Genetic Algorithms Based Optimisation of Composite Ship Structures

1. Genetic Algorithms Based Optimisation of Composite Ship Structures Komsan Maneepan Supervisor : Prof. R.A. Shenoi Co-supervisor : Dr. J.I.R Blake Sponsor : Royal Thai Navy Acknowledgements : Dr. H.K. Jeong, EU FP6 Marstruct Program ?????????........??????????????????????????? ?????? ?????, ????????????? ?????????????????????????? ???? ????? ?????? ?.?. ???????? ???????? ????????????? ??????????????????? 36 ?? ??.??????? ???? 93 ????????? ???????????????????? ???? ????????????????????? ??????????????? ?, ???????????????? ??? ?????????????? southampton ???? naval architecture ????????????????????? ????????? composite structures ???? Genetic Algorithm ????????????????????? ??? Prof. R.A. Shenoi, Co-supervisor: Dr. J.I.R. Blake, ???????????: ????????????? ????????: Dr. H.K Jeong, EU FP6 Marstruct Program ?????????........??????????????????????????? ?????? ?????, ????????????? ?????????????????????????? ???? ????? ?????? ?.?. ???????? ???????? ????????????? ??????????????????? 36 ?? ??.??????? ???? 93 ????????? ???????????????????? ???? ????????????????????? ??????????????? ?, ???????????????? ??? ?????????????? southampton ???? naval architecture ????????????????????? ????????? composite structures ???? Genetic Algorithm ????????????????????? ??? Prof. R.A. Shenoi, Co-supervisor: Dr. J.I.R. Blake, ???????????: ????????????? ????????: Dr. H.K Jeong, EU FP6 Marstruct Program

2. Content Introduction Literature reviews Optimisation methodology Structural analysis Genetic algorithm Applications and problem definition Unidirectional stiffened plate Cross stiffened plate Unstiffened plate Conclusion Further works ?????????????????????????????? ???????? ?. ???????, ?. ???????????????????, ?. ???????????, ?. ??????????????????????, ?. Genetic Algorithm, ?. ???????????????????????????????, ?. ?????????????????????????????????????????, ?. ???????????????????????????????????????, ?. ?????????? ????????? ?????????????????? ?????????????????????????????? ???????? ?. ???????, ?. ???????????????????, ?. ???????????, ?. ??????????????????????, ?. Genetic Algorithm, ?. ???????????????????????????????, ?. ?????????????????????????????????????????, ?. ???????????????????????????????????????, ?. ?????????? ????????? ??????????????????

3. Introduction FRP composite ? fibre, resin, fibre volume fraction ? composite form, woven roving, CSM, unidirectional laminate ? production process Marine applications ?small craft, Naval ship ?Top-hat stiffened plates, sandwich plate FRP ??????? Fibre Reinforced Plastic ??? ??????????????????? fibre ????? resin ????? fibre volume fraction, ????????? composite ??? ?????????????? ???????????? ??????????????????????? ????? Fibre ?????? Matrix ???? Resin ??????? unidirectional lamina ????????????? lamina ????????????????? Laminate ?????????????? ??? ?????????? sandown ?????????????????? FRP Resin ???????????? fibre ??????????? ???????????????? resin ???????????????????? ???? ????????????????????????????????????? fibre, ?????????? load ???????????????????????????, ????????????????????????????????????????????? ??? ??????????????????? ?????????????????????? resin ???????? Polyesters, Vinyl-ester ??? Epoxies ????????????? Epoxies ???????????????????????????? ????????????????????????????? fibre ??????? fibre ??????????????? ??????????????????????????????????????????? fibre ???????????????????????? ???? E-glass, S-glass, Carbon fibre E-glass ????????? ????? tensile strength ??? fatigue resistance ?????????????????? ??????? Carbon ????????????????????????? ???? Fibre volume fraction ???????????? 0.4-0.6 ????????? fibre volume fraction ?????? fibre ?????????????? ?????????? delaminate ??????????????????????????? ????????? composite ???????????? mechanical properties ???? unidirectional laminate ??????????????????? fibre, woven roving ????????????? ????????????????????? in-plane shear, CSM ????????????? assume ???? ISOTROPIC ???????????? ???????????????????????????????????????? ?????????????? composite ?????? hand layup, spray layup, resin infusion ??????? ????????????????? resin infusion ??? composite ??????????? ???????????????????????????? ????????????????????? ?????????????????????????? ???????????????????? ?????? composite ??????????? marine small crafts ??? naval ship. ??????????????? ???????????????????? tophat stiffened single skin, Monocoque, Sandwich ??? Corrugated structure. ????????????????????????????????? ????? ??????????????????????????????????????? ???????????????????? ??? ??.????????????? ???????? focus ????? structure ??? FRP ??????? Fibre Reinforced Plastic ??? ??????????????????? fibre ????? resin ????? fibre volume fraction, ????????? composite ??? ?????????????? ???????????? ??????????????????????? ????? Fibre ?????? Matrix ???? Resin ??????? unidirectional lamina ????????????? lamina ????????????????? Laminate ?????????????? ??? ?????????? sandown ?????????????????? FRP Resin ???????????? fibre ??????????? ???????????????? resin ???????????????????? ???? ????????????????????????????????????? fibre, ?????????? load ???????????????????????????, ????????????????????????????????????????????? ??? ??????????????????? ?????????????????????? resin ???????? Polyesters, Vinyl-ester ??? Epoxies ????????????? Epoxies ???????????????????????????? ????????????????????????????? fibre ??????? fibre ??????????????? ??????????????????????????????????????????? fibre ???????????????????????? ???? E-glass, S-glass, Carbon fibre E-glass ????????? ????? tensile strength ??? fatigue resistance ?????????????????? ??????? Carbon ????????????????????????? ???? Fibre volume fraction ???????????? 0.4-0.6 ????????? fibre volume fraction ?????? fibre ?????????????? ?????????? delaminate ??????????????????????????? ????????? composite ???????????? mechanical properties ???? unidirectional laminate ??????????????????? fibre, woven roving ????????????? ????????????????????? in-plane shear, CSM ????????????? assume ???? ISOTROPIC ???????????? ???????????????????????????????????????? ?????????????? composite ?????? hand layup, spray layup, resin infusion ??????? ????????????????? resin infusion ??? composite ??????????? ???????????????????????????? ????????????????????? ?????????????????????????? ???????????????????? ?????? composite ??????????? marine small crafts ??? naval ship. ??????????????? ???????????????????? tophat stiffened single skin, Monocoque, Sandwich ??? Corrugated structure. ????????????????????????????????? ????? ??????????????????????????????????????? ???????????????????? ??? ??.????????????? ???????? focus ????? structure ???

4. Compare composite with metal ?????? 1 ?????????????????? ?????????????????????????????? ??????? composite ?????????????????????????? ????? Al ??? Steel ????????????????????????? Compsite ????????? Composite ???? stiffness ?????????? AL ??? Steel ??????????????????????????? stiffness ?????????????? 1 ?????????????????? ?????????????????????????????? ??????? composite ?????????????????????????? ????? Al ??? Steel ????????????????????????? Compsite ????????? Composite ???? stiffness ?????????? AL ??? Steel ??????????????????????????? stiffness ????????

5. ???????????? corvette ????????? carbon fibre ?????????????????????????????????????????????????? ?????????????????????? handlayup ??????????????????????????????????? ????????????????????? Resin infusion ??????????????? composite ????????? ???????????? corvette ????????? carbon fibre ?????????????????????????????????????????????????? ?????????????????????? handlayup ??????????????????????????????????? ????????????????????? Resin infusion ??????????????? composite ?????????

6. Physical significance of stiffness terms in Force and Moment Resultants ???????????????????????????????????? ??????????????????????? laminate ????????????????????? Laminate ???????? ??????? [A] stiffness ????????????????????????, ?????? A16, A26 ???? ????????????? shear ???? ??????? [B] stiffness ?????????? Bending ??? Extension ???? [D] ?)?????? Bending ?????? D16, D26 ????????????????????????????????? ???????????? ???????????? ?????????????????? Laminate ????????? ??????? ABD stiffness ?????????? 0 ????????????????????? ???????????????????????????????????? ??????????????????????? laminate ????????????????????? Laminate ???????? ??????? [A] stiffness ????????????????????????, ?????? A16, A26 ???? ????????????? shear ???? ??????? [B] stiffness ?????????? Bending ??? Extension ???? [D] ?)?????? Bending ?????? D16, D26 ????????????????????????????????? ???????????? ???????????? ?????????????????? Laminate ????????? ??????? ABD stiffness ?????????? 0 ?????????????????????

7. Production cost ???? slide ????? ???????????????????????? composite ???????????????? simulation ??????? ????????????????? ?????? ??? vosper technocop ????????? ???????????????? ??????????????????? conference ??? ????????? ????? Multi-objective minimisation of cost ??? weight ?????????????????? objective ?????????????????? ???? ?????????????? direct ??? indirect cost >>>>>> ???? indirect cost ??????????? ?????????, ??????? ??????? ????????????? simulate ?????? ???? direct cost ??? ??????????????? ??? ????????????? ???? slide ????? ???????????????????????? composite ???????????????? simulation ??????? ????????????????? ?????? ??? vosper technocop ????????? ???????????????? ??????????????????? conference ??? ????????? ????? Multi-objective minimisation of cost ??? weight ?????????????????? objective ?????????????????? ???? ?????????????? direct ??? indirect cost >>>>>> ???? indirect cost ??????????? ?????????, ??????? ??????? ????????????? simulate ?????? ???? direct cost ??? ??????????????? ??? ?????????????

8. Reviews on optimisation methods Many papers using the classical optimisation method, show the optimum fibre angle, the main design variable for composite structure, is not suitable for manufacturing processes. Moreover, the global optimum could not be obtained if the starting point is near a local optimum. The GA is the most popular in the stochastic types of optimisation methods as a results of their simplicity. ?????? review ??????????????? optimisation method ???????????? composite structures ??????? classical optimisation methods ??????????????????????????????? ?????????????? fibre angle ???????????? real number ????????? ?????? design space ????????? peak ???????? ??? classical optimisation methods ?????????????????????? starting point ???????? ????????????????? ???????? ?????????????????????? ??? ????????????? ?????????????????????????????? genetic algorithm ??????????????????????????? ??????????????????????? ?????? review ??????????????? optimisation method ???????????? composite structures ??????? classical optimisation methods ??????????????????????????????? ?????????????? fibre angle ???????????? real number ????????? ?????? design space ????????? peak ???????? ??? classical optimisation methods ?????????????????????? starting point ???????? ????????????????? ???????? ?????????????????????? ??? ????????????? ?????????????????????????????? genetic algorithm ??????????????????????????? ???????????????????????

9. Reviews on the structural analysis Stiffened plate can be solved by Grillage assumption, although force method provide the exact solution, the computational time increase when the number of intersection is high. The energy method required only one equation to be solved. Other method is orthotropic plate method. It is justified only when stiffeners are closely spaced. For unstiffened plate, 3-D, CLPT, FSDT, HSDT are available. The 3-D is exact solution. CLPT is unique, but the less accuracy comparing to others. HSDT is the best in the equivalent single layer theories. FEM is the universal method for the solutions of mechanics problems and there are plenty of commercial FEM software packages available. ??????????? structural analysis ????????????????? ? ???? ?. structural analysis ?????? stiffened plate ?. structural analysis ?????? unstiffened plate ?????? stiffened plate,??????????????????? mechanical response ?????? ? ???? ??????? Grillage analysis, Orthotropic plate, ??? Folded plate method. Grillage analysis ???????????? Displacement method, Force method and Energy methods. Displacement method ??????????? beam ????????????? ??????????????????????? deflection ??? slopes ???? Force method ??????? beam ????????????? ??????????????????????? reaction forces ?????????????? exact solution ?????? grillage ????????????? computational time ?????????????????????????????????? ??????????????????????? ??? ????????? ???????? ??????? energy method ????????????????????????????????? ???????????????????? ????????????????? deflection ?????? orthotropic plate method, stiffeners ?????????????????? based plate ????????????? stiffness ??????????????? energy method ????? plate equation ?????????????????? ??????????????? ????????????????????????? stiffeners ?????????????????????? ???? folded plate method ???????????????????????????? ?????????? FPM ?????????? stiffened plate ??????? plate ??? beam element ?????? plate ??? beam equation ???????? element ????????? displacement ??? force method ??????? element ??????? ????? equation ?????????? ????????? ??????????????? plate ????????????????????????????????????? For unstiffened plate (in this work it means laminated plate between stiffener), the method can be used are 3D elasticity, equivalent single layer theory. 3-D elasticity provided exact solutions but it�s complicate following the number of layers. Within the ESL, the CLPT is the simplest and unique but provide the cross results. The HSDT provide the accurate results without the shear correction factors. ?????? unstiffened plate ??????????????? laminated plate ??????????? stifferner ??????????? structural analysis ????????????????? ? ???? ?. structural analysis ?????? stiffened plate ?. structural analysis ?????? unstiffened plate ?????? stiffened plate,??????????????????? mechanical response ?????? ? ???? ??????? Grillage analysis, Orthotropic plate, ??? Folded plate method. Grillage analysis ???????????? Displacement method, Force method and Energy methods. Displacement method ??????????? beam ????????????? ??????????????????????? deflection ??? slopes ???? Force method ??????? beam ????????????? ??????????????????????? reaction forces ?????????????? exact solution ?????? grillage ????????????? computational time ?????????????????????????????????? ??????????????????????? ??? ????????? ???????? ??????? energy method ????????????????????????????????? ???????????????????? ????????????????? deflection ?????? orthotropic plate method, stiffeners ?????????????????? based plate ????????????? stiffness ??????????????? energy method ????? plate equation ?????????????????? ??????????????? ????????????????????????? stiffeners ?????????????????????? ???? folded plate method ???????????????????????????? ?????????? FPM ?????????? stiffened plate ??????? plate ??? beam element ?????? plate ??? beam equation ???????? element ????????? displacement ??? force method ??????? element ??????? ????? equation ?????????? ????????? ??????????????? plate ????????????????????????????????????? For unstiffened plate (in this work it means laminated plate between stiffener), the method can be used are 3D elasticity, equivalent single layer theory. 3-D elasticity provided exact solutions but it�s complicate following the number of layers. Within the ESL, the CLPT is the simplest and unique but provide the cross results. The HSDT provide the accurate results without the shear correction factors. ?????? unstiffened plate ??????????????? laminated plate ??????????? stifferner

10. Structural Analysis ????????????????????????????????????????? ??????????????????????? ??????????? Grillage Analysis ????????????????? ????????????????????????????????????????? ??????????????????????? ??????????? Grillage Analysis ?????????????????

11. Stress component and orthotropic lamina ????????? ???????? composite material ??????? ???????????????????????? ????????????? ??? stresses ??????????????? ????????? ???????????????????? in-plane stress ????????????????????? ????????????????????????????????? ??????????? stress ????????????????? x-y ??????? ??????????????? Failure index ??????? transform stress ???????? ???????????????? LT ????????? ???????? composite material ??????? ???????????????????????? ????????????? ??? stresses ??????????????? ????????? ???????????????????? in-plane stress ????????????????????? ????????????????????????????????? ??????????? stress ????????????????? x-y ??????? ??????????????? Failure index ??????? transform stress ???????? ???????????????? LT

12. Optimisation methodology ??? Literature review ?????????????? ?????????? optimisation method ??????????????????? design space ??????????????? ???? discrete design variables ??? ??????????????? design variables ???????????????? ??? ???????????????? global optimum ??????? ?????????? GA ????? ???????????? ?????????????? applications ??? optimisation methodology ???????????? GA ??? Evaluation ??????? structural analysis structural analysis ?????????????? Grillage analysis ?????? stiffened plate ??? HSDT ?????? unstiffened plate ??? Literature review ?????????????? ?????????? optimisation method ??????????????????? design space ??????????????? ???? discrete design variables ??? ??????????????? design variables ???????????????? ??? ???????????????? global optimum ??????? ?????????? GA ????? ???????????? ?????????????? applications ??? optimisation methodology ???????????? GA ??? Evaluation ??????? structural analysis structural analysis ?????????????? Grillage analysis ?????? stiffened plate ??? HSDT ?????? unstiffened plate

13. Structural analysis For stiffened plate, the energy method based on Navier�s solution is adapted by introducing the flexural rigidity of composite material cross section into energy terms. For unstiffened plate, HSDT is selected because the displacement field is close to the deformation of plate in real situation. ?????????????? stiffened plate ????????? composite ???????????????????????????? Energy method ??????????????????? steel grillage ??????????????? ????????? flexural rigidity ??? composite cross section ?????? energy terms ??????????????????? ?????????????? layer ??? ???????????? plate ?????????????? stiffeners, ???????? TSDT ?????????????????????????????????????????????????????? ?????? ?????? assumption ???????? laminated plate theory ?????????????? stiffened plate ????????? composite ???????????????????????????? Energy method ??????????????????? steel grillage ??????????????? ????????? flexural rigidity ??? composite cross section ?????? energy terms ??????????????????? ?????????????? layer ??? ???????????? plate ?????????????? stiffeners, ???????? TSDT ?????????????????????????????????????????????????????? ?????? ?????? assumption ???????? laminated plate theory

14. Assumption of stiffened plate ?????? grillage analysis ??????????????? ??????????? ????????? stiffened plate ???? Grillage ???????????????????? ???????????????????? assumption ??? cross section ??? stiffeners ?????? grillage analysis ??????????????? ??????????? ????????? stiffened plate ???? Grillage ???????????????????? ???????????????????? assumption ??? cross section ??? stiffeners

15. ??????????????????? ?????????? derive ??? Grillage Analysis ??????????????? FRP ??????? ??? ????? equivalent elastic properties ????????????????????????? ??????????? flexural rigidity ?????? ?????????? strain energy ????????????? ?????????????? ????????????? load ?????????????? ??????????????? deflection ??? ?????????? stress ????????????? differential deflection ??????????????? ??????????????????? ?????????? derive ??? Grillage Analysis ??????????????? FRP ??????? ??? ????? equivalent elastic properties ????????????????????????? ??????????? flexural rigidity ?????? ?????????? strain energy ????????????? ?????????????? ????????????? load ?????????????? ??????????????? deflection ??? ?????????? stress ????????????? differential deflection ???????????????

16. Equivalent elastic properties ????????????? ??? equivalent elastic properties ????????? element ?????? load Nx ?????????????????? ??????????????????? Load ??? strain ????????? ?????????????????????? Nx = stress*t ??????????????? ?????????? Equivalent elastic properties ????????????? ??? equivalent elastic properties ????????? element ?????? load Nx ?????????????????? ??????????????????? Load ??? strain ????????? ?????????????????????? Nx = stress*t ??????????????? ?????????? Equivalent elastic properties

17. Output Output ??????? ??? ??? ??? deflection ???????? ??? stress ??????? longitudinal ??? transverse stiffeners ???????????? stress ?????????????? stiffener cross section ??? shear stress ?? webOutput ??????? ??? ??? ??? deflection ???????? ??? stress ??????? longitudinal ??? transverse stiffeners ???????????? stress ?????????????? stiffener cross section ??? shear stress ?? web

18. Genetic Algorithm (GA) A stochastic search method mimic the laws of natural evolution Initial population : it is randomly generated. Evaluation : the fitness is directly related to the value of objective function of the phenotype of chromosome Selection operator : it is for exploiting the design space by a randomised procedure to create a new population. For example, Roulette wheel selection select chromosomes from pool by determining their survival probability. Crossover : it creates offspring by combining parents features Mutation : it cause GA search to increase population diversity by introducing new genetic material. ??????? GA ??? ?????????????? ????? natural evolution ???????? ???????????????? 4 ?????? initial population, evaluation, selection, crossover ??? mutation ???????? chromosome ????? encoded ???????? binary number ?? initial population stage, chromosome ???????????????????? ??? chromosome length ??? population size ????????????? ????????????????? Gene ?????????? Evaluation process ?????????????????????? pool ?????????? survival probability ??????? ?????????????????????? ?????????????????? ??????????? chromosome ???????????????????? ????????? crossover ??????? Gene ??? pool ??????????????????????????????? ??????? GA ??? ?????????????? ????? natural evolution ???????? ???????????????? 4 ?????? initial population, evaluation, selection, crossover ??? mutation ???????? chromosome ????? encoded ???????? binary number ?? initial population stage, chromosome ???????????????????? ??? chromosome length ??? population size ????????????? ????????????????? Gene ?????????? Evaluation process ?????????????????????? pool ?????????? survival probability ??????? ?????????????????????? ?????????????????? ??????????? chromosome ???????????????????? ????????? crossover ??????? Gene ??? pool ???????????????????????????????

19. Flow chart of GA and design variables representation ????????????????????????? loop ??? GA ????????? binary number ?????? ??????????? ??????????? ???? chromosome ????????????????????????? loop ??? GA ????????? binary number ?????? ??????????? ??????????? ???? chromosome

20. Validation of structural analysis ????????????????????????????????? structural analysis ????? validate ?????????????????? grillage analysis ?? validate ??? Clarkson 1965 ??? Equivalent elastic properties of symmtric laminate ??? validate ??? datoo 1991 ???? HSDT ?? validate ??? Reddy 1997, Pagano 1970 ??? kant 2002 ????????????????????????????????? structural analysis ????? validate ?????????????????? grillage analysis ?? validate ??? Clarkson 1965 ??? Equivalent elastic properties of symmtric laminate ??? validate ??? datoo 1991 ???? HSDT ?? validate ??? Reddy 1997, Pagano 1970 ??? kant 2002

21. Validation of GA program GA program ?????????????? ??????????????? vary GA operators ??????????????? ??? vary starting point ???????????? ??????????????? ??? converge ??????? ????????????????????????? ????????????????? vary ????? starting point ??? operator ???????????????????????? ???????????????????????????????????GA program ?????????????? ??????????????? vary GA operators ??????????????? ??? vary starting point ???????????? ??????????????? ??? converge ??????? ????????????????????????? ????????????????? vary ????? starting point ??? operator ???????????????????????? ???????????????????????????????????

22. Comparison of the proposed methodology with Ansys ??????????????????????????????????????????????????? optimisation ??? ANSYS ??????????? ???????????????????? STIFFENER ????????????????????????????????????? 376 ???? ??????? ansys ??? 285 ?????? ???? ??????????? ??????? 0.76 ?????? ??????????????????????????????????????????????????? optimisation ??? ANSYS ??????????? ???????????????????? STIFFENER ????????????????????????????????????? 376 ???? ??????? ansys ??? 285 ?????? ???? ??????????? ??????? 0.76 ??????

23. Application to composite ship structures Cross stiffened plates Unidirectional stiffened plates Unstiffened plate Optimisation framework ??????????? 3 ??????? plate ?????????????????? ?????????????????????????????? tophat stiffener ??????????????????? ??????????? cross stiffened plate ??? unidirectional stiffened plate ???? secondary structures plate ?????????????? stiffener ??? tertiary structures Optimisation problem ?????????????? 1. Objective, 2. Constraints ??? 3. Design variables ??????? plate ?????????????????????????????? ?????????????? cross stiffened plate ?????? ??? ??????? 6096 mm, ??? ????????? 2540 mm ???? design variables ???????????????? strip plate element ?????? ????????????, ,??? fibre, ??????? fibre, areal weight ??????????????? ???????????????? ???? beam ??? girder spacing Optimisation framework ??????????? 3 ??????? plate ?????????????????? ?????????????????????????????? tophat stiffener ??????????????????? ??????????? cross stiffened plate ??? unidirectional stiffened plate ???? secondary structures plate ?????????????? stiffener ??? tertiary structures Optimisation problem ?????????????? 1. Objective, 2. Constraints ??? 3. Design variables ??????? plate ?????????????????????????????? ?????????????? cross stiffened plate ?????? ??? ??????? 6096 mm, ??? ????????? 2540 mm ???? design variables ???????????????? strip plate element ?????? ????????????, ,??? fibre, ??????? fibre, areal weight ??????????????? ???????????????? ???? beam ??? girder spacing

24. Design variables ??????????????????? ??????? design variables ????????????? design variables ???????????? ???????? design variables ???????????? ??? ?????????????????????? ???????????????????????????????? ??????????????????? ??????? design variables ????????????? design variables ???????????? ???????? design variables ???????????? ??? ?????????????????????? ????????????????????????????????

25. Considering positions Constraints ?????????????? stiffness constraint, strength constraint ??? stability constraint (buckling) stiffness constraint ????????????? deflection ????????????? plate, ???? strength constraint ????????????????? ??? crown element, web element ??? ??????? based plate ???? buckling constraint ??????????? constraints ???????? plate ??????? stiffeners Constraints ?????????????? stiffness constraint, strength constraint ??? stability constraint (buckling) stiffness constraint ????????????? deflection ????????????? plate, ???? strength constraint ????????????????? ??? crown element, web element ??? ??????? based plate ???? buckling constraint ??????????? constraints ???????? plate ??????? stiffeners

26. Material properties of resin and fibre ??????????????? ???????????? resin ??? fibre ???????????? HS ??????????? E-glass ????????? UHM ????? Young�s modulus ???????????? ??? E-glass ???????????? ?? Fibre ???? 4 ?????????????????????? ???????????? resin ??? fibre ???????????? HS ??????????? E-glass ????????? UHM ????? Young�s modulus ???????????? ??? E-glass ???????????? ?? Fibre ???? 4 ???????

27. Unidirectional stiffened plates Maximise stiffness [UHM](8)? high modulus material is selected Girder spacing is upper-bound value Maximise strength [E-glass](8)?low modulus material with high areal weight is selected. Weight minimisation [UHM](8) ?reduce the maximum deflection [HS](2)?reduce the magnitude of failure index Slides ????????????????????????????????????????? ?????????? ?????????????? ?????? unidirectional stiffened plate ????? deflection ?????????? ????? Girder spacing ????????????????, ?????????? fibre ????????? 0 ????????????????????????? UHM ?????????????????? element ??????????????????????????????? FI ?????????? ??????? fibre ????????? E-glass ????????? ??? areal weight ?????? ????????????? FI ?????????? Crown element fibre ?????????????????????????? direct stress ?? crown element FI ?????????? web fibre ??????????? 45 ???? ??????????????? plate ????? ??.????????? ?????? constraints ???????? ???????????? E-glass ???????????????? UHM ????????????????? deflection ??? HS ???????????????????????? index Slides ????????????????????????????????????????? ?????????? ?????????????? ?????? unidirectional stiffened plate ????? deflection ?????????? ????? Girder spacing ????????????????, ?????????? fibre ????????? 0 ????????????????????????? UHM ?????????????????? element ??????????????????????????????? FI ?????????? ??????? fibre ????????? E-glass ????????? ??? areal weight ?????? ????????????? FI ?????????? Crown element fibre ?????????????????????????? direct stress ?? crown element FI ?????????? web fibre ??????????? 45 ???? ??????????????? plate ????? ??.????????? ?????? constraints ???????? ???????????? E-glass ???????????????? UHM ????????????????? deflection ??? HS ???????????????????????? index

28. ???????????????????????????????????? ????? ??????????????? deflection ??????????, ??????? ??????????????? FI ??????? ???????????????????????????????????? ????? ??????????????? deflection ??????????, ??????? ??????????????? FI ???????

29. Weight minimisation of unidirectional stiffened plate ????????????????????????? ?????? stiffness ??? strength constraint????????????????????????? ?????? stiffness ??? strength constraint

30. Cross-stiffened plates Maximise stiffness High modulus fibre (UHM) is building material Beam spacing is wider than girder spacing Maximise strength E-glass is used to increase the strength at the web Weight minimisation Crown element is highest thickness The weight of plate mainly rely on stiffness constraints ???????????????????? cross stiffened plate ????????????? plate ????? deflection ???????? ????? Beam spacing ?????????? Girder spacing ???? Beam ?????????? Girder ???????????? ??? unidirectional stiffened plate ???????????????????????? Web fibre 45 ???????????? ????? E-glass ???????????? ??????????? weight minimisation ????????????????? varying limit ??? constraint crown element ???????????? sensitive ?????? ??? ??.??? plate ????? ?????????????? stiffness constraints ???????????????????? cross stiffened plate ????????????? plate ????? deflection ???????? ????? Beam spacing ?????????? Girder spacing ???? Beam ?????????? Girder ???????????? ??? unidirectional stiffened plate ???????????????????????? Web fibre 45 ???????????? ????? E-glass ???????????? ??????????? weight minimisation ????????????????? varying limit ??? constraint crown element ???????????? sensitive ?????? ??? ??.??? plate ????? ?????????????? stiffness constraints

31. ????????????????? ?????? ?????? ????? maximize stiffness ??? maximise strength ????????????????? ?????? ?????? ????? maximize stiffness ??? maximise strength

32. Weight minimisation of cross stiffened plate ???????????? weight minimisation ?????? stiffness ??? strength constraint ???????????? weight minimisation ?????? stiffness ??? strength constraint

33. Un-stiffened plate Maximise stiffness Maximise strength Maximise critical buckling load ??????? ?????????????? ????? design variable ??????? optimal results ???????? ??????????????????????????? design variable deflection ?????????????? ?????????????? ??? FI (FI ????? 90% ?????????? vary ????????????????) ??? ??? critical buckling load ?????????? plate ????????? optimal result ?????? ??????? E-glass ??? ??? areal weight ????????????????? ??????? ?????????????? ????? design variable ??????? optimal results ???????? ??????????????????????????? design variable deflection ?????????????? ?????????????? ??? FI (FI ????? 90% ?????????? vary ????????????????) ??? ??? critical buckling load ?????????? plate ????????? optimal result ?????? ??????? E-glass ??? ??? areal weight ?????????????????

34. ???????????????????????????? central deflection ??? ??????? ??? ?????????????? ??? ????????????? ???????????????????????????? central deflection ??? ??????? ??? ?????????????? ??? ?????????????

35. Maximisation of buckling load for unstiffened laminated plate ???????? ????????????????? plate ??????????? buckling ????????????????? ????????????????? plate ??????????? buckling ?????????

36. Conclusion The unique optimisation framework is introduced for composite ship framework by adapting grillage analysis. The validation of the subroutine program is shown. Applications of the optimisation framework to three plate types is presented. ??????? ??????????? ???????????????????????????????? composite ship structure ?????? ??????? ???????????????????? ??? ???????????? Tophat stiffened plate ????? composite Program ??????????????? validate ????????? ??? Applications ?????????????????? ??????? ??????????? ???????????????????????????????? composite ship structure ?????? ??????? ???????????????????? ??? ???????????? Tophat stiffened plate ????? composite Program ??????????????? validate ????????? ??? Applications ??????????????????

37. Further works The extension this work for midship section. Multi-objective could be added. Plates with other supported conditions and various load types. Material data base will be replace the evaluation formulation of material properties Parallel computing should be used to help GA for fast convergence to optimum results. ???????????????????????? ???? ????????????????????????? midship section ??? ???????? multi-objective ????????????????? ?????????????? ????????????? ????????????????????? simply support ????????????? boundary ??? load ???? ????????? ????????????????????????????? ????????? ????????????????????????????? ??????? material data based ???????????? frame work ??????? ????????????????????????????????? ????????? parallel computing ???? ???????????????????????? ???? ????????????????????????? midship section ??? ???????? multi-objective ????????????????? ?????????????? ????????????? ????????????????????? simply support ????????????? boundary ??? load ???? ????????? ????????????????????????????? ????????? ????????????????????????????? ??????? material data based ???????????? frame work ??????? ????????????????????????????????? ????????? parallel computing ????

38. List of publications Maneepan K., Jeong H.K. and Shnoi R.A. (2005) Optimisation of FRP tophat stiffened single skin and monocoque sandwich plates using genetic algorithm, ISOPE, June 19-24, Seoul, Korea, pp. 513-518 Maneepan K., Shenoi R.A., Jeong H.K. and Blake J.I.R. (2006) Multi-objective optimisation of orthogonally tophat-stiffened composite laminates plates, OMAE, June 4-9,Hamburge, Germany Maneepan K., Shenoi R.A., Blake J.I.R. and Jeong H.K. (2006) Genetic Algorithms (GAs) based optimisation of FRP composite plated grillages in ship structures, International Journal of Maritime Engineering (RINA).