【作者】 马上；

【导师】 张雄； 周旭；

【作者基本信息】 清华大学 ， 力学， 2009， 博士

【摘要】 冲击爆炸问题在国民经济和科学技术中有广泛而重要的应用。数值模拟是进行这类问题研究的重要手段，但冲击爆炸问题涉及多种学科，往往非常复杂，对数值方法提出了很大的挑战。无网格法在处理大变形问题以及涉及材料破坏的问题具有优势，为冲击爆炸问题的数值模拟提供了有效工具。一些质点类无网格法，如光滑质点动力学方法（SPH）已经取得了相当丰富的成果，得到了工程界的认可。本文针对超高速碰撞和爆炸问题，基于无网格物质点法（MPM），研究适合对冲击爆炸问题进行模拟的数值方法，研制三维物质点法程序，建立有效的数值模拟工具。针对有限元在求解超高速碰撞问题遇到的网格畸变这一困难，本文借鉴物质点法的思想，提出了物质点有限元法。在物质点有限元法中，仍用有限单元离散物体，在大变形区域布置背景网格，被背景网格覆盖的区域将结点视为物质点，用物质点法进行计算，其他区域仍用有限元法求解，从而解决有限元法在处理大变形问题时网格畸变的问题。通过Taylor杆碰撞的模拟和弹丸超高速碰撞薄板的模拟，说明了此方法在效率上和在描述碎片云的形成过程上都比有限元法具有优势。针对物质点法存在的数值断裂问题，本文提出了在物质点法中自适应分裂质点的方案，使物质点法可以在质点变形最大的方向上自适应分裂质点，从而避免了数值断裂。将自适应分裂质点物质点法用于激波管、爆轰驱动飞片、聚能射流等问题的模拟和分析，取得了较好的效果。在理论和算法研究的基础上，研制了用于冲击爆炸问题的三维显式物质点法程序MPM3DPP。从影响点搜索、形函数、稳定性、时间积分、边界条件和接触算法等方面对物质点法和SPH方法进行了比较，通过Taylor杆问题和超高速碰撞问题的模拟了进行比较和分析。更多还原

【Abstract】 The impact and explosion problems have broad and significant applications in thenational economy and technology. Numerical simulation is an important study ap-proach for this kind of problems. However, the impact and explosion problems covera broad range of disciplines, and are often very complicated. It is a great challengefor numerical methods. Meshfree methods have advantages in dealing with large de-formation and material fracture. They are effective tools for simulation of impact andexplosion problems. Some meshfree particle methods, such as smoothed particle hy-drodynamics (SPH), have many successful applications in this area, and are acceptedby engineers. In this paper, studies are carried out based on the material point method(MPM) with the aim of solving hypervelocity impact and explosion problems. Thenumerical methods for impact and explosion problems are investigated. A three di-mensional material point method code has been developed as an effective numericalsimulation tool.Finite element method has the difficulty of mesh distortion in solving the hyper-velocity impact problems. An explicit material point finite element method is proposedby using the idea of the material point method. The material domain is discretized byfinite elements. The momentum equations are solved on a predefined computationalgrid (like the material point method) in the large deformation zone, and on the finiteelement mesh (like the traditional finite element method) elsewhere. Mesh distortionproblem is avoided in material point finite element method. The advantages of theproposed method in efficient and depicting debris cloud are illustrated by simulatingTaylor bar impact problem and hypervelocity impact problem.To solve the numerical fracture problem existing in the material point method , anadaptive particle splitting scheme was proposed. The particle can be split adaptively inthe direction with the largest deformation. The adaptive material point method has beenapplied in the shock tube, explosively driven ?yer, and shaped charge jet formation problems with good performance.Based on theoretical and algorithmic studies, three dimensional explicit materialpoint method code MPM3DPP is developed. SPH and MPM are compared in neighborsearching, approximation functions, consistency of shape functions, instability, timeintegration, boundary conditions and contact algorithm. The taylor bar impact problemand hypervelocity impact problem are analyzed by the two methods for comparison.更多还原