Numerical solution of inverse and optimization problems for designing steady forming processes

A formulation for solving inverse/optimization problem for designing steady-state metal forming processes has been developed. This work involves solving realistic but incompletely defined problems of industrial process design in an explicit manner rather than by trial and error solution. This formulation determines the optimum process parameters to help control product quality and reduce cost in certain forming operations. The main contribution of this work is a new stable and efficient numerical algorithm for solving these problems.; Two specific cases are considered in the work. Both involve shape optimization. The first case is to determine the optimal process geometry to minimize the power (and therefore cost) required to carry out the process. The second case is to determine the optimal process geometry, and in some problems the optimal speed, to generate specified material properties in the final product (maximize quality). Steady-state (or approximately steady-state) processes, such as rolling, drawing, and extrusion are considered. This work derives the inverse problem formulation by modifying an Eulerian viscoplastic formulation for the forward problem solution. The solution procedure proposed herein is divided into three parts: sensitivity analysis, function minimization, and examination of results. First, the adjoint method and a semi-analytical procedure are applied to determine an explicit matrix of sensitivity coefficients which is used in the updating formula for the solution. Then, a nonlinear minimization algorithm is used to find a solution.; The work presented herein is the first of its kind. Specifically, this work presents an algorithm for determining the optimal forming shape for steady forming processes to minimize the power requirement including friction effects and a material model with an evolving state variable. Previous work in this area has often neglected friction and in every case assumed a simple material which did not evolve with the deformation. The second case of determining the optimal forming shape for steady forming processes to generate specified material properties in the product has not been done before.