Initial solution estimation of one-step inverse isogeometric analysis for sheet metal forming with complex topologies

• Published in: Computer methods in applied mechanics and engineering Vol. 391; p. 114558
• Main Authors: Wang, Changsheng, Zhang, Xi, Zhang, Zhigong, Zhang, Xiangkui, Hu, Ping
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.03.2022; Elsevier BV
• Subjects: Algorithms; Coordinate transformations; Coordination compounds; Finite element method; Initial solution estimation; Isogeometric analysis; Metal forming; Metal sheets; One-step inverse approach; Sheet metal forming; Stamping; Surface analysis (chemical); Topology; One-step inverse approach; Isogeometric analysis; Sheet metal forming; Initial solution estimation
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2021.114558

The one-step inverse isogeometric analysis method has been successfully applied in sheet metal forming with simple geometries. Generally, actual stamping parts frequently contain numerous trimmed NURBS-based CAD surfaces. The key step in sheet metal forming is to unfold the undevelopable CAD model onto a planar domain and obtain a good initial solution. In this study, we estimate the initial solution of stamping parts with complex topologies using an energy-based algorithm. The trimmed surface analysis technique and Nitsche’s method are adopted for trimmed and multi-patch isogeometric analysis. A new coordinate transformation system is used to avoid special treatment for negative angle and vertical wall problems, which are common in metal sheet forming. We demonstrate our algorithm with three examples and compare the results with one-step inverse isogeometric analysis of simple geometry or the traditional finite element method. These examples illustrate the performance of the new method and its applicability for the integration of design and analysis in sheet metal forming with complex topologies. •The initial solution is estimated for stamping parts with complex topologies.•The trimmed surface analysis technique and Nitsche’s method are adopted for the stiffness matrix.•The quaternion method is used to avoid special treatment for negative angle and vertical wall issues.