Optimal sizing using automatic differentiation

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, finite differences may be used. In order to handle also several hundreds of varying thickness parameters, we use the reverse mode of automatic differentiation for differentiating the function evaluation. This approach works fine 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 got a fast and flexible gradient evaluation procedure. The presented numerical results show the potential of this approach and imply that this method can also be used for finding an initial guess for a shape optimization.