Research On Isogeometric One-step Inverse Algorithm For Sheet Metal Stamping

There are many body cover parts,and most of them are stamping parts with complex shapes and high assembly precision requirements.Therefore,the requirements for the design and manufacture of molds for body parts are also improved accordingly.In order to shorten the production cycle of the car body,the sheet metal stamping forming simulation can obtain the formability analysis of the stamping parts and the shape of the initial configuration in the early stage of design,and improve the efficiency of mold design.In this paper,the isogeometric onestep inverse method of sheet metal stamping is studied,and the Kirchhoff-Love shell surface element is applied to the isogeometric one-step inverse simulation to consider the bending effect in the process of sheet metal stamping.The main research contents of this paper include:(1)Isogeometric analysis method represents geometric models and analytical models.In this paper,the geometric model is expressed as the tensor product of basis functions and control points in two directions by the isogeometric method.The geometric model is also used as an analytical model for the subsequent one-step inverse forming simulation.There is no need to divide the mesh model,and the data interaction between CAD and CAE is eliminated.(2)An initial solution prediction algorithm for isogeometric one-step inverse shaping is studied.The discrete surface Ricci flow algorithm in computational conformal geometry is introduced into the initial solution algorithm of one-step inverse shaping.The energy mapping method and the discrete surface Ricci flow algorithm are compared and studied.Based on the strong applicability of the latter and the subsequent elastic iterations can converge faster due to the unfolding model of control net,the discrete surface Ricci flow algorithm is used in this paper as the unfolding algorithm.The unfolding control net obtains the initial solution through elastic iteration,which takes the deformation of the control net as elastic deformation to solve the internal force balance,and obtains a better initial solution.The initial solutions obtained by elastic iteration under the unfolding models of two different unfolding algorithms are almost completely coincident,which verifies the stability and effectiveness of the prediction algorithm of the initial solution.(3)Construction of an isogeometric one-step inverse forming algorithm based on Kirchhoff-Love shells.According to the strain tensor and geometric deformation relationship of Kirchhoff-Love shell element,the principal elongation and principal strain of surface element are deduced.Then,the virtual work equation,stiffness matrix expression and internal force expression of the element are deduced by considering the strain component expression of the element and considering the thickness change during the stamping process.The punch force and blank holder force in the stamping process are equivalent to the control point as external forces.And the punch force is equivalent to the control point by solving the normal vector of the control point with the aid of Greville abscissae.The finally obtained nonlinear equation system is solved by the Newton-Raphson iterative algorithm,and the shape of the initial configuration and the thickness distribution of the final configuration are obtained.The profile and thickness distribution obtained by the examples verify the effectiveness of the algorithm considering the punch force and blank holder force.