Application of Parametric Programming to the Optimal Design of Stiffened Plates

Abstract

Stiffened plates are used in various areas of engineering. Examples of their use are f.e. box girder bridge, bridge decks and in ship construction. The use of stiffeners will increase the collapsing load of the structure without increasing the weight and the costs to much. A typical example of a plate stiffened in one direction is shown in figure 1. The designer of such structures aims to keep the weight and the costs of the stiffened plate as low as possible and the collapsing load as high as possible. Thus, the designer is confronted with the problem of satisfying a number of conflicting objectives, i.e. with a vector optimization problem of the following type:

VOP. Minimize the objective functions

$${\text{p}}_1 \left( {\text{x}} \right),\,{\text{p}}_2 \left( {\text{x}} \right),\,{\text{p}}_3 \left( {\text{x}} \right)$$

subject to the side conditions

$$\mathop \forall \limits_{{\text{j}} \in {\text{J}}} \,\,{\text{A}}_{\text{j}} \left( {\text{x}} \right)\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}\to { \leqslant } \,0.$$