Research On One-step Inverse Isogeometric Forming Analysis Method Of The Trimmed CAD Model

One-step inverse forming method based on plastic deformation theory is a common method for numerical simulation in the field of stamping forming.When using the classic one-step inverse finite element method to predict the stamping parts,the model needs to be meshed,and the effective fusion of CAD and CAE cannot be achieved.The isogeometric analysis method can solve this problem.Industrial CAD software uses B-rep method and constructing solid geometry to describe CAD models.Both methods require a Boolean sum operation,which results in a large number of trimmed surfaces.This article mainly studies the one-step inverse geometric analysis method of the trimmed CAD models.The main contents include:The geometric processing of the trimmed CAD model,including: use the inversion function to invert the refined node vector of the trimmed curve into the parameter space of the NURBS surface,and then use the Newton-Raphson iterative algorithm to calculate the intersection point;determine the trimmed unit by the element index;Classify the trimmed unit according to the shape of the trimmed unit;use Bézier surface patches to reconstruct the trimmed unit,etc.Based on the local method,the stiffness matrix and internal force vector of the trimmed model are calculated,and the nonlinear equations are constructed.The Newton-Raphson iterative algorithm is used to solve the final nonlinear equilibrium equation.The distribution of physical quantities such as equivalent stress,equivalent strain and thickness in the final configuration is obtained.The procedure of one-step inverse geometric analysis method is used to perform stamping simulation calculation on different trimmed NURBS surface models,and the calculation result is compared with the calculation result of the classic grid-based one-step inverse finite element method.The final numerical results verify that the method studied in this paper has good convergence and accuracy in processing the stamping forming simulation of the trimmed NURBS surface model.