PERFORMANE MEASURE HISORY PERFORMANE OPIMIZAION HISORY OS vm53 vm54 vm76 vm84 Fy IER h Uivsiy of Floida oll of Eii

30 DESIGN PARAMEER HISORY PARAMEER u u u3 u4 u5 u6 u7 u8 u9 DESIGN PARAMEER HISORY IER h Uivsiy of Floida oll of Eii

31 OPIMIZED WINDSHIELD BLADE Opimum Shap Aalysis of Opimum Dsi h Uivsiy of Floida oll of Eii