Optimization of dimension of weldment locus by method of geometric programming

Abstract

This paper, on the example of a typical loaded welded assembly, made optimization of its dimensions in terms of the cost of welding. In such an elaboration the mathematical optimization model with limitation functions has also been presented and it should be taken into account in the process of designing by the technologist and designer. To solve the presented problem the method of geometric programming was proposed that has in detail been elaborated in the paper in the form of an algorithm suitable for the application. In this way the optimization or primary task was reduced to a dual task through a proper function, which is much easier to solve. The method has been illustrated on a practical computational example with a different number of limitation functions. It is shown that in case of a lower degree of complexity the solution can be reached by maximizing the corresponding dual function by means of mathematical analysis. In case of a higher degree of complexity, it is necessary to use some of the methods of non-linear programming. In this case the solution of the problem is simplified due to the minimization of a linear equation.

Keywords

• alphabetic loaded welded structures
• the mathematical model of optimization
• the cost function
• feature limitations
• geometric programming
• positive polynomials
• dual function