Research On Initial Solution Algorithm Of One-Step Inverse Isogeometric Stamping For Complex Trimmed CAD Model

Automobile panel molds is a special and important stamping parts.With the continuous maturity of finite element basic theory,sheet metal numerical simulation technology has been widely used in the stamping and forming analysis of body covering parts,which provides a strong technical guarantee for the rapid development of the automobile industry and brings huge economic benefits to enterprises.One-step inverse method based on plastic deformation theory is widely used in the initial design stage of stamping parts because of its simple input and high computational efficiency.The one-step inverse isogeometric analysis method has been successfully applied in sheet metal forming with simple geometry,but the stamping parts in actual industrial production usually contain a large number of trimmed NURBS surfaces.The key step of sheet metal forming is to expand the unexpandable stamping parts CAD model into a plane domain to obtain a good initial solution.The initial solution is used for the subsequent calculation by the Newton-Raphson iterative method to solve the equivalent stress,equivalent strain and thickness of the final configuration.Therefore,the quality of the initial solution directly affects the calculation of the plastic iteration.In this paper,an initial solution prediction algorithm based on energy method is used to solve the one-step inverse isogeometric initial solution of the complex trimmed model.The trimmed NURBS surfaces are treated by trimmed surface analysis method.The key problems such as data structure processing and numerical integration of trimmed surface are studied in detail.The intersection coordinates of the trimmed element were obtained by using the data information of the intact surface before trimming,and the trimmed element was decomposed into several triangle integral domains,thus the stiffness matrix of the trimmed element was calculated.The Nitsche’s method is used to deal with the coupling of the non-conforming surface.Based on the equilibrium equation,the formula of solving the coupling matrix in Nitsche’s method is deduced.Nitsche’s method is combined with the trimmed surface analysis method to introduce the principle of selecting the integral interval when integrating along the trimmed curve.It is applied to the initial solution prediction algorithm based on the energy method.Through three numerical examples of square box,S-Rail and B-pillar upper joint,the initial solution contour of complex trimmed model was obtained.The results were compared with the corresponding initial solution of single-patch model or the initial solution obtained by finite element analysis method,which proved the effectiveness of the proposed method when dealing with complex trimmed model for sheet metal forming analysis.