Optimal Shape Design and Optimal Sizing of Industrial Components

This paper deals with minimizing the mass of the frame of an injection moulding machine as an example for a typical optimal sizing problem. Due to lack of space we omit the shape optimization part (see [5]). Since we want to use standard optimization procedures (such as SQP) we focus our interest on the efficient and flexible calculation of the gradients. Since implementing analytic derivatives is an improper approach, we present a very flexible approach using automatic differentiation. In order to get also an efficient and fast method, automatic differentiation has to be coupled with a well-known approach from shape optimization — the so-called adjoint method. Numerical results show the strength of this approach.