1 / 13

Combining materials for composite-material cars

Combining materials for composite-material cars. Ford initiated research at a time when they took a look at making cars from composite materials. Graphite-epoxy is too expensive, glass-epoxy is not stiff enough.

yuval
Download Presentation

Combining materials for composite-material cars

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Combining materials for composite-material cars • Ford initiated research at a time when they took a look at making cars from composite materials. • Graphite-epoxy is too expensive, glass-epoxy is not stiff enough. • Grosset, L., Venkataraman, S., and Haftka, R.T., “Genetic optimization of two-material composite laminates,” Proceedings, 16th ASC Technical Meeting, Blacksburg, VA, September 2001

  2. Multi-material laminate • “Materials”: one material = 1 ply ( matrix or fiber materials)E.g.: glass-epoxy, graphite-epoxy, Kevlar-epoxy… • Use two materials in order to combine high efficiency (stiffness) and low cost • Graphite-epoxy: very stiff but expensive; glass-epoxy: less stiff, less expensive • Objective: use graphite-epoxy only where most efficient, use glass-epoxy for the remaining plies

  3. Multi-criterion optimization • Two competing objective functions: WEIGHT and COST • Design variables: • number of plies • ply orientations • ply materials • No single design minimizes weight and cost simultaneously: A design is Pareto-optimal (non-dominated) if there is no design for which both Weight and Cost are lower • Goal: construct the trade-offcurve between weight and cost (set of Pareto-optimal designs, also called Pareto front)

  4. Graphite-epoxy Longitudinal modulus, E1: 20.01 106 psi Transverse modulus, E2: 1.30 106 psi Shear modulus, G12: 1.03 106 psi Poisson’s ratio, 12: 0.3 Ply thickness, t: 0.005 in Density, : 5.8 10-2 lb/in3 Ultimate shear strain, ult: 1.5 10-2 Cost index: $8/lb Glass-epoxy Longitudinal modulus, E1: 6.30 106 psi Transverse modulus, E2: 1.29 106 psi Shear modulus, G12: 6.60 105 psi Poisson’s ratio, 12: 0.27 Ply thickness, t: 0.005 in Density, : 7.2 10-2 lb/in3 Ultimate shear strain, ult: 2.5 10-2 Cost index: $1/lb Material properties

  5. Optimization problem • Minimize weight and cost of a 30”x36” plate • By changing ply orientations and material mi • subject to a frequency constraint:

  6. Constructing the Pareto trade-off curve • Simple method: weighting method. A composite function is constructed by combining the 2 objectives:W: weight C: cost: weighting parameter (01) • A succession of optimizations with  varying from 0 to 1 is solved. The set of optimum designs builds up the Pareto trade-off curve • This is not a fool-proof approach (Why?), and it is time consuming. Genetic algorithms provide a shortcut.

  7. Multi-material Genetic Algorithm • Two variables for each ply: • Fiber orientation • Material • Each laminate is represented by 2 strings: • Orientation string • Material string • Example:[45/0/30/0/90] is represented by: • Orientation: 45-0-30-0-90 • Material: 2-2-1-2-1 • GA maximizes fitness: Fitness = -F 1: graphite-epoxy2: glass-epoxy

  8. Simple vibrating plate problem • Minimize the weight (W) and cost (C) of a 36”x30” rectangular laminated plate • 19 possible ply angles from 0 to 90 in 5-degree step • Constraints: • Balanced laminate (for each + ply, there must be a - ply in the laminate) • first natural frequency > 25 Hz Frequency calculated using Classical Lamination Theory

  9. How constraints are enforced • Balance constraint hard coded in the strings: stacks of ± are usedExample: (45-0-30-25-90) represents [±45/0/±30/±25/90]s • Frequency constraint is incorporated into the objective function by a penalty, which is proportional to the constraint violation

  10. Genetic operators • Roulette wheel selection based on rank • Two-point crossover • Mutation and permutation • Ply deletion and addition • Operators apply to each chromosome individually. • Best individual passed to the next generation (elitist)

  11. Pareto Trade-off curve A (16.3,16.3) point C • 64% lighter than A; 17% more expensive • 53% cheaper than B; 25% heavier (lb) C B (6.9,55.1) ($)

  12. Optimum laminates Intermediate optimum laminates:sandwich-type laminates • Cost minimization: [±5010/0]s, cost = 16.33, weight = 16.33 • Weight minimization: [±505/0]s, cost = 55.12, weight = 6.89 • Intermediate design: [±502/±505]s,cost = 27.82, weight = 10.28 Graphite-epoxy as outer pliesfor a high frequency Midplane Glass-epoxy in the core layersto increase the thickness

  13. Problems two-material laminate • Check the reasonableness of the weight ratio of the two extreme laminates (16.3/6.9) with simple calculation. • Illustrate the difference between crossover of two laminates when (a) the materials and angles are segregated into two chromosomes and (b) there is one string with the two numbers for each ply being together. • Why does the figure of the Pareto front not show values of alpha between 0 and 0.7?

More Related