Initial solution estimation for one-step inverse isogeometric analysis in sheet metal stamping

Abstract

Recently, Isogeometric Analysis (IGA) based on incremental methods for simulating the stamping process has been researched. To the best of our knowledge, however, few studies have combined IGA and One-step inverse approach which is based on total deformation theory of plasticity. A key step for One-step inverse IGA is to estimate a good initial solution. Traditional mesh-based initial solution algorithms for One-step inverse approach are not suitable for One-step inverse NURBS-based IGA. In this paper, we presented a method which can rapidly unfold the undevelopable NURBS surface onto a planar domain and obtain a good initial solution estimation for One-step inverse IGA. The key idea of the presented method is unfolding the control net of a NURBS surface for isogeometric analysis by energy-based initial solution estimation algorithm. In addition, we developed a “cutting-stitching” algorithm which can separate a complex control net into several parts with simple shapes. Numerical examples illustrate the initial solutions using the presented method are approaching the final results by One-step inverse finite element method. This implies that the iterative steps and computational time of One-step inverse IGA will be reduced significantly compared with that of One-step inverse finite element method.