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Materials Selection Without Shape

Materials Selection Without Shape. ...when function is independent of shape. Selection Procedure. Performance Indices. Component performance described by the objective function p = f [(Functional requirement, F), (Geometric parameters, G), (Materials properties, M)]

hakeem-holmes
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Materials Selection Without Shape

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  1. Materials Selection Without Shape ...when function is independent of shape...

  2. Selection Procedure

  3. Performance Indices • Component performance described by the objective functionp= f[(Functional requirement, F), (Geometric parameters, G), (Materials properties, M)] • p may mean mass, volume, cost or life, etc. • If F, G and M are not inter-related, i.e. p = f1(F)f2(G)·f3(M), then the choice of material is independent of geometric details of the design. • p can then be optimized by optimizing f3, called performance index.

  4. P P Example to illustrate the Procedure - A Tie Rod • Mass of rod, m = Al • Tie rod must be able to carry a stress • The lightest tie rod without failing under P is that with largest performance index, M = f/ • For a light stiff tie rod, M = E/ Sf: safety factor

  5. P P Example - A Light Stiff Column A=r2 • Buckling load • Mass of column, • For buckling, M = E1/2/ • Note the changes in M due to changes in loading direction while the geometry remains unchanged

  6. Common Features of the Steps for the 2 Examples • The length, l, of the rod is specified • The mass, m, of the rod is to be minimized • Write the objective function, i.e. the equation for m. • The constraints are either no yielding or no buckling under the prescribed load, P • The free variables (geometric parameters in these cases) are eliminated

  7. Procedure for Deriving a Performance Index • Identify the attribute to be maximized or minimized • Develop equation for this attribute in terms of the functional requirements, the geometry and the material properties (the objective function) • Identify the free (unspecified) variables • Identify the constraints; rank them in order of importance • Develop equations for the constraints (no yield; no fracture; no buckling, maximum heat capacity, cost below target, etc.)

  8. Procedure for Deriving a Performance Index (cont.) • Substitute for the free variables from the constraints into the objective function • Group the variables into three groups: functional requirements, F, G and M, thus: ATTRIBUTE  f(F,G,M) • Read off the performance index, expressed as a quantity M, to be maximized • Note that a full solution is not necessary in order to identify the material property group

  9. Some Commonly Used Performance Indices

  10. Procedure for Selecting Materials (Primary Constraints) • Some non-negotiable constraints exists, e.g. operating temperature, conductivity, etc. • Either P > Pcirt or P < Pcrit • These constraints appear as horizontal or vertical lines on materials selection chart • Those satisfying the constraints are in the viable search region

  11. Procedure for Selecting Materials (Primary Constraints)

  12. Procedure - Performance Maximizing Criteria • To seek in the search region the materials which maximize the performance • e.g. Performance Index for tie is E/ (= C) • log E = log  + log C represents a set of straight lines, known as design guidelines on MS chart for various C. • All materials lying on the same guideline perform equally well; those above are better and those below are worse.

  13. Procedure - Performance Maximizing Criteria

  14. Multiple Constraints • Most materials selection problems are overconstrained, i.e. more constraints than free variables. • For aircraft wing spar, weight must be minimized, but with constraints on stiffness, strength, toughness, etc. • Performance maximization can be done in steps by considering the most important constraint first and apply the second constraint to the subset, and so on.

  15. Multiple Constraints • The materials in the search region become the candidates for the next stage of the selection process • Judgement is needed for prioritizing the constraints and the size of the subset in each stage.

  16. Reduce the Need for Judgement for Multiple Constraints Problems • E.g. one free variable, two constraints • The ratio of the two performance indices is therefore fixed by the functional and geometric requirements

  17. Example for Multiple Constraints • A tie loaded in tension • minimum weight without failing or elastic deformation less than u (specified!)

  18. Multiple Design Goals • There are always more than one quantity to be optimized, e.g. weight, cost, safety, etc. • One possible way is to assign weighting factors to each goal, e.g. weight (10) and cost (6), etc. • A more objective way is to convert all goals into the same ‘currency’, e.g. small weight can reduce transportation cost, and means less fuel cost, etc.

  19. Summary • Fully constrained problem identify performance index to be maximized or minimized • Over constrained problem  optimize in stages or, preferably, derive the coupling equation for the performance indices • Multiple goals problem  convert the design goals into common ‘currency’

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