Research And Application On Fast And Stable Integration Method In Finite Element Method For Elastomer Simulation

In the area of computer graphics,simulation of 3D elastic objects,based on physical methods,possesses plentiful applications.The Finite Element Method requires complicated numerical calculation,which leads to large computational cost.In the real application,it is necessary to make the simulation efficient and stable.Therefore,how to improve the Finite Element Method to achieve such goal is difficult.This thesis mainly completes the following three works:(1)an unconditionally stable explicit integration method is proposed.This thesis adopts the numerical method in the field of structural mechanics to analyze the amplification matrix of the transfer function for the linear and nonlinear system.By making the spectral radius of the amplification matrix less than 1 to propose an unconditionally stable explicit integration method;(2)a data-driven implicit integration method is proposed.A cross-correction training strategy is proposed to improve long-term stability.Besides,a supervision item on the timestep of k is designed to further reduce the error accumulation;(3)the application of the fast finite element method to force haptic feedback devices is realized.Based on the force haptic feedback devices developed by our group,the thesis realizes the collision and interaction modules for the tissue stiffness perception application and a MFC based interaction platform.The experimental results of this thesis are as follow:(1)the proposed unconditionally stable explicit integration method has high computational efficiency and unconditionally stable calculation.Moreover,its accuracy is not only better than the commonly used explicit and implicit integration methods,but also better than several unconditionally stable explicit integration methods in recent years;(2)the proposed data-driven implicit integration method can significantly improve the computational efficiency,and the deformation simulation process is stable with realistic visual effects;(3)for the application of the tissue stiffness perception application,the interaction part is smooth and stable,the virtual tissue deformation simulation can truly and accurately reflect the user's touch effect and the operator can correctly perceive the different stiffness information of the model.