Optimal Sizing Using Automatic Diierentiation

This paper is devoted to optimal sizing. As a model example we consider the minimization of the mass of the frame of an injection moulding machine. The deformation of the frame is described by a generalized plane stress state with an elasticity modulus scaled by the thickness. This constrained nonlinear optimization problem is solved by sequential quadratic programming (SQP) which requires gradients of the objective and the constraints with respect to the design parameters. As long as the number of design parameters is small, nite diierences may be used. In order to handle also several hundreds of varying thickness parameters , we use the reverse mode of automatic diierentiation for diierentiating the function evaluation. This approach works ne but requires huge memory and disk capabilities. Furthermore, the use of iterative solvers for the governing state equations is limited. Therefore, we combine it with the adjoint method to get a fast and exible gradient evaluation procedure. The presented numerical results show the potential of this approach and imply that this method can also be used for nding an initial guess for a shape optimization.