基于键型近场动力学非连续Galerkin有限元法的爆炸毁伤模拟

Blast Damage Simulation With the Discontinuous Galerkin Finite Element Method of Bond-Based Peridynamics

近场动力学是一种积分型非局部的连续介质力学理论,已广泛应用于固体材料和结构的非连续变形与破坏分析中,其数值求解方法主要采用无网格粒子类的显式动力学方法.近年来,弱形式近场动力学方程的非连续Galerkin有限元法得到发展,该方法不仅可以描述考察体的非局部作用效应和非连续变形特性,还可以充分利用有限单元法高效求解的特点,并继承了有限元法能直接施加局部边界条件的优点,可有效避免近场动力学的表面效应问题.该文阐述了键型近场动力学的非连续Galerkin有限元法的基本原理,导出了计算列式,给出了具体算法流程和细节,计算模拟了脆性玻璃板动态开裂分叉问题,并对爆炸冲击荷载作用下混凝土板的毁伤过程进行了计算分析.研究结果表明,该方法能够再现爆炸冲击荷载作用下结构的复杂破裂模式和毁伤破坏过程,且具有较高的计算效率,是模拟结构爆炸冲击毁伤效应的一种有效方法.

The peridynamics(PD)as an integral non-local continuum mechanics theory,is widely used in the discontinuous deformation and failure analyses of solid materials and structures,mainly with the explicit dynamic solution method for meshless particles.In recent years,the discontinuous Galerlin finite element method for weak-form peridynamic equations has been developed.This method can not only describe the non-local action effects and discontinuous deformation characteristics of the investigated body,but also make full use of the finite element method.It has the advantages of efficient solution,direct application of local boundary conditions,and effective avoidance of the surface effects in peridynamics.The basic principle of the discontinuous Galerkin finite element method of bond-based peridynamics was expounded,the calculation formula was derived,the specific algorithm flowchart and details were given,and the dynamic cracking and bifurcation problems of brittle glass plates were simulated.The damage processes of concrete slabs under blast impact loads were calculated and analyzed.The research results show that,the proposed method can predict the complex rupture mode and the damage process of the structure under blast impact loads,with high computational efficiency,and makes an effective way to the simulation of the structural blast damage effects.