moko (version 1.0.3)

nowacki_beam: Test function: The Nowacki Beam

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 beam for minimum cross-sectional area and lowest bending stress subject to a number of constraints.

Usage

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 corresponds the normalized breadth and height of the beam

g

vector of length 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

# NOT RUN {
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))
# }