基于态型近场动力学的准静态数值仿真方法  

Numerical method of quasi-static simulations using state-based peridynamics

作　　者：孙璐妍 余音[2] 郑晓玲[1] SUN Lu-yan;YU Yin;ZHENG Xiao-ling(Shanghai Aircraft Design and Research Institute,Shanghai 201210,China;School of Aeronautics and Astronautics,Shanghai Jiao Tong University,Shanghai 200240,China)

机构地区：[1]上海飞机设计研究院,上海201210 [2]上海交通大学航空航天学院,上海200240

出　　处：《计算力学学报》2022年第4期518-522,共5页Chinese Journal of Computational Mechanics

摘　　要：近场动力学PD(Peridynamics)是一种通过空间积分方程描述力学行为的方法,对不连续问题的求解有重要的应用前景。本文构建了一种基于态型PD理论的准静态数值仿真方法,推导了节点刚度矩阵和结构刚度矩阵的表达关系,改进了Kilic在键型PD理论中运用的动力松弛法,将其引入态型PD理论,综合绝对和相对收敛准则得到了一种修正的迭代收敛准则。用该方法对薄板轴压稳定性进行了数值仿真,采用了方板晶格的离散方法,以此减小计算规模提高计算效率,成功捕获了三次屈曲现象,对比经验公式和试验结果等过往研究结论,一致性良好。Peridynamics(PD) is a method describing mechanical behavior by a spatial integral equation, and has a great potential for solving discontinuous problems.A numerical method of quasi-static simulations using state-based PD theory is developed: relation between nodes and structural stiffness matrix is derived;dynamic relaxation method is modified on the basis of what Kilic used in bond-based PD theory and is introduced into state-based PD theory;modified convergence criteria are derived from the combination of absolute and relative criterion.This method is applied to simulating the stability of a thin metallic panel under axial compression, the panel is proposed to discretized into nodes that represents square plate lattices to reduce the calculation scale and improve calculation efficiency.The initial buckling, secondary bifurcation buckling and tertiary snap-through buckling are successfully captured in the simulation, and the result shows a good agreement among empirical formula, test result, etc, in the present research.

关 键 词：态型近场动力学 板壳屈曲 稳定性 动力松弛法 收敛准则 

分 类 号：O302[理学—力学]