Test function: The Nowacki Beam

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Description

This function is a variation of the classic multi-objective optimization problem (NOWACKI, 1980). In this problem the aim is to design a tip loaded cantilever eam for minimum cross-sectional aera and lowest bending stress subject to a number of constraints.

Usage

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nowacki_beam(x, g = c(5, 240, 120, 10, 2), l = 1500, F = 5000,
  E = 216620, G = 86650, v = 0.27, box = data.frame(b = c(10, 50), h =
  c(20, 250)))

Arguments

x

vector of length 2 correspon the normalized beath and height of the beam

g

vector of lenght 5 containing the upper limits of each constraint

l

numeric length of the beam

F

numeric force applied at the beam tip

E

numeric elastic longitudinal moduli

G

numeric elastic transversal moduli

v

numeric poison ratio

box

data.frame structure containing the upper and lower limits for b and h

Value

vector of objective and constrain responses

References

Forrester, A., Sobester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.

Examples

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grid <- expand.grid(seq(0, 1, , 50),seq(0, 1, , 50))
res <- apply(grid, 1, nowacki_beam, box = data.frame(b = c(10, 50), h = c(50, 250)))
par(mfrow = c(3,3))
for(i in 1:nrow(res))
 contour(matrix(res[i,],50))