A generally suited method to get initial guess solutions for one-step and multi-step simulations of tube and profile forming based on parameterization

Abstract

SUMMARYIn one-step and multi-step simulations, how to get initial guess solutions effectively is a key point, which has gained great attention during the past decades. However, most of the achievements have been targeted at sheet metal forming, rarely at tube or profile forming, which hinders the applications of oneand multi-step approach to tube and profile forming. A new method, based on the parameterization in computer graphics, is presented in this paper, in which a sort of parameterized computation defined in the cylindrical coordinate system is utilized to produce initial guess solution for initial configuration, and a simple but effective geometric algorithm on the basis of the parameterization is proposed for intermediate configuration. Different from the original plane parameterization, the parameterized computation in this method is to map mesh onto initial straight tube or profile surface instead of plane. The method is highly efficient since only one set of large sparse linear equations needs to be solved in the parameterized computation and the geometric algorithm for intermediate configuration is also fast in mesh-mapping. In order to verify the validity and efficiency of the presented method, several numerical examples are provided and the obtained initial guess meshes are satisfactory.

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

“…Owing to its advantages in evaluating the forming difficulties at the early design stages, performing fast estimation of the blank shape and making fast analysis of the sensitivity of some process parameters (Batoz et al, 2005), the inverse approach (IA) is widely studied in the past few decades (Batoz et al, 1998(Batoz et al, , 2005Chung and Richmond, 1992a, b;Fu et al, 2009Fu et al, , 2011Guo et al, 1990Guo et al, , 2000Guo et al, , 2003Huang et al, 2006;Lan et al, 2005;Lee and Huh, 1998;Naceur et al, 2002Naceur et al, , 2004Park et al, 1999;Parsa and Pournia, 2007;Tang et al, 2007aTang et al, , b, 2010Wang et al, 2002;Zhou et al, 2009). There are two types of inverse methods among them: one is on the principle of virtual work (Guo et al, 1990;Batoz et al, 1998) and the other on the ideal forming theory (Chung and Richmond, 1992a, b).…”

“…Lu et al (2004) further proposed the section curve expanding method to overcome the difficulty for searching a symmetry curve and element overlapping confronted by the geometric mapping method. However, all these methods have their own application limitations since they are greatly influenced by the geometric shapes of deformed surfaces (Fu et al, 2011). Therefore, finding a universal and robust method to get a reasonable initial guess is still a problem deserving of study.…”

“…As the initial guess estimation process can be seen as a one-to-one mapping from the 3D mesh surface to a 2D planar domain, the mesh parameterization method which is widely used in computer graphics is gradually becoming an alternative initial guess method in recent years (Tang et al, 2007a, b;Fu et al, 2011;Zhang et al, 2007). As for the details of the mesh parameterization, readers can refer to the Floater and Hormann (2005) and Sheffer et al (2006).…”

“…Tang et al (2007a, b) utilized the conforming mapping methodology to obtain the initial solution by Desbrun quadratic energy mapping method. A similar method was adapted by Fu et al (2011) in tube or profile forming. As it is based on a linear approximation of the harmonic mapping, the obtained initial guess can get a minimized distortion of the 3D original mesh and it is more robust than the geometric mapping method.…”