# nowacki_beam: Test function: The Nowacki Beam In moko: Multi-Objective Kriging Optimization

## 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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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

 ```1 2 3 4 5``` ```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)) ```

moko documentation built on July 2, 2020, 3:59 a.m.