Continuum-based Shape Sensitivity Analysis for Steady-state Metal Forming Processes
In this research, a continuum-based shape sensitivity analysis for steady-state metal forming processes is developed. This approach utilizes nonlinear continuum mechanics and discrete finite element analysis results. An identity integral is formulated from the nonlinear constitutive laws of the deformation process. Then, an explicit sensitivity formulation is derived by defining an adjoint finite element analysis with a new set of continuum conditions, which are obtained from the first order derivatives of identity integral equation and objective/constraint functions. The formulation is further modified to contain the terms that can be computed only with continuum field variables. Thus, the approach significantly reduces the computational cost. Additionally, it opens a new era in shape sensitivity analysis for metal forming processes by combining the continuum plasticity mechanics and the commercial software analysis packages without intervening in the finite element matrices. The detailed design sensitivity analysis for the extrusion process is presented to demonstrate the methodology.
Jalaja REPALLE, Ramana V. GRANDHI, Joo Hoo CHOI
Shape Sensitivity Analysis, Continuum Mechanics, Finite Element Analysis, Material Derivatives, Metal Forming, Extrusion.