Page 182 - Using ANSYS for Finite Element Analysis Dynamic, Probabilistic, Design and Heat Transfer Analysis

Design optimization • 169
infeasible. In defining feasible design space, a tolerance is added to each
state variable limit. So if X is a given design set defined as:
*

X =   X * 1 X * 2 X * 3  X * n   (5.7)
*
The design is deemed feasible only if:

,, ,……
g x
g = ( ) ≤ g + ( i = 12 3 , m ) (5.8)
a
*
*
i
i
i
i
1
hx (
h − b i ≤ h = ( ) = ,, , ……, m ) (5.9)
i
*
*
3
12
i
i
i
2
W − g i ≤ W * i = Wx ( ) ≤ W − ( i = ,, , ……, m ) (5.10)
*
g
3
12
i
i
i
i
3
Where: a , b and g = tolerances
i
i
i
And
i (
X ≤ X * i ≤ Xi = ,, , ……, n) (5.11)
3
12
i
(Equation 5.8) to (Equation 5.11) are the defining statements of a fea-
sible design set. As design sets are generated by methods or tools (dis-
cussed as follows) and if an objective function is defined, the best design
set is computed and its number is stored. The best set is determined under
one of the following conditions.
1. If one or more feasible sets exist the best design set is the feasi-
ble one with the lowest objective function value. In other words,
it is the set that most closely agrees with the mathematical goals
expressed by (Equation 5.3) to (Equation 5.6).
2. If all design sets are infeasible, the best design set is the one closest
to being feasible, irrespective of its objective function value.
5.1.1 oPTiMUM DeSign FUnDAMenTALS
Some of the fundamental concepts needed to understand optimization pro-
cess are explained as follows:
Problem formulation: Problem formulation is normally the most
difficult part of the process. It is the selection of design variables, con-
straints, objectives, and models of the disciplines. A further consideration
is the strength and breadth of the interdisciplinary coupling in the problem.