Advanced Gradient Based Optimization Techniques Applied on Sheet Metal Forming

The computational-costs for finite element simulations of general sheet metal forming processes are considerable, especially measured in time. In combination with optimization, the performance of the optimization algorithm is crucial for the overall performance of the system, i.e. the optimization algorithm should gain as much information about the system in each iteration as possible. Least-square formulation of the object function is widely applied for solution of inverse problems, due to the superior performance of this formulation.In this work focus will be on small problems which are defined as problems with less than 1000 design parameters; as the majority of real life optimization and inverse problems, represented in literature, can be characterized as small problems, typically with less than 20 design parameters.We will show that the least square formulation is well suited for two classes of inverse problems; identification of constitutive parameters and process optimization.The scalability and robustness of the approach are illustrated through a number of process optimizations and inverse material characterization problems; tube hydro forming, two step hydro forming, flexible aluminum tubes, inverse identification of material parameters