Some Advantages of Product Criteria in Component Optimization

Abstract

In optimum design the optimizing criterion is a mathematical compromise among performance, cost, life, and conformity to constraints. This paper makes use of the fact that for every linear sum criterion there exists an equivalent product criterion which yields the same solution (extremum function). A method to obtain the proper form of this criterion is presented along with several distinct advantages of using it, including: (1) elimination of the variable “constant” which changes whenever a constraint changes (such as Lagrange multipliers); (2) separation of independent solutions (such as material and shape); (3) great reductions in the work required to obtain a solution when the mathematical models take the form of products. These advantages are demonstrated in three example problems utilizing a novel approach to finding the functions which render products of definite integrals extremum.