Design of large-deformation steady elastoplastic manufacturing processes. Part II: sensitivity analysis and optimization

SUMMARYA computational framework is presented to evaluate the shape as well as non-shape (parameter) sensitivity of ÿnite thermo-inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo-mechanical deformation of hyperelastic thermoviscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are deÿned in a rigorous sense and the sensitivity analysis is performed in an inÿnite-dimensional continuum framework. The e ects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity ÿelds. The direct deformation and sensitivity deformation problems are solved using the ÿnite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by ÿnite di erence approximations (i.e. using the solution of a deformation problem with perturbed design variables). The e ectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes.

A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes

Ganapathysubramanian

Zabaras

2002

On the computation of design derivatives for Huber–Mises plasticity with non‐linear hardening

Wisniewski

Kowalczyk

Turska

2003

SUMMARYThis paper concerns design sensitivity analysis (DSA) for an elasto-plastic material, with material parameters depending on, or serving as, design variables. The considered constitutive model is HuberMises deviatoric plasticity with non-linear isotropic=kinematic hardening, one which is applicable to metals.The standard radial return algorithm for linear hardening is generalized to account for non-linear hardening functions. Two generalizations are presented; in both the non-linearity is treated iteratively, but the iteration loop contains either a scalar equation or a group of tensorial equations. It is proven that the second formulation, which is the one used in some parallel codes, can be equivalently brought to a scalar form, more suitable for design di erentiation. The design derivatives of both the algorithms are given explicitly, enabling thus calculation of the 'explicit' design derivative of stresses entering the global sensitivity equation.The paper addresses several issues related to the implementation and testing of the DSA module; among them the concept of veriÿcation tests, both outside and inside a FE code, as well as the data handling implied by the algorithm. The numerical tests, which are used for veriÿcation of the DSA module, are described. They shed light on (a) the accuracy of the design derivatives, by comparison with ÿnite di erence computations and (b) the e ect of the ÿnite element formulation on the design derivatives for an isochoric plastic ow.

Design sensitivity analysis and optimization for polymer sheet extrusion and mold filling processes

Smith

2003

SUMMARYA polymer processing design methodology is presented which can be used to improve the production of plastic components manufactured via extrusion and injection molding processes. The design method combines polymer process modelling, design sensitivity analysis and numerical optimization. It is applicable to systems with creeping ow of purely viscous non-Newtonian uids through thin cavities where the lubrication approximation may be applied. An analysis and an adjoint design sensitivity analysis are presented for the steady-state coupled system which describes the pressure and residence time distributions in sheeting dies. The resulting methodology is then used to deÿne the optimal die cavity shape and relevant process parameters in a sheeting die design example. A second example considers tooling and process design for the polymer injection molding process. A coupled transient mold ÿlling analysis and design sensitivity analysis based on the direct di erentiation method are developed where attention is given to describing the location of the gates in the mold cavity. The latter is illustrated through the process design of a plastic automotive component.