Engineering Optimization: Theory and Practice, Fourth Edition

Problems 543

subject to

Fi(k)

xiσi∗

≤ 1 , i= 1 , 2 ,... , n, k= 1 , 2 ,... , q (2)

∑n

i= 1

Fi(k)li

xiE∗i

sij≤ 1 , j= 1 , 2 ,... , m, k= 1 , 2 ,... , q (3)

whereFi(k)is the tension in theith member in thekth load condition,xithe cross-sectional
area of memberi,lithe length of memberi,Eis Young’s modulus,σi∗the maximum
permissible stress in memberi, and∗jthe maximum allowable displacement of nodej.
Develop a suitable transformation technique and express the problem of Eqs. (1) to (3)
as a geometric programming problem in terms of the design variablesxi.