An initial solution estimation method based on As‐Rigid‐As‐Possible mesh parameterization for one‐step simulation

Abstract

Purpose -The purpose of this paper is to propose a universal, robust and efficient method to obtain a reliable initial guess solution for the one-step finite element simulation. Design/methodology/approach -In one-step simulation, getting initial guess solutions effectively is essential to ensure the success of the non-linear resolution in the implicit static solver and to speed up the convergence of the Newton-Raphson iterations. A newly emerging mesh parameterization approach named As-Rigid-As-Possible method, which is widely used in computer graphics, is proposed as an effective initial guess estimation method in this paper. It is almost an isometric parameterization and showing excellent area-preserving capability than other state-of-the-art approaches. Several numerical examples are provided to verify the validity and efficiency of the presented method. Findings -Compared with the geometry mapping methods, the presented ARAP method shows its universality in handling types of workpieces whether they have quasi-vertical walls or they are long and complicated. Complex 3D workpieces with many local convex and concave features can also be well handled without large element shape distortions. In contrast to the energy based mapping algorithm, the method presented in this paper does not need to predefine the boundary nodes which will introduce less distortion to the elements near the boundary. Originality/value -This paper is the first to utilize the As-Rigid-As-Possible mesh parameterization algorithm to obtain an initial guess for the one-step simulation. The numerical experiments show that the approach is universal, robust and efficient and can be further utilized in the optimum blank design or blank shape optimization.One-step simulation 379 1. Introduction Sheet metal forming processes generally experience very complicated deformation effected by several process parameters such as the die geometry, the blank shape, the sheet thickness, the blank holding force, friction, lubrication and so on (Lee and Huh, 1998). The traditional trial-and-error approach to determine the optimum condition of process parameters is usually unreliable and costly because it requires the competence of qualified engineers during a long period. To avoid these long and expensive experimental try-out procedures, the numerical sheet forming simulation is widely used in the past few decades with the rapid development of finite element method (FEM) and computer technology.There are mainly two approaches for sheet metal forming simulation: the incremental approach and the inverse FEM. The incremental FEM, based on the flow theory of plasticity, gives full consideration to those process factors such as deformation history, exact boundary, contact conditions and so on. This method provides very precise solution and is widely used to verify the formability of products in the final design stage. However, it needs detailed design parameters and so requires numerical trial-and-error with enormous time and cost, which is not suitable for the concep...