Perturbation-based stochastic FE analysis and robust design of inelastic deformation processes

The study addresses the perturbation-based stochastic finite element analysis and the robust design optimization of deformation processes of inelastic solids. The perturbation equations for the stochastic moment analysis of both steady-state and non-stationary processes are presented. An iteration scheme based on the secant system operator is given for the solution of the perturbation equations in case that a tangent matrix is not available. The robust design of deformation processes is stated as a two-criteria optimal design problem that attempts best mean properties of the outcome at minimum variability. The task is solved using optimization techniques based on sequential quadratic programming in conjunction with the stochastic finite element analysis. The proposed method is applied to the design of an extrusion die for robustness with respect to friction variability, and to a workpiece preform design problem. The numerical results show the potential of the method for applications regarding the design of robust deformation processes.