Summary of Findings for GA, Beams & Plates for Thesis

Domain

Vary

Invariant

Optimal

Remarks

GA
  • Theory
  • Implementation
  • Simple GA processes
  • GA refinements
  • Comparison (sequential)
  • Reliability (GA-Gradient & GA-V)
  • Discussions
  • Theory of processes
  • Binary chromos.
  • Cantilever plate optimal control problem
  • Sequential: analyse all feasible solutions
  • Gen, pop, n, m, N, M, Pm, Pc
    		•
  • Optimized output in elements, code, etc.
  • Locations (indept)
  • Voltages (indept)
  • For actuator pairs only
    		•
  • Process settings for crossover, mutation & reproduction
  • Sample testing with sequential
  • Empirical minimum GA parameters
  • Reliability studies

    • Parameter settings
    • Crossover schemes (5) at Pc=0.9
    • Mutation schemes (Pm)
    • Reproduction schemes (5) at final crossover & mutation
  • At basis of Pc=0.9, Pm=0.1, Simple GA, pop_sz=9, gen_sz=50
    		•
  • Lowest best fitness level
  • If equal, take intuition (Pm lower)
    		•
  • Average fitness overall population convergence
  • Best fitness rep. Optimal chromo.
  • Fitness values magnitudes (diff. obj. function)

    • Sample testing
    • Sequential & GA
    • Mesh density
    • Patch size & number
  • At basis of Pc=0.9, Pm=0.1, Simple GA, pop_sz=9, gen_sz=earliest
    		•
  • Gen. changes
  • Patch changes
  • Mesh changes
  • Fitness compare
  • Locations
  • Fitness mag. (diff. obj. function)
  • Numbering (diff. B.C.)
  • Smart control inferences

    • Empirical GA settings
    • Gen_sz
    • Pop_sz
    • Pm & Pc
  • GA processes
  • Mesh: 64e
  • Patch: <5p, 2*2
    		•
  • For near optimal results
    		•
  • Use subject to invariant parameters only

    • Reliability studies
    • GA-Gradient
    • GA-V
    • Gs = 5, 10, 15
  • V=50V
  • Vmax=100V
  • Ps=9, Pc=0.9, Pm=0.1
    		•
  • Fitness, location , volts, reliability
    		•
  • Fitness values 3 sf
  • Others around same region & V
  • N.B. locations well-optimised, voltage poorer due to Simple GA used

    •  

     

     

    Domain

    Vary

    Invariant

    Optimal

    Remarks

    Beams
    • Broad
    • Narrow
  • Basic config.
    		•
  • Region, details
    		•
  • Strains, moments, curvatures, patch

    • Aspect ratio L/D
    • Fitness decrease, L/D increase
  • Locations for small/medium L/D
    		•
  • fixed, but shift out for large L/D
    		•
  • fitness kinks

    • Mesh density
    • f high, mesh high
  • Locations for each load
    		•
  • fixed for UDL, out for CL
    		•
  • CL use fine mesh, UDL any mesh

    • Layers
    • Layers high, f high
    • Even f > odd f
  • Locations
    		•
  • Fixed end
    		•
  • Upward kink for CL

    • Symmetry
    • Fitness changes
    • Asym > Sym
    • UDL > CL
  • Location
    		•
  • Fixed end
    		•
  • Kink in sym. UDL

    • Ply angles & sequence
    • Larger angle differential, lower fitness
    • CL < UDL
  • Location for all load & angles
  • Angle sequence
    		•
  • Fixed end
    		•
  • Upward kinks

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    Domain

    Vary

    Invariant

    Optimal

    Remarks

    Beams
    • Broad
    • Narrow
  • Basic config.
    		•
  • Region, details
    		•
  • Strains, moments, curvatures, patch

    • Patch length
    • Length high, fitness low
  • Location
    		•
  • Fixed end
    		•
  • Upward kink

    • CF, wd
    • Fitness plot shape (linear to curved)
    • F low, higher order
  • Location
  • Shape of fitness plot
    		•
  • Fixed end
    		•
  • Meet at worst f
  • F follows wd

    • SS
    • Curved fitness
    • F low, higher order
    • Longer p, low f
  • Location, shape of fitness plot
    		•
  • At supports
    		•
  • Both fitness curved, thus f plot depends on strain

    • CC
    • Curved
    • F low, higher order
    • Longer p, low f
  • Location, shape of plots
    		•
  • At fixed end supports
    		•
  • Common intersections for all single p fitness plots

    • CS
    • Curved
    • Diff: shorter p, low f (CL)
    • Diff: UDL, longer p, low f
  • Shape of plots
    		•
  • Shifts from fixed end or at hinged support
    		•
  • Diff.: plots for loads
  • Shapes for loads
  • UDL single optimum
  • CL double optima

    • S3
    • Longer p, higher f gradient & range
    • F low, higher order
  • Optimal region
    		•
  • Interior support
    		•
  • Presence of optimal p length
  • Intersection of plots
  • Shift due to plotting using patch datum
  • 3 supports, 3 minima

    • S5
    • Longer p, higher f gradient & range, higher fitness
    • F low, higher order
  • Optimal region
    		•
  • Interior supports
  • Outer interior
    		•
  • No intersection
  • 5 supports, 5 minima
  • Shorter p, smaller range, flatter contour

    • S7
    • Longer p, higher f gradient & range, higher fitness
    • F low, higher order
    • Longer unsupported span, higher fitness
  • Optimal region
    		•
  • Interior supports
  • Middle support
    		•
  • No intersection
  • 7 supports, 7 minima
  • Shorter p, smaller range, flatter contour

    • S9
    • Longer p, higher f gradient & range, higher fitness
    • F low, higher order
  • Optimal region
    		•
  • Interior supports
    		•
  • No intersection
  • 9 supports, 9 minima
  • Shorter p, smaller range, flatter contour

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    Domain

    Vary

    Invariant

    Optimal

    Remarks

    Plates
    • Broad
    • Narrow
  • Basic config.
    		•
  • Region, details
    		•
  • Strains, moments, curvatures, patch

    • Mesh density
    • Mesh finer, f low
    • CL > UDL, except at finest
  • Location
    		•
  • Fixed end
    		•
  • Relatively similar

    • Dimensions (L/W)
    • Larger plate, higher f
    • CL > UDL
  • Location
    		•
  • Fixed end
    		•
  • Same L/W ratio, same fitness
  • Proportionality

    • Aspect ratio (L/D)
    • Location change at low aspect ratio
    • L/D low, f low
    • CL > UDL
  • Location for higher L/D
    		•
  • Fixed end or shifted out
    		•
  • Plate thickness affects f

    • Layers
    • Different locations for even & odd
    • More layers, higher fitness
  • Location for even or odd
    		•
  • Fixed end:
  • Middle, even
  • Shifted, odd
    		•
  • Layering sequence has common effect on fitness

    • Symmetry
    • Diff. Locations for Asym & Sym
    • CL > UDL
    • Asym > Sym
  • Location for asym or sym
    		•
  • Fixed end:
  • Middle, Asym
  • Shifted, Sym
    		•
  • Asym: symmetric fitness contour
  • Sym: skewed fitness contour

    • Ply angles & sequence
    • Larger angle difference, lower fitness
  • Location for all angles & sequence
  • Sequence invariant
    		•
  • Fixed end middle
    		•
  • Best: cross ply
  • Mutually reinforcing

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    Domain

    Vary

    Invariant

    Optimal

    Remarks

    Plates
    • Broad
    • Narrow
  • Basic config.
    		•
  • Region, details
    		•
  • Strains, moments, curvatures, patch

    • Patch size
    • Larger size, low f
  • Location
  • Fixed end
    		•
  • Single optima & larger region, larger patch size

    • Patch thickness
    • High thickness, low fitness
  • Location
    		•
  • Fixed end middle
    		•
  • High thickness, lower f gradient

    • FCCC
    • Larger p, lower f, steeper f grad., larger f range
  • Location
    		•
  • At CC junctions, corners
    		•
  • Non-intersecting contours, equal fitness, fixity / strain
  • Free: more intersections

    • FCFC
    • Larger p, steeper f grad.
    • But higher fitness
  • Locations
    		•
  • Fixed ends middle
    		•
  • Dual symmetrical

    • FFCC
    • Larger p, lower f, steeper f grad., larger f range
  • Locations
    		•
  • Free-fixed corners
    		•
  • Contours intersect fixed end, due to non-uniform distribution of strains
  • Fixity / distribution

    • CCCC
    • Larger p, lower f, steeper f grad., larger f range
  • Locations
    		•
  • Fixed-fixed corners
    		•
  • 2*2 contour shifted right, due to plotting using patch datum

    • FSSS
    • Larger p, steeper f grad., larger f range
    • But higher f
  • Locations
    		•
  • SS corners
    		•
  • Fitness valley near to free end
  • Free end stiffened by opposite SS

    • FSFS
    • Larger p, steeper f grad., larger f range
    • But higher f
  • Locations
    		•
  • Free-hinged corners
    		•
  • Valley at center
  • Dual symmetric

    • FFSS
    • Larger p, lower f, steeper f grad., larger f range
  • Locations
    		•
  • SS corner, different from FFCC
    		•
  • Higher fixity at SS corner
  • Steeper gradient

    • SSSS
    • Larger p, steeper f grad., larger f range
    • But higher f
  • Locations
    		•
  • SS corners
    		•
  • Optimal region limits patch size

    • Single line of symmetry
    • B.C. changes
    • CFFF, FFSS, FSSS, FFCC, FCCC
  • None
    		•
  • C, SS corner, SS corners, CF corners, CC corner
    		•
  • Higher fixity, more supports, lower f
  • Half of mesh needs analyzing

    • Dual lines of symmetry
    • B.C. changes
    • FSFS, SSSS, FCFC, CCCC
    • 4 p 1*1
  • None
    		•
  • SS ends, SS corners, fixed ends, CC corners
    		•
  • Higher fixity, more supports, lower f
  • A quarter of mesh needs analyzing

    • Arbitrary plates under CL only
    • Load & B.C. changes
    • Half CFFF, CFFF, SSFS, CCFC
  • None
    		•
  • Edge of fixed end, fixed end skewed off center, free center, free-fixed corners
    		•
  • Higher fixity & strains, lower fitness, higher fitness contour concentration
  • In line with previous observations

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