基于罚函数法的大变形冲击碰撞问题显式健壮格式  

Robust explicit computational strategies based on penalty method for large-deformation impact problems

作　　者：初东阳 戎宇飞 周章涛[1,2] 伍星星 汪俊 王海坤[1,2] CHU Dongyang;RONG Yufei;ZHOU Zhangtao;WU Xingxing;WANG Jun;WANG Haikun(China Ship Scientific Research Center,Wuxi 214082,Jiangsu,China;TaiHu Laboratory on Deep Sea Technology and Science,Wuxi 214082,Jiangsu,China)

机构地区：[1]中国船舶科学研究中心,江苏无锡214082 [2]深海技术科学太湖实验室,江苏无锡214082

出　　处：《爆炸与冲击》2025年第3期154-167,共14页Explosion and Shock Waves

基　　金：国家重点研发计划(2022YFB3306200)。

摘　　要：为了提高基于罚函数法的显式有限元对大变形接触-碰撞问题仿真的精确性和健壮性,基于前增量位移中心差分方法,发展了一种新的大变形接触非侵入算法。将动力方程求解步分解为不考虑接触的预估步和考虑接触的修正步,在当前时刻,采用罚函数法施加接触惩罚力,使其满足非侵入条件,从而提高显式接触计算的精确性;在仅能获得下一时刻位移的情况下,为了精确计算下一时刻的大变形内力,基于任意参考构型大变形理论,将动力学方程内力项映射到已知的参考构型求解,避免使用相关物理量的中间构型近似值,从而降低由大变形计算引入的数值误差。更严格的几何非线性算法以及接触算法可有效抑制实体间的非物理穿透和大变形碰撞过程中的单元畸变,提高计算程序的健壮性。对典型碰撞及侵彻算例进行仿真,并与商业软件的结果进行对比,验证了所发展的大变形接触-碰撞显式算法的正确性,并证明了在高速大变形碰撞仿真方面,当前接触-碰撞显式算法比基于蛙跳格式中心差分和罚函数法的经典接触-碰撞算法更加健壮。To improve the accuracy and robustness of the explicit finite element algorithm based on penalty method for simulating large deformation impact-contact problem,a new large-deformation non-penetration contact algorithm based on forward incremental displacement central difference(FIDCD)is developed.On the one hand,according to FIDCD,the solving step of the dynamic equation is decomposed into an estimated step without considering contact and a correction step considering contact constraint.At the current moment,a contact force is applied through the penalty method to make the deformation of entities satisfy the non-penetration condition.The contact force is calculated by a soft constraint penalty stiffness,which helps to maintain stability of contact localization.It refines the numerical accuracy of the explicit contact computation.On the other hand,to accurately calculate the large-deformation internal force of the next moment while only obtaining the displacement,the internal force term of the dynamic equation is mapped to a known configuration for solution based on the arbitrary reference configurations(ARC)theory.It avoids using the values of variables at intermediate configuration to approximate them,thereby improving the numerical accuracy of the large deformation computation.More rigorous contact algorithms and geometric nonlinear solution strategy can effectively suppress mesh distortion and nonphysical penetration between entities during large-deformation impact simulation.This thus improves the robustness of the new explicit algorithm.Finally,the computational program written according to the new developed algorithm is applied to simulate several impact and penetration examples with different impact velocities.By comparing the simulation results with those obtained from commercial software,the correctness of the developed algorithm and computational program is verified.At the same time,it can also be proven that the algorithm proposed is more robust in simulating high-speed and large-deformation impact pro

关 键 词：接触-碰撞 显式有限元方法 接触算法 几何大变形 罚函数法 

分 类 号：O347.3[理学—固体力学]