A continuum sensitivity based design procedure for multi-stage metal forming processes

Abstract

A continuum based sensitivity method is introduced to evaluate the gradients of objective function and constraints in the computational design of multi-stage metal forming processes. To deal with design problems of multi-stage processes, all field variables in both direct problem and sensitivity problem are transferred from current stage to the following stage. To compute the sensitivity in the current stage, weak sensitivity equilibrium equations are derived for the large deformation of the workpiece where the kinematic sensitivity problem is linearly coupled with the corresponding constitutive sensitivity, contact sensitivity and thermal sensitivity sub-problems. The effectiveness of the proposed methodology is demonstrated with the solution of one practical problems in the design of two-stage metal forming processes.