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

摘要

In 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 one-and 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.