A new method to get initial guess configuration for multi-step sheet metal forming simulations
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ORIGINAL ARTICLE
A new method to get initial guess configuration for multi-step sheet metal forming simulations Yongcai Liu 1,2 & Wenliang Chen 1 & Qingwan Hu 2 & Chunhui Yang 3 & Yidong Bao 1 Received: 5 April 2020 / Accepted: 9 August 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract This study aims to develop a universal, robust, and linear method to obtain an initial guess configuration for the multi-step finite element method (FEM) solver of sheet metal forming. Using the decoupling theory, the deformation at each step in the multi-step FEM solver of the sheet metal forming is decoupled into two independent deformation modes: bending-dominated deformation and stretching-dominated deformation. The configuration of the bending-dominated deformation constrained by the sliding constraint surface is considered as the initial guess configuration for the current step in multi-step FEM solver. To get an accurate initial configuration at each step, the method of Laplace-Beltrami operator (LBO) on a simplicial surface is employed to obtain the initial guess configuration effectively. Several numerical examples are provided for validation and verification of the proposed method through its applications for complicated sheet metal workpieces of finite element simulations. The results show that the proposed method on the simplicial surface for the initial guess configuration within a few iterations to be significantly effective. Keywords Sheet metal forming . Multi-step FEM solver . Decoupling theory . Initial guess configuration . Laplace-Beltrami operator . Simplicial surface
1 Introduction Sheet metal forming is a material process of complicated deformation, which is significantly influenced by die geometry, blank shape, blank holding force, blank-tool friction, lubrication, and so on [1–4]. Traditional trial-and-error technology would involve many long and expensive tryouts. To reduce the time and costs, the sheet metal forming simulation with the finite element method (FEM) has been widely applied in the past decades. The FEM simulation falls into two types: explicit and implicit formulation [5]. The implicit formulation can be implemented through one-step or through a multi-step
* Yidong Bao [email protected] 1
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, Jiangsu, People’s Republic of China
2
Department of Mathematics and Statistics, Qujing Normal College, Qujing 655011, Yunnan, People’s Republic of China
3
School of Engineering, Western Sydney University, Locked Bag 1797, Penrith, NSW 2751, Australia
mold. Either mold must produce the initial guess configuration, which is often solved by the nonlinear equation with any numerical method such as the Newton-Raphson (N-R) iterative solver. As well known, the convergence is the key issue for any iterative solver, so a good initial guess configuration is very important to the implementation of the implicit formulation of the FEM. Both one-step FEM and multi-step FEM so
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