崔潇骁. 空中爆炸与靶标相互作用的物质点有限差分法研究. 清华大学博士学位论文，2014年4月
空中爆炸与靶标相互作用问题在公共安全和国防等诸多领域中具有重要的应 用背景,其过程中涉及炸药起爆、爆轰波传播和材料特大变形,是具有很强非线 性的流固耦合问题,因而给传统的单一数值方法带来了很大的困难。针对这一问 题,本文吸收了无网格物质点法和有限差分法的思想,分别在时间和空间上将二 者相结合,提出了交替物质点有限差分法和耦合物质点有限差分法,充分发挥了 物质点法和有限差分法的优势,为空中爆炸与靶标相互作用过程的分析提供了一 种有效的新型数值分析手段。
针对空中爆炸与靶标相互作用过程中各物理阶段的不同特性,本文提出了交 替物质点有限差分法,采用物质点法求解炸药起爆过程和结构毁伤过程,采用有 限差分法求解爆轰波传播过程,分阶段交替求解爆炸毁伤过程。为了克服单纯欧 拉方法追踪物质界面的困难,同时避免粒子类方法在物质界面处出现的非物理穿 透现象,本文采用物质点及其退化而成的无质量示踪点交替地在各个求解阶段对 物质界面进行追踪。本文采用该方法求解了二维和三维的空中爆炸问题,并且将 其应用于空中爆炸与钢板相互作用问题的模拟,取得了良好的效果。
针对空中爆炸与靶标相互作用过程各区域内所发生物理过程的不同特性,本 文提出了耦合物质点有限差分法,将求解域划分为流体区和流固耦合区,并分别 在欧拉框架下和拉格朗日框架下采用有限差分法和物质点法对各区域离散求解。 为了完成两个区域间的数据交换和守恒变量的输运,本文在二者的交界面处构造 了“握手区”。流固物质界面位于同一求解框架内并且两个求解区域的交界面位 于同一材料区域 (流体),因而有效地减小了物质界面处的界面效应。本文采用该 方法求解了二维空中爆炸问题,进而将其应用于高能炸药爆炸对混凝土板破坏过 程的模拟和 RHA 钢靶板在空中爆炸载荷下的动态响应分析,均取得了与实验和理论分析相一致的结果。
蜂窝夹芯板结构质量轻、吸能效率高、抗爆性能好,因此在安全防护领域中具有很广泛的应用前景。本文采用耦合物质点有限差分法,对蜂窝夹芯板结构在 空中爆炸载荷下的响应问题进行了多组工况的模拟,从蜂窝芯质的几何形状、几 何尺寸、芯质材料等方面对其抗爆性进行了研究,提出了蜂窝夹芯板防护结构抗 爆性能的定性规律,研究结果可为蜂窝夹芯板防护结构的设计提供参考。
The air explosion and its interaction with targets have important application background in the fields of public security and national defense. The process, which involves high explosive detoation, dispersion of the detonation wave and extreme deformation of materials, is a fluid-structure interaction problem with strong nonlinearity, and a big challenge to the traditional numerical methods. To effectively model this kind of problems, an alternating finite difference material point (AFDMP) method and a coupled finite difference material point (CFDMP) method are proposed by combining the material point method (MPM) and finite difference method (FDM) in time and space, respectively. These two methods, which fully combine the advantages of MPM and FDM, are effective numerical methods for studying the air explosion and its interaction with targets.
Based on the physical processes of the air explosion and its interaction with targets, the alternating finite difference material point is first proposed, in which the initiatory detonation and eventual fluid structure interaction are simulated by the standard MPM, while the finite difference method is employed to simulate the dispersion of the detonation products into the surrounding air. The MPM particles and their degenerated massless marker points are employed to track the moving interface between detonation products and air. Hence, the difficulties of tracking material interface in Euler methods are overcomed, while the non-physics penetration near the material interface in particle methods are avoided as well. To study its accuracy and efficiency, AFDMP is applied to simulate 2D and 3D air explosion problems. An air explosion problem and interaction with a steel plate target nearby is also simulated. Numerical results are in good agreement with theoretical solutions or empirical formulae.
Based the physical processes in different space regions in the air explosion and its interaction with targets, the coupled finite difference material point is then proposed, in which the problem domain is partitioned into a fluid region and a FSI region in space. FDM is employed to simulate a large proportion of the fluid region, while MPM is employed in the FSI region which contains the structures and the fluid near the structures. A bridging region is employed to exchange the infomation and to transport the conservative variables. Therefore, the interface of fluid and structure located in the same solution region and the interface between two computational regions is located in the same material region (fluid), so the interface effect could be significantly reduced. CFDMP is applied to simulate a 2D air explosion problem and then study the damage of the concrete slab under air blast loading. The response of steel plate targets subjected to air-blast loading is also studied by CFDMP and the numerical results are in good agreement with those of experiments.
The honeycomb sandwich panel structure possesses lots of advantages such as low mass, high efficiency of energy absorbing and high quality of anti-explosion, so it has broad application prospect in the field of security protection. Therefore, several cases of air explosion and its interaction with honeycomb sandwich panels are simulated by using CFDMP. The effects of honeycomb’s geometry, dimension and material are studied to develop a qualitative law of the anti-explosion performance of honeycomb sandwich panels, which would be helpful to design the honeycomb sandwich panel structures.