Engineering Optimization: Theory and Practice, Fourth Edition

Problems 371

Figure 6.18 Tapered cantilever beam.

Figure 6.19 Three-degree-of-freedom spring–mass system.

6.4 The steady-state temperatures at points 1 and 2 of the one-dimensional fin(x 1 andx 2 )
shown in Fig. 6.20 correspond to the minimum of the function [6.1]:

f (x 1 , x 2 )= 0. 6382 x 12 + 0. 3191 x 22 − 0. 2809 x 1 x 2

− 67. 906 x 1 − 14. 290 x 2

Plot the functionf in the(x 1 , x 2 )space and identify the steady-state temperatures of

points 1 and 2 of the fin.