10.1 Introduction and synopsisThese case studies illustrate how the techniques described in the previous chapter really work. Two'were sketched out there: the light, stijJ; strong beam, and the light, cheap, stiff beam. Here wedevelop four more. The first pair illustrate multiple constraints; here the active constraint method isused. The second pair illustrate compound objectives; here a value function containing an exchangeconstant. £$, is formulated. The examples are deliberately simplified to avoid clouding the illustra-tion with unnecessary detail. The simplification is not nearly as critical as it may at first appear:the choice of material is determined primarily by the physical principles of the problem, not bydetails of geometry .The principles remain the same when much of the detail is removed so thatthe selection is largely independent of these.Further case studies can be found in the sources listed under Further reading.con-rods for10.2 Multiple constraints -high-performance enginesA connecting rod in a high perfonnance engine, compressor or pump is a critical component: ifit fails, catastrophe follows. Yet -to minimize inertial forces and bearing loads -it must weighas little as possible, implying the use of light, strong materials, stressed near their limits. Whencost, not perfonnance, is the design goal, con-rods are frequently made of cast iron, because it isso cheap. But what are the best materials for con-rods when performance is the objective?The modelTable 10.1 sultlmarizes the design requirements for a connecting rod of minimum weight withtwo constraints: that it must carry a peak load F without failing either by fatigue or by bucklingelastically. For simplicity, we assume that the shaft has a rectangular section A = bw (Figure 10.1).The objective function is an equation for the mass which we approximate asm = fJALp(10.1)where L is the length of the con-rod and p the density of the material of which it is made, A thecross-section of the shaft and .8 a constant multiplier to allow for the mass of the bearing housings.Case studies: multiple constraints and compound objectives 10.1 Introduction and synopsis
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