有限元法与光滑粒子法的耦合算法研究
|
摘要
材料的大变形和破坏广泛存在于工程实际问题中,如侵彻、爆炸、金属成型、流体流动等。研究模拟此类问题的数值方法具有重要的应用价值。有限元法对于小变形问题计算精度好、效率高,但对于大变形问题会遭遇单元畸变,其求解精度和效率都会显著降低。光滑粒子法具有很强的大变形求解能力,易于模拟材料的破碎和飞溅等复杂物理现象,但是在计算效率和边界条件处理方面不如有限元法。耦合有限元法与光滑粒子法,可以充分利用两种算法的优势,为大变形问题的模拟提供一条有效的途径。在涉及大变形的部分用光滑粒子法求解,而对其他部分用有限元法求解,这样既能克服单元畸变,又能保持较好的计算效率。由于耦合算法的研究起步较晚,并且光滑粒子法本身也还存在一些问题,所以,在计算精度、效率和稳定性等方面还有很多问题需要深入研究和解决。
本文先从精度和效率上对光滑粒子法进行了一些改进,在此基础上系统地研究了有限元法与光滑粒子法的固定耦合算法和自适应耦合算法,并应用耦合算法开展了高速冲击问题的数值模拟研究,同时还初步探讨了耦合算法在流体与结构相互作用模拟中的应用。本文具体开展和完成了如下工作：
(1)介绍了光滑粒子法的基本原理,从拉伸不稳定性、接触界面处理和相邻粒子搜索三方面对其进行了改进。讨论了消除拉伸不稳定性的人工应力法,提出了轴对称问题的人工应力计算和施加方法,通过橡胶球撞击问题验证了其有效性。将基于罚函数的粒子接触算法拓展到二维轴对称和三维问题中,通过测试算例验证了接触算法的正确性,并应用带接触算法的光滑粒子法模拟了铝板的正侵彻和斜侵彻,得到了与实验相符的模拟结果,模拟的精度远高于无接触算法的光滑粒子法。讨论了常用的相邻粒子搜索法,简要介绍了树形搜索法和Point-In-Box(PIB)搜索法；分析了PIB搜索法存在的问题及其原因,提出了改进的条形化PIB搜索法；通过测试算例对比了三种算法的性能,结果表明条形化PIB搜索法优于PIB搜索法和树形搜索法,能显著地提高光滑粒子法的计算效率
(2)对耦合算法中单元与粒子的接触和耦合两个关键问题进行了研究。首先,基于单元接触算法的思想,引入粒子半径,得到了单元-粒子接触算法,通过测试算例验证了算法的正确性；提出基于相邻粒子搜索的过滤算法,减少从节点数和参与接触搜索的主面段数,使单元-粒子接触搜索效率得到提高。然后,提出了两种单元-粒子耦合算法。一种是基于粒子与单元边连接的算法,即：将粒子与单元边上的点固连,使两者具有共同的速度和位移；通过测试算例验证了算法的正确性,分析了粒子密度对其计算精度的影响,结果表明取合适的粒子密度时该算法可以获得理想的计算精度,但在耦合界面处会出现局部的应力振荡。另一种是基于虚粒子和等效力的算法,即：通过将祸合界面附近的单元作为虚粒子包含到光滑粒子法计算中,得到单元对粒子的作用力,同时根据耦合界面附近的粒子应力确定作用在单元边上的等效面力并将其等效到单元节点上,得到粒子对单元节点的作用力；通过测试算例验证了算法的可行性和正确性,研究了光滑长度对算法的计算精度的影响,得到了不同分布形式的粒子与单元耦合时光滑长度的合理取值；将该算法与现有的一些算法进行对比,结果表明该算法具有更佳的计算精度。
(3)基于前述的基本算法,建立了有限元法与光滑粒子法的固定耦合算法,编制了相应的计算程序,并开发了二维冲击仿真软件。应用固定耦合算法和光滑粒子法对泰勒杆实验和铝板的正侵彻进行了对比模拟,检验了固定耦合算法在高速冲击模拟中的可行性和正确性,同时表明固定耦合算法在获得与光滑粒子法相近的计算精度时能有效地提高计算效率。在固定耦合计算程序中嵌入耦合粘塑性和延性损伤的本构模型,模拟了平头弹撞击金属靶板的冲塞失效过程；将模拟结果与实验结果进行对比,结果表明固定耦合算法能有效地预测弹体剩余速度、弹靶变形以及靶板的失效形式等。
(4)在固定耦合算法的基础上,提出最小内角转化准则和单元分组转化方式,实现单元向粒子的转化,建立了有限元法与光滑粒子法的自适应耦合算法,编制了相应的计算程序。应用自适应耦合算法模拟了泰勒杆实验,将计算结果与实验结果以及其他算法的计算结果对比,验证了该算法在高速冲击模拟中的可行性和正确性。进一步应用该算法模拟了侵彻问题,包括：铝板的正侵彻、混凝土的正侵彻以及柱体斜侵彻铝板。模拟结果表明该算法能比较准确地预测了弹体剩余速度,较好地模拟材料的破坏以及再现脆性材料的破碎和飞溅等现象；而且,该算法在计算效率方面比固定耦合算法更具优势,特别是对于难以准确预知材料破坏区域的问题。
(5)基于固定耦合算法模拟了流体与结构相互作用问题。模拟中,对流体和结构分别采用光滑粒子法和有限元法求解,通过单元-粒子接触算法处理两者间的交界面。对弹性板在时变水压作用下的变形以及倒塌水柱冲击弹性结构的过程进行了模拟,计算结果与实验结果以及已有数值结果符合良好,展现了该算法在流体与结构相互作用模拟中的可行性和良好应用前景。
Large deformation and fracture of materials are involved in many engineering problems, such as penetration, explosion, metal forming, fluid flow, and so on. It is very useful to develop numerical methods to simulate this kind of problems. Finite Element Method (FEM) has good calculation accuracy and efficiency for small deformation problems, but its accuracy and efficiency decrease significantly due to the element distortion when it is used for problems involving large deformations and material fracture. Smoothed Particle Hydrodynamics (SPH) has strong ability in modeling large deformations and is easy to simulate material fragmentation and splash, but its calculation efficiency and ability in treating boundary conditions is not as good as FEM. Coupling FEM and SPH can make use of the advantages of the two methods and provides an effective approach for the simulation of large deformation problems. The large deformation regions are solved with SPH, and the other regions are solved with FEM. By doing so, not only can element distortion be avoided, but also good efficiency can be obtained. However, the study on coupling algorithm has just started, and SPH still has some deficiencies. Thus, there are many problems required to be further studied and solved for the coupling algorithm of FEM and SPH in aspects of accuracy, efficiency and stability.
In this paper, some improvements for the efficiency and accuracy of SPH are presented. Based on this, fixed and adaptive coupling algorithms of FEM and SPH are systematically studied and applied to numerical simulations of high-velocity impact (HVI) problems. Moreover, the coupling algorithm is extended to the application of the simulation of fluid-structure interaction (FSI) problems. The research work done in this paper is given as follows:
(1) The basic principle of SPH is described systematically, and some improvements are presented for it to remove tensile instability, treat contact and search neighboring particles. The artificial stress method for removing tensile instability is discussed. A calculation method of artificial stress for axisymmetric problems is suggested. It is verified by calculating a rubber ball impacting on a rigid wall. A particle contact algorithm based on penalty method is extended for two-dimensional axisymmetric and three-dimensional problems and is validated by some test examples. The particle contact algorithm is used for the simulation of normal and oblique penetration of aluminum plates. Simulation results by SPH with particle contact algorithm are in good agreement with experimental results and show much better accuracy than that of SPH without contact algorithm. Some usually used neighboring particle search algorithms are discussed. The tree and Point-In-Box (PIB) search algorithms are briefed. The problem and its reason in PIB search algorithm are analyzed, and an improved strip-like PIB search algorithm is proposed. Some test examples are calculated to compare the performance of the three algorithms. Calculated results show that strip-like PIB search algorithm is better than PIB and tree search algorithm and can improve the calculation efficiency of SPH markedly.
(2) Two key problems in coupling algorithm, namely the treatment of contact and coupling between elements and particles, are studied. Firstly, an element-particle contact algorithm is obtained by introducing particle radius in contact algorithm of FEM and validated by calculating some test examples. A filtration algorithm based on neighboring particle search is presented to reduce the number of slave nodes and master segments required for contact search, and the efficiency of element-particle contact search is improved. Then, two different element-particle coupling algorithms are constructed. One is an algorithm based on attaching particles to element sides, in which a particle is fixed at a point of an element side so that they have the same velocities and displacements. Test examples are calculated to validate the algorithm and analyze the effect of particle density on accuracy. Calculated results indicate good coupling accuracy can be obtained when reasonable particle density is taken, but local stress oscillation at coupling interfaces is observed. The other one is an algorithm based on imaginary particles and equivalent tractions. In this algorithm, to calculate forces on particles from elements, elements near coupling interfaces are treated as imaginary particles and included in SPH calculations. To calculate forces on element nodes from particles, equivalent tractions are determined with particle stresses at coupling interfaces and transmitted to element nodes. The feasibility and validity of the algorithm are demonstrated through several test examples. The effect of smoothing length on calculation accuracy is investigated, and its reasonable values are obtained for the coupling cases with different particle distributions. The algorithm is compared with some existing algorithms and found to produce better accuracy than them.
(3) A fixed coupling algorithm of FEM and SPH is constructed with the fundamental algorithms previously described. The corresponding program is developed, and a two-dimensional impact simulation software is developed. The fixed coupling algorithm is used to simulate Taylor bar experiment and normal penetration of aluminum plates and compared with SPH. The simulation results demonstrate the feasibility and validity of the fixed coupling algorithms in HVI simulation and indicate it gives similar accuracy but higher efficiency compared with SPH. Embedding a coupled constitutive model of viscoplasticity and ductile damage in the fixed coupling program, plugging failure during blunt projectiles penetrating into metal plates is simulated. Simulation results are compared with experiment results. It is found the fixed coupling algorithm can effectively predict residual velocities of projectiles, deformations of projectiles and targets, failure pattern of targets, and so on.
(4) Based on the fixed coupling algorithm, an adaptive coupling algorithm of FEM and SPH is constructed by establishing a minimum interior angle conversion criterion and a group-based conversion manner to achieve the automatic conversion of distorted elements to particles. The algorithm is applied to simulate the Taylor bar experiment. Simulated results are compared with experiment results and other algorithm's results, which demonstrate the feasibility and validity of the algorithm. The algorithm is further applied to simulate penetration problems, which include normal penetration of aluminum and concrete plates and oblique penetration of an aluminum plate by a cylinder. Simulated results indicate the algorithm can predict residual velocities of projectiles accurately, model material fracture effectively, and reproduce the fragmentation and splash phenomenon of brittle materials. It is also observed the algorithm has advantages over fixed coupling algorithm in calculation efficiency, especially for problems where material fracture regions are difficult to be estimated in advance.
(5) Simulations of FSI problems using fixed coupling algorithm are presented. In the simulations, fluids and structures are solved with SPH and FEM, respectively. The coupling interfaces between fluids and structures are treated with element-particle contact algorithm. Elastic plate subjected to time-dependent water pressure and collapsed water column on an elastic structure are calculated. Calculated results are in good agreements with experimental and existing numerical results. This indicates the coupling algorithm is feasible and promising in FSI simulation.
本文先从精度和效率上对光滑粒子法进行了一些改进,在此基础上系统地研究了有限元法与光滑粒子法的固定耦合算法和自适应耦合算法,并应用耦合算法开展了高速冲击问题的数值模拟研究,同时还初步探讨了耦合算法在流体与结构相互作用模拟中的应用。本文具体开展和完成了如下工作：
(1)介绍了光滑粒子法的基本原理,从拉伸不稳定性、接触界面处理和相邻粒子搜索三方面对其进行了改进。讨论了消除拉伸不稳定性的人工应力法,提出了轴对称问题的人工应力计算和施加方法,通过橡胶球撞击问题验证了其有效性。将基于罚函数的粒子接触算法拓展到二维轴对称和三维问题中,通过测试算例验证了接触算法的正确性,并应用带接触算法的光滑粒子法模拟了铝板的正侵彻和斜侵彻,得到了与实验相符的模拟结果,模拟的精度远高于无接触算法的光滑粒子法。讨论了常用的相邻粒子搜索法,简要介绍了树形搜索法和Point-In-Box(PIB)搜索法；分析了PIB搜索法存在的问题及其原因,提出了改进的条形化PIB搜索法；通过测试算例对比了三种算法的性能,结果表明条形化PIB搜索法优于PIB搜索法和树形搜索法,能显著地提高光滑粒子法的计算效率
(2)对耦合算法中单元与粒子的接触和耦合两个关键问题进行了研究。首先,基于单元接触算法的思想,引入粒子半径,得到了单元-粒子接触算法,通过测试算例验证了算法的正确性；提出基于相邻粒子搜索的过滤算法,减少从节点数和参与接触搜索的主面段数,使单元-粒子接触搜索效率得到提高。然后,提出了两种单元-粒子耦合算法。一种是基于粒子与单元边连接的算法,即：将粒子与单元边上的点固连,使两者具有共同的速度和位移；通过测试算例验证了算法的正确性,分析了粒子密度对其计算精度的影响,结果表明取合适的粒子密度时该算法可以获得理想的计算精度,但在耦合界面处会出现局部的应力振荡。另一种是基于虚粒子和等效力的算法,即：通过将祸合界面附近的单元作为虚粒子包含到光滑粒子法计算中,得到单元对粒子的作用力,同时根据耦合界面附近的粒子应力确定作用在单元边上的等效面力并将其等效到单元节点上,得到粒子对单元节点的作用力；通过测试算例验证了算法的可行性和正确性,研究了光滑长度对算法的计算精度的影响,得到了不同分布形式的粒子与单元耦合时光滑长度的合理取值；将该算法与现有的一些算法进行对比,结果表明该算法具有更佳的计算精度。
(3)基于前述的基本算法,建立了有限元法与光滑粒子法的固定耦合算法,编制了相应的计算程序,并开发了二维冲击仿真软件。应用固定耦合算法和光滑粒子法对泰勒杆实验和铝板的正侵彻进行了对比模拟,检验了固定耦合算法在高速冲击模拟中的可行性和正确性,同时表明固定耦合算法在获得与光滑粒子法相近的计算精度时能有效地提高计算效率。在固定耦合计算程序中嵌入耦合粘塑性和延性损伤的本构模型,模拟了平头弹撞击金属靶板的冲塞失效过程；将模拟结果与实验结果进行对比,结果表明固定耦合算法能有效地预测弹体剩余速度、弹靶变形以及靶板的失效形式等。
(4)在固定耦合算法的基础上,提出最小内角转化准则和单元分组转化方式,实现单元向粒子的转化,建立了有限元法与光滑粒子法的自适应耦合算法,编制了相应的计算程序。应用自适应耦合算法模拟了泰勒杆实验,将计算结果与实验结果以及其他算法的计算结果对比,验证了该算法在高速冲击模拟中的可行性和正确性。进一步应用该算法模拟了侵彻问题,包括：铝板的正侵彻、混凝土的正侵彻以及柱体斜侵彻铝板。模拟结果表明该算法能比较准确地预测了弹体剩余速度,较好地模拟材料的破坏以及再现脆性材料的破碎和飞溅等现象；而且,该算法在计算效率方面比固定耦合算法更具优势,特别是对于难以准确预知材料破坏区域的问题。
(5)基于固定耦合算法模拟了流体与结构相互作用问题。模拟中,对流体和结构分别采用光滑粒子法和有限元法求解,通过单元-粒子接触算法处理两者间的交界面。对弹性板在时变水压作用下的变形以及倒塌水柱冲击弹性结构的过程进行了模拟,计算结果与实验结果以及已有数值结果符合良好,展现了该算法在流体与结构相互作用模拟中的可行性和良好应用前景。
Large deformation and fracture of materials are involved in many engineering problems, such as penetration, explosion, metal forming, fluid flow, and so on. It is very useful to develop numerical methods to simulate this kind of problems. Finite Element Method (FEM) has good calculation accuracy and efficiency for small deformation problems, but its accuracy and efficiency decrease significantly due to the element distortion when it is used for problems involving large deformations and material fracture. Smoothed Particle Hydrodynamics (SPH) has strong ability in modeling large deformations and is easy to simulate material fragmentation and splash, but its calculation efficiency and ability in treating boundary conditions is not as good as FEM. Coupling FEM and SPH can make use of the advantages of the two methods and provides an effective approach for the simulation of large deformation problems. The large deformation regions are solved with SPH, and the other regions are solved with FEM. By doing so, not only can element distortion be avoided, but also good efficiency can be obtained. However, the study on coupling algorithm has just started, and SPH still has some deficiencies. Thus, there are many problems required to be further studied and solved for the coupling algorithm of FEM and SPH in aspects of accuracy, efficiency and stability.
In this paper, some improvements for the efficiency and accuracy of SPH are presented. Based on this, fixed and adaptive coupling algorithms of FEM and SPH are systematically studied and applied to numerical simulations of high-velocity impact (HVI) problems. Moreover, the coupling algorithm is extended to the application of the simulation of fluid-structure interaction (FSI) problems. The research work done in this paper is given as follows:
(1) The basic principle of SPH is described systematically, and some improvements are presented for it to remove tensile instability, treat contact and search neighboring particles. The artificial stress method for removing tensile instability is discussed. A calculation method of artificial stress for axisymmetric problems is suggested. It is verified by calculating a rubber ball impacting on a rigid wall. A particle contact algorithm based on penalty method is extended for two-dimensional axisymmetric and three-dimensional problems and is validated by some test examples. The particle contact algorithm is used for the simulation of normal and oblique penetration of aluminum plates. Simulation results by SPH with particle contact algorithm are in good agreement with experimental results and show much better accuracy than that of SPH without contact algorithm. Some usually used neighboring particle search algorithms are discussed. The tree and Point-In-Box (PIB) search algorithms are briefed. The problem and its reason in PIB search algorithm are analyzed, and an improved strip-like PIB search algorithm is proposed. Some test examples are calculated to compare the performance of the three algorithms. Calculated results show that strip-like PIB search algorithm is better than PIB and tree search algorithm and can improve the calculation efficiency of SPH markedly.
(2) Two key problems in coupling algorithm, namely the treatment of contact and coupling between elements and particles, are studied. Firstly, an element-particle contact algorithm is obtained by introducing particle radius in contact algorithm of FEM and validated by calculating some test examples. A filtration algorithm based on neighboring particle search is presented to reduce the number of slave nodes and master segments required for contact search, and the efficiency of element-particle contact search is improved. Then, two different element-particle coupling algorithms are constructed. One is an algorithm based on attaching particles to element sides, in which a particle is fixed at a point of an element side so that they have the same velocities and displacements. Test examples are calculated to validate the algorithm and analyze the effect of particle density on accuracy. Calculated results indicate good coupling accuracy can be obtained when reasonable particle density is taken, but local stress oscillation at coupling interfaces is observed. The other one is an algorithm based on imaginary particles and equivalent tractions. In this algorithm, to calculate forces on particles from elements, elements near coupling interfaces are treated as imaginary particles and included in SPH calculations. To calculate forces on element nodes from particles, equivalent tractions are determined with particle stresses at coupling interfaces and transmitted to element nodes. The feasibility and validity of the algorithm are demonstrated through several test examples. The effect of smoothing length on calculation accuracy is investigated, and its reasonable values are obtained for the coupling cases with different particle distributions. The algorithm is compared with some existing algorithms and found to produce better accuracy than them.
(3) A fixed coupling algorithm of FEM and SPH is constructed with the fundamental algorithms previously described. The corresponding program is developed, and a two-dimensional impact simulation software is developed. The fixed coupling algorithm is used to simulate Taylor bar experiment and normal penetration of aluminum plates and compared with SPH. The simulation results demonstrate the feasibility and validity of the fixed coupling algorithms in HVI simulation and indicate it gives similar accuracy but higher efficiency compared with SPH. Embedding a coupled constitutive model of viscoplasticity and ductile damage in the fixed coupling program, plugging failure during blunt projectiles penetrating into metal plates is simulated. Simulation results are compared with experiment results. It is found the fixed coupling algorithm can effectively predict residual velocities of projectiles, deformations of projectiles and targets, failure pattern of targets, and so on.
(4) Based on the fixed coupling algorithm, an adaptive coupling algorithm of FEM and SPH is constructed by establishing a minimum interior angle conversion criterion and a group-based conversion manner to achieve the automatic conversion of distorted elements to particles. The algorithm is applied to simulate the Taylor bar experiment. Simulated results are compared with experiment results and other algorithm's results, which demonstrate the feasibility and validity of the algorithm. The algorithm is further applied to simulate penetration problems, which include normal penetration of aluminum and concrete plates and oblique penetration of an aluminum plate by a cylinder. Simulated results indicate the algorithm can predict residual velocities of projectiles accurately, model material fracture effectively, and reproduce the fragmentation and splash phenomenon of brittle materials. It is also observed the algorithm has advantages over fixed coupling algorithm in calculation efficiency, especially for problems where material fracture regions are difficult to be estimated in advance.
(5) Simulations of FSI problems using fixed coupling algorithm are presented. In the simulations, fluids and structures are solved with SPH and FEM, respectively. The coupling interfaces between fluids and structures are treated with element-particle contact algorithm. Elastic plate subjected to time-dependent water pressure and collapsed water column on an elastic structure are calculated. Calculated results are in good agreements with experimental and existing numerical results. This indicates the coupling algorithm is feasible and promising in FSI simulation.
引文
[1]张雄,刘岩.无网格法.北京：清华大学出版社,2004
[2]刘更,刘天祥,谢琴.无网格法及其应用.西安：西北工业大学出版社,2005
[3]Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Sociaty,1943,49(1):1-23
[4]Clough R W. The finite element method in plane stress analysis. In:Proceedings of American Society of Civil Engineers,2nd Conference on Electronic Computations. Pittsburg,1960,345-378
[5]Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal,1977,82(12):1013-1024
[6]Gingold R A, Monaghan J J. Smoothed particle hydrodynamics:theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society,1977,181(2):375-389
[7]Gingold R A, Monaghan J J. Binary fission in damped rotating polytropes. Monthly Notices of the Royal Astronomical Society,1978,184(2):481-499
[8]Gingold R A, Monaghan J J. A numerical study of the Roche and Darwin problems for polytropic stars. Monthly Notices of the Royal Astronomical Society,1979,188:45-58
[9]Gingold R A, Monaghan J J. The Roche problem for polytropes in central orbits. Monthly Notices of the Royal Astronomical Society,1980,191: 897-924
[10]Gingold R A, Monaghan J J. Kernel estimates as a basis for general particle methods in hydrodynamics. Journal of Computational Physics,1982,46(3): 429-453
[11]Monaghan J J, Gingold R A. Shock simulation by the particle method SPH. Journal of Computational Physics,1983,52(2):374-89
[12]Monaghan J J. Extrapolating B splines for interpolation. Journal of Computational Physics,1985,60(2):253-62
[13]Monaghan J J. Particle methods for hydrodynamics. Computer Physics Reports,1985,3(2):71-124
[14]Monaghan J J. On the problem of penetration in particle methods. Journal of Computational Physics,1989,82(1):1-15
[15]Bate M A, Bonnell I A, Bromm V. The formation mechanism of brown dwarfs. Monthly Notice of the Royal Astronomical Society,2002,332(3):65-68
[16]Berczik P. Modeling the star formation in galaxies using the chemo-dynamical SPH code. Astronomy and Astrophysics,2000,271(2): 103-126
[17]Benz W. Applications of smooth particle hydrodynamics (SPH) to astrophysical problems. Computer Physics Communication,1988,48(1): 97-105
[18]Rasio F A, Lombardi J C. Smoothed particle hydrodynamics calculations of stellar interactions. Journal of Computational and Applied Mathematics,1999, 109(1-2):213-230
[19]Lattanzio J C, Schwarz M P, Monaghan J J. Interstellar cloud collisions. Monthly Notices of the Royal Astronomical Society,1985,215(1):125-148
[20]Lee W H. Newtonian hydrodynamics of the coalescence of black holes with neutron stars II:Tidally locked binaries with a soft equation of state. Monthly Notices of the Royal Astronomical Society,1998,308:780-794
[21]Monaghan J J. Simulating free surface flows with SPH. Journal of Computer Physics,1994,110(2):399-406
[22]Ferrari A, Dumbser M, Toro E F, et al. A new 3D parallel SPH scheme for free surface flows. Computers & Fluids,2009,38(6):1203-1217
[23]Zhu Y, Fox P J, Morris J P. A pore-scale numerical model for flow through porous media. International Journal for Numerical and Analytical Methods in Geomechanics,1999,23(9):881-904
[24]Morris J P, Zhu Y, Fox P J. Parallel simulations of pore-scale flow through porous media.Couputers and Geotechnics,1999(4),25:227-246
[25]Jiang F M, Oliveira M S A, Sousa A C M. Mesoscale SPH modeling of fluid flow in isotropic porous media. Computer Physics Communications,2007, 176(7):471-480
[26]Shao S D. Incompressible SPH flow model for wave interactions with porous media. Coastal Engineering,2010,57(3):304-316
[27]Pereira G G, Prakash M, Cleary P W. SPH modelling of fluid at the grain level in a porous medium. Applied Mathematical Modelling,2011,35(4): 1666-1675
[28]Monaghan J J, Kocharyan A. SPH simulation of multi-phase flow. Computer Physics Communications,1995,87(1-2):225-235
[29]Valizadeh A, Shafieefar M, Monaghan J J, et al. Modeling two-phase flows using SPH method. Journal of Applied Sciences,2008,8(21):3817-3826
[30]Monaghan J J. SPH compressible turbulence. Monthly Notice of the Royal Astronomical Society,2002,335(3):843-852
[31]Liu M B, Liu G R, Zong Z, et al. Computer simualation of high explosive explosion using smoothed particle hydrodynamics methodology. Computers & fluids,2003,32(3):305-322
[32]强洪夫,王坤鹏,高巍然.基于完全变光滑长度SPH方法的高能炸药爆轰过程数值试验.含能材料,2009,17(1)：27-31
[33]Swegle J W, Attaway S W. On the feasibility of using smoothed particle hydrodynamics for underwater explosion. Computational Mechanics,1995,17(3): 151-168
[34]Liu M B, Liu G R, Zong Z, et al. Smoothed particle hydrodynamics for numerical simulation of underwater explosions. Computational mechanics, 2003,30(2):106-118
[35]Yang G, Han X, Hu D A. Computer simulation of two-dimensional linear-shaped charge jet using smoothed particle hydrodynamics. Engineering Computations,2011,28(1):58-75
[36]Tanaka K. Numerical studies of explosive welding by SPH. Materials Science Forum,2007,566:61-64
[37]Wang X, Zheng Y Y, Liu H X, et al. Numerical study of the mechanism of explosive/impact welding using smoothed particle hydrodynamics method. Materials & Design,2012,35:210-219
[38]Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. International Journal for Numerical Methods in Engineering, 2003,56(10):1421-1444
[39]Hayhurst C, Clegg R A. Cylindrically symmetric SPH simulations of hypervelocity impacts on thin plates. International Journal of Impact Engineering, 1997,20(1-5):337-348
[40]Hiermaier S, Konke D, Stilp A J, et al. Computational simulation of the hypervelocity impact of Al-spheres on thin plates of different materials. International Journal of Impact Engineering,1997,20(1-5):363-374
[41]Faraud M, Destefanis R, Palmieri D, et al. SPH simulations of debris impacts using two different computer codes. International Journal of Impact Engineering, 1999,23(1):249-260
[42]贾光辉,黄海,胡震东.超高速撞击数值仿真结果分析.爆炸与冲击,2005,25(1)：47-53
[43]贾光辉,黄海.超高速撞击航天器二次碎片云能量特性分析.北京航空航天大学学报,2007,33(3)：257-260
[44]管公顺,张伟,庞宝君,等.铝球弹丸高速正撞击薄铝板穿孔研究.高压物理学报,2005,19(2)：132-138
[45]贾斌,马志涛,庞宝君.含泡沫铝防护结构的超高速撞击数值模拟研究.高压物理学报,2009,23(6)：453-459
[46]徐金中,汤文辉,徐志宏,超高速碰撞碎片云特征的SPH方法数值分析.高压物理学报,2008,22(4)：377-383
[47]Seo S, Min O, Lee J. Application of an improved contact algorithm for penetration analysis in SPH. International Journal of Impact Engineering,2008, 35(6),578-588
[48]Lee M, Yoo Y H. Analysis of ceramic/metal armour systems. International Journal of Impact Engineering,2001,25(9):819-829
[49]张伟,胡德安,韩旭.弹体侵彻运动陶瓷/金属复合装甲SPH模拟.固体力学学报,2010,S1：70-75
[50]Benz W, Asphaug E. Simulations of brittle solids using smooth particle hydrodynamics. Computer Physics Communications,1995,87(1-2):253-265
[51]Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Method in Engineering,2000,47(6): 1189-1214
[52]Cleary P W, Prakash M, Ha J. Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. Journal of Materials Processing Technology,2006,177(1-3):41-48
[53]Heinstein M, Segalman D. Simulation of orthogonal cutting with smoothed particle hydrodynamics. Report no. SAND97-1961, Sandia National Laboratoties,1997
[54]Limido J, Espinosa C, Salaun M, et al. A new approach of high speed cutting modelling:SPH method. Journal of Physiscs IV,2006,134(1):1195-1200
[55]姜涛,张宪,乔欣,等.基于SPH法的土壤切削刀具三维数值模拟及优化.机电工程,2009,26(6)：44-46
[56]Oger G, Doring M, Alessandrini B, et al. Two-dimensional SPH simulations of wedge water entries. Journal of Computational Physics,2006,213(2):803-822
[57]Gong K. Water entry with of a wedge based on SPH model with an improved boundary treatment. Journal of Hydrodynmics,2009,21(6):750-757
[58]Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid-structure interaction by SPH. Computers & Structures,2007,85(11-14):879-890
[59]Rafiee A, Thiagarajan K P. An SPH projection method for simulating fluid-hypoelastic structure interaction. Computer Methods in Applied Mechanics and Engineering,2009,198(33-36):2785-2795
[60]Muller M, Schirm S, Teschner M. Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. Technology and Health Care,2004,12(1):25-31
[61]Sinnott M, Cleary P W, Prakash M. An investigation of pulsatile blood flow in a bifurcation artery using a grid-free method. In:Fifth International Conference on CFD in the Process Industries. Melbourne,2006,13-15
[62]Jin Q, Pang W M, Nguyen B P, et al. Particle-based simulation of blood flow and vessel wall interactions in virtual surgery. In:2010 Symposium on Information and Communication Technology. Hanoi,2010,128-133
[63]Tanaka N, Takano T, Masuzawa T.3-dimensional micro-simulation of blood flow with SPH method. Nihon Kikai Gakkai Ryutai Kogaku Bunion Koenkai Koen Ronbunshu (CD-ROM),2004,82:7-12
[64]Tanaka N, Takano T. Microscopic-scale simulation of blood flow uing SPH method. International Journal of Computational Methods,2005,2(4):555-568
[65]Tsubota K, Wada S, Kamada H, et al. A particle method for blood flow simulation, application to flowing red blood cells and platelets. Journal of the Earth Simulator,2006,5:2-7
[66]Bonet J, Lok T-S L. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering,1999,180(1-2):97-115
[67]Bonet J, Kulasegaram S, Rodriguez-Paz M X, et al. Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Computer Methods in Applied Mechanics and Engineering,2004,193(12-14): 1245-1256
[68]Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. Journal of Computational Physics 1995,116(1):123-134
[69]Dyka C T, Ingel R P. An approach for tension instability in smoothed particle hydrodynamics. Computers & Structures 1995,57(4):573-580
[70]Dyka C T, Randles P W, Ingel R P. Stress points for tension instability in SPH. International Journal for Numerical Methods in Engineering,1997,40(13): 2325-2341
[71]Randles P W, Libersky L D. Normalized SPH with stress pointss. International Journal for Numerical Method in Engineering,2000,48(10): 1445-1462
[72]Hicks D L, Swegle J W, Attaway S W. Conservative smoothing stabilizes discrete-numerical instabilities in SPH material dynamics computations. Applied Mathematics and Computation,1997,85(2-3):209-226
[73]Monaghan J J. SPH without a tensile instability. Journal of Computational Physics,2000,159(2):290-311
[74]Gray J P, Monaghan J J, Swift R P. SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering,2001,190(49-50):6641-6662
[75]Sigalotti L D G, Lopez H. Adaptive kernel estimation and SPH tensile instability. Computers & Mathematics with Applications,2008,55(1):23-50
[76]傅学金,强洪夫,杨月诚.固体介质中方法的拉伸不稳定性问题研究进展.力学进展,2007,37(3)：375-388
[77]Campbell P M. Some new algorithms for boundary value problems in smoothed particle hydrodynamics. Report no. DNA-TR-88-286, Mission Research Corporation,1989
[78]Libersky L D, Petschek A G, Carney T C, et al. High strain Lagrangian hydrodynamics:a three-dimensional SPH code for dynamic material response. Journal of Computational Physics,1993,109(1):67-75
[79]Randles P W, Libersky L D. Smoothed particle hydrodynamics:some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering,1996,139(1-4):375-408
[80]Randies P W, Libersky L D.Boundary conditions for a dual particle method. Computers & Structures,2005,83(17-18):1476-1486
[81]Monaghan J J, Kajtar J B. SPH particle boundary forces for arbitrary boundaries. Computer Physics Communications,2009,180(10):1811-1820
[82]Campbell J, Vignjevic R, Libersky L D. A contact algorithm for smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering,2000,184(1):49-65
[83]Seo S, Min O. Axisymmetric SPH simulation of elasto-plastic contact in the low velocity impact. Computer Physics Communications,2006,175(9):583-603
[84]Liu W K, Jun S, Zhang Y F. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering,1995,20(8-9): 1081-1106
[85]Johnson G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 1996,39(16):2725-2741
[86]Chen J K, Beraun J E, Carney T C. A corrective smoothed particle method for boundary value problems in heat conduction. International Journal for Numerical Methods in Engineering,1999,46(2):231-252
[87]Zhang G M, Batra R C. Modified smoothed particle hydrodynamics method and its application to transient problems. Computational Mechanics,2004, 34(2):137-146
[88]Batra R C, Zhang G M. SSPH basis functions for meshless methods, and comparison of solutions with strong and weak formulations. Computational Mechanics,2008,41(4):527-545
[89]Shintate K, Sekine H. Numerical simulation of hypervelocity impacts of a projectile on laminated composite plate targets by means of improved SPH method. Composites:Part A,2004,35(6):683-692
[90]卞梁,王肖钧,章杰.高速碰撞数值计算中的SPH自适应粒子分布法.爆炸与冲击.2009,29(6)：607-612
[91]Xu F, Chen J S, Huang Q Q. The study of numerical stability in the SPH method. Advanced Materials Research,2008,33-37(1-4):839-844
[92]赵燕,徐绯,李玉龙,陈刘定.一种改进的可阻止SPH数值断裂的方法.爆炸与冲击,2009,29(5)：503-508
[93]Zhao Y, Xu F, Li Y L, et al. A simple method in preventing numerical fractures of SPH computations. Advanced Materials Research,2008, 33-37(1-4):845-850
[94]赵燕,徐绯,李玉龙.一种适用于颗粒非规则分布的阻止SPH数值断裂的方法.航空学报,2009,30(11)：2100-2105
[95]陈刘定,姚磊江,李自山,等.光滑质点流体动力学方法中数值断裂的防止.机械强度,2010,32(1)：148-152
[96]Hernquis L. Some cautionary remarks about smoothed particle hydrodynamics.The Astrophysical Journal.1993,404(2):717-722
[97]Nelson R P, Papalozizou J C B. Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics. Monthly Notices of the Royal Astronomical Society.1994,270(1):1-20
[98]Springel V, Hernquist L. Cosmological smoothed particle hydrodynamics simulations:the entropy equation. Astronomy & Astrophysics.2002,333(3): 649-664
[99]强洪夫,高巍然.修正变光滑长度SPH方法及其应用.解放军理工大学学报.2007,8(5)：419-424
[100]Johnson G R, Beissel S R. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering,1996,139(1-4): 347-373
[101]Johnson G R. Linking of Lagrangian particle methods to standard finite element methods for high velocity impact simulations. Nuclear Engineering and Design,1994,150(2-3):265-274
[102]Attaway S W, Heinstein M W, Swegle J W. Coupling of Smooth particle hydrodynamic with finite element method. Nuclear Engineering and Design, 1994,150(2-3):199-205
[103]De Vuyst T, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods. International Journal of Impact Engineering,2005,31(8): 1054-1064
[104]Sauer M. Adaptive Kopplung des Netzfreien SPH-Verfahrens mit Finiten Elementen zur Berechnung von Impaktvorgangen:[dissertation]. Munich: Universitat der Bundeswehr Munchen,2000
[105]Xiao Y H, Han X, Hu D A. A coupling algorithm of finite element method and smoothed particle hydrodynamics for impact computations. Computers, Materials & Continua,2011,23(1):9-34
[106]王吉,王肖钧,卞梁.光滑粒子法与有限元的耦合算法及其在冲击动力学中的应用.爆炸与冲击,2007,27(6)：522-528
[107]张志春,强洪夫,高巍然.一种光滑粒子流体动力学-有限元法转换算法及其在冲击动力学中的应用.西安交通大学学报,2011,45(1)：105-110
[108]Fernandez-Mendez S, Bonet J, Huerta A. Continuous blending of SPH with finite elements. Computers and Structures,2005,83(17-18):1448-1458
[109]Rabczuk T, Xiao S P, Sauer M. Coupling of mesh-free method with finite elements:basic concepts and test results. Communications for Numerical Methods in Engineering,2006,22(10):1031-1065
[110]Johnson G R, Stryk R A, Stephen R, et al. An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. International Journal of Impact Engineering,2002,27(10): 997-1013
[111]Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles during dynamic deformation durinh dynamic deformation. International Journal of Impact Engineering,2003,28(9):947-966
[112]Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finite elements and meshfree particles. International Journal of Impact Engineering,2006,33(1-12):80-90
[113]Johnson G R. Numerical algorithms and material models for high-velocity impact computations. International Journal of Impact Engineering,2011,38(6): 456-472
[114]Johnson G R, Petersen E H, Stryk R A. Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations. International Journal of Impact Engineering,1993,14(1-4):385-394
[115]Sauer M. Simulation of high velocity impact in fluid-filled containers using finite elements with adaptive coupling to smoothed particle hydrodynamics. International Journal of Impact Engineering,2011,38(6):511-520
[116]Caleyron F, Chuzel-Marmot Y, Combescure A. Modeling of reinforced concrete through SPH-FE coupling and its application to the simulation of a projectile's impact onto a slab. International Journal for Numerical Methods in Biomedical Engineering,2009,27(6):882-898
[117]Lu Y, Wang Z Q, Chong K. A comparative study of buried structure in soil subjected to blast load using 2D and 3D numerical simulations. Soil Dynamics and Earthquake Engineering,2005,25(4):275-288
[118]蔡清裕,崔伟峰,向东,等.模拟刚性动能弹丸侵彻混凝土的FE-SPH方法.国防科学技术大学学报,2003,25(6)：87-90
[119]纪冲,龙源,方向.基于FEM-SPH耦合法的弹丸侵彻钢纤维混凝土数值模拟.振动与冲击,2010,29(7)：69-74
[120]嵇晓宇.弹丸掩击问题的FE-SPH耦合模拟：[中国科学技术大学硕士论文].合肥：中国科学技术大学,2007
[121]宋顺成,才鸿年.模拟战斗部对混凝土侵彻与爆炸耦合作用的计算.弹道学报,2004,16(4)：23-28
[122]Xu J X, Liu X L. Analysis of structural response under blast loads using the coupled SPH-FEM approach. Journal of Zhejiang University SCIENCE A,2008, 9(9):1184-1192
[123]张忠,陈卫东,陈浩FEM/SPH耦合算法的射弹冲击起爆仿真.系统仿真学报,2009,21(22)：7080-7083
[124]武玉玉,何远航,李金柱.耦合方法在超高速碰撞数值模拟中的应用.高压物理学报,2005,19(4)：385-389
[125]冷冰林,许金余,邵宁.等.刚性弹丸侵彻金属靶体的FEM-SPH耦合计算.弹箭与制导学报,2008,28(5)：105-108
[126]卞梁,王肖钧,章杰SPH/FEM耦合算法在陶瓷复合靶抗侵彻数值模拟中的应用.高压物理学报,2010,24(3)：161-167
[127]张洪涛,赵美英,任磊,等.SPH和FEM耦合方法分析机翼前缘鸟撞的响应问题.科学技术工程,2009,9(7)：1802-1806
[128]宿崇,唐亮,侯俊铭,等.基于FEM与SPH耦合算法的金属切削仿真研究.系统仿真学报,2009,21(16)：5002-5005
[129]刘飞宏,王建明,余丰,等.基于SPH耦合有限元法的喷丸残余应力场数值模拟.山东大学学报,2010,40(6)：67-71
[130]王建明,余丰,刘飞宏,等.SPH和FEM耦合法模拟磨料水射流中单磨粒加速过程.山东大学学报,2011,41(5)：114-119
[131]马利,陶伟明,郭乙木,等.SPH耦合有限元方法的水射流弹塑性碰撞模拟.浙江大学学报,2008,42(2)：259-263
[132]Fourey G, Oger G, Le Touze D, et al. Violent fluid-structure interaction simulations using a coupled SPH/FEM method. IOP Conference Series:Materials Science and Engineering,2010,10(1)
[133]Groenenboom P H L, Cartwright B K. Hydrodynamics and fluid-structure interaction by coupled SPH-FE method. Journal of Hydraulic Research,2010, 48(S1):61-73
[134]许庆新,沈荣瀛.充液容器跌落过程的SPH模拟方法.振动与冲击,2007,27(6)：13-16
[135]Johnson G R, Stryk S R, Beissel S R. Interface effects for SPH impact computations. Structures under shock and impact IV,1996:285-294
[136]Liu G R, Liu M B. Smoothed particle hydrodynamics:a meshfree particle method. Singapore:World Scientific,2003
[137]杨刚.光滑粒子法的改进及其若干典型应用：[湖南大学博士论文].长沙：湖南大学,2011,42-45
[138]Belytschko T, O. Neal M. Contact-impact by the pinball algorithm with penalty and lagrangian methods. International Journal for Numerical Methods in Engineering,1991,31(3):547-572
[139]Sulsky, D. The material point method for large deformation solid mechanics. In:Third US Congress on Computational Mechanics. Dallas,1995,214
[140]Dilts G A. Moving least-squares particle hydrodynamics II:conservation and boundaries. International Journal for Numerical Methods in Engineering,2000, 48(10):1503-1524
[141]Haque A, Dilts G A. Three-dimensional boundary detection for particle methods. Journal of Computational Physics,2007,226(2):1710-1730
[142]Piekutowski A J, Forrestal M J, Poormon K L, et al. Perforation of aluminum plates with ogive-nose steel rods at normal and oblique impacts. International Journal of Impact Engineering,1996,18(7-8):877-887
[143]Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the Seventh International Symposium on Ballistics. The Hague,1983,541-547
[144]Kmetyk L N, Yarrington P. CTH analyses of steel rod penetration into aluminum and concrete targets with comparison to experiment data. Report No. SAND94-1498, Sandia National Laboratories,1994
[145]Swegle J W. Search Algorithm. Sandia National Laboratories,1992
[146]Swegle J W, Attaway S W, Heinstein M W, et al. An Analysis of Smoothed Particle Hydrodynamics. Report No. SAND93-2513, Sandia National Laboratories,1994
[147]Heinstein M W, Mello F J, Attaway S W, et al. Contact-impact modeling in explicit transient dynamics. Computer Methods in Applied Mechanics and Engineering,2000,187(3-4):621-640
[148]Davis M E, Heinstein M W, Attaway S W, et al. Optimizing the Point-in-Box search algorithm for the Cray Y-MP supercomputer. Report No. SAND93-0933, Sandia National Laboratories,1998
[149]Flanagan D P, Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. International Journal for Numerical Methods in Engineering,1981,17(5):679-706
[150]Johnson G R, Stryk R A. Symmetric contact and sliding interface algorithm for intense impulsive loading computations. Computer Methods in Applied Mechanics and Engineering,2001,190(35-36):4531-4549
[151]Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive model constants. Journal of Applied Physics,1988,64(8):3901-3910
[152]B(?)rvik T, Hopperstad O S, Berstad T, et al. Numerical simulation of plugging failure in ballistic penetration. International Journal of solids and structures,2001, 38(34-35):6241-6264
[153]Borvik T, Hopperstad O S, Berstad T, et al. A computational model of viscoplasticity and ductile damage for impact and penetration. European Journal of Mechanics-A/Solids,2001,20(5):685-712
[154]Recht R F, Ipson T W. Ballistic perforation dynamics. Journal of Applied Mechanics,1963,30(3):384-390
[155]Holmquist T J, Johnson G R. A computational constitutive model for concrete subjected to large strains, high strain rates and high pressure. In:14th International Symposium on Ballistics. Quebec,1995,591-600
[156]Hanchak S J, Forrestal M J, Young E R, et al. Perforation of concrete slabs with 48MPa and 140MPa unconfined compressive strenths. International Journal of Impact Engineering,1992,12(1):1-7
[157]蒋莉,沈孟育.求解流体与结构相互作用问题的ALE有限体积方法.水动力学研究与进展,2000,15(2)：148-55
[158]Le Tallec P, Mouro J. Fluid structure interaction with large structural displacements. Computer Methods in Applied Mechanics and Engineering, 2001,190(24-25):3039-3067
[159]Legay A, Chessa J, Belytschko T. An Eulerian-Lagrangian method for fluid-structure interaction based on level sets. Computer Methods in Applied Mechanics and Engineering,2006,195(17-18):2070-2087
[160]Walhorn E, Kolke A, Hubner B, et al. Fluid-structure coupling within a monolithic model involving free surface flows. Computers & Structures,2005, 83(25-26):2100-2111
[161]Idelsohn S R, Marti J, Limache A, et al. Unified Lagrangian formulation for elastic solids and incompressible fluids:Application to fluid-structure interaction problems via the PFEM. Computer Methods in Applied Mechanics and Engineering,2008,197(19-20):1762-1776
[2]刘更,刘天祥,谢琴.无网格法及其应用.西安：西北工业大学出版社,2005
[3]Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Sociaty,1943,49(1):1-23
[4]Clough R W. The finite element method in plane stress analysis. In:Proceedings of American Society of Civil Engineers,2nd Conference on Electronic Computations. Pittsburg,1960,345-378
[5]Lucy L B. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal,1977,82(12):1013-1024
[6]Gingold R A, Monaghan J J. Smoothed particle hydrodynamics:theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society,1977,181(2):375-389
[7]Gingold R A, Monaghan J J. Binary fission in damped rotating polytropes. Monthly Notices of the Royal Astronomical Society,1978,184(2):481-499
[8]Gingold R A, Monaghan J J. A numerical study of the Roche and Darwin problems for polytropic stars. Monthly Notices of the Royal Astronomical Society,1979,188:45-58
[9]Gingold R A, Monaghan J J. The Roche problem for polytropes in central orbits. Monthly Notices of the Royal Astronomical Society,1980,191: 897-924
[10]Gingold R A, Monaghan J J. Kernel estimates as a basis for general particle methods in hydrodynamics. Journal of Computational Physics,1982,46(3): 429-453
[11]Monaghan J J, Gingold R A. Shock simulation by the particle method SPH. Journal of Computational Physics,1983,52(2):374-89
[12]Monaghan J J. Extrapolating B splines for interpolation. Journal of Computational Physics,1985,60(2):253-62
[13]Monaghan J J. Particle methods for hydrodynamics. Computer Physics Reports,1985,3(2):71-124
[14]Monaghan J J. On the problem of penetration in particle methods. Journal of Computational Physics,1989,82(1):1-15
[15]Bate M A, Bonnell I A, Bromm V. The formation mechanism of brown dwarfs. Monthly Notice of the Royal Astronomical Society,2002,332(3):65-68
[16]Berczik P. Modeling the star formation in galaxies using the chemo-dynamical SPH code. Astronomy and Astrophysics,2000,271(2): 103-126
[17]Benz W. Applications of smooth particle hydrodynamics (SPH) to astrophysical problems. Computer Physics Communication,1988,48(1): 97-105
[18]Rasio F A, Lombardi J C. Smoothed particle hydrodynamics calculations of stellar interactions. Journal of Computational and Applied Mathematics,1999, 109(1-2):213-230
[19]Lattanzio J C, Schwarz M P, Monaghan J J. Interstellar cloud collisions. Monthly Notices of the Royal Astronomical Society,1985,215(1):125-148
[20]Lee W H. Newtonian hydrodynamics of the coalescence of black holes with neutron stars II:Tidally locked binaries with a soft equation of state. Monthly Notices of the Royal Astronomical Society,1998,308:780-794
[21]Monaghan J J. Simulating free surface flows with SPH. Journal of Computer Physics,1994,110(2):399-406
[22]Ferrari A, Dumbser M, Toro E F, et al. A new 3D parallel SPH scheme for free surface flows. Computers & Fluids,2009,38(6):1203-1217
[23]Zhu Y, Fox P J, Morris J P. A pore-scale numerical model for flow through porous media. International Journal for Numerical and Analytical Methods in Geomechanics,1999,23(9):881-904
[24]Morris J P, Zhu Y, Fox P J. Parallel simulations of pore-scale flow through porous media.Couputers and Geotechnics,1999(4),25:227-246
[25]Jiang F M, Oliveira M S A, Sousa A C M. Mesoscale SPH modeling of fluid flow in isotropic porous media. Computer Physics Communications,2007, 176(7):471-480
[26]Shao S D. Incompressible SPH flow model for wave interactions with porous media. Coastal Engineering,2010,57(3):304-316
[27]Pereira G G, Prakash M, Cleary P W. SPH modelling of fluid at the grain level in a porous medium. Applied Mathematical Modelling,2011,35(4): 1666-1675
[28]Monaghan J J, Kocharyan A. SPH simulation of multi-phase flow. Computer Physics Communications,1995,87(1-2):225-235
[29]Valizadeh A, Shafieefar M, Monaghan J J, et al. Modeling two-phase flows using SPH method. Journal of Applied Sciences,2008,8(21):3817-3826
[30]Monaghan J J. SPH compressible turbulence. Monthly Notice of the Royal Astronomical Society,2002,335(3):843-852
[31]Liu M B, Liu G R, Zong Z, et al. Computer simualation of high explosive explosion using smoothed particle hydrodynamics methodology. Computers & fluids,2003,32(3):305-322
[32]强洪夫,王坤鹏,高巍然.基于完全变光滑长度SPH方法的高能炸药爆轰过程数值试验.含能材料,2009,17(1)：27-31
[33]Swegle J W, Attaway S W. On the feasibility of using smoothed particle hydrodynamics for underwater explosion. Computational Mechanics,1995,17(3): 151-168
[34]Liu M B, Liu G R, Zong Z, et al. Smoothed particle hydrodynamics for numerical simulation of underwater explosions. Computational mechanics, 2003,30(2):106-118
[35]Yang G, Han X, Hu D A. Computer simulation of two-dimensional linear-shaped charge jet using smoothed particle hydrodynamics. Engineering Computations,2011,28(1):58-75
[36]Tanaka K. Numerical studies of explosive welding by SPH. Materials Science Forum,2007,566:61-64
[37]Wang X, Zheng Y Y, Liu H X, et al. Numerical study of the mechanism of explosive/impact welding using smoothed particle hydrodynamics method. Materials & Design,2012,35:210-219
[38]Rabczuk T, Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. International Journal for Numerical Methods in Engineering, 2003,56(10):1421-1444
[39]Hayhurst C, Clegg R A. Cylindrically symmetric SPH simulations of hypervelocity impacts on thin plates. International Journal of Impact Engineering, 1997,20(1-5):337-348
[40]Hiermaier S, Konke D, Stilp A J, et al. Computational simulation of the hypervelocity impact of Al-spheres on thin plates of different materials. International Journal of Impact Engineering,1997,20(1-5):363-374
[41]Faraud M, Destefanis R, Palmieri D, et al. SPH simulations of debris impacts using two different computer codes. International Journal of Impact Engineering, 1999,23(1):249-260
[42]贾光辉,黄海,胡震东.超高速撞击数值仿真结果分析.爆炸与冲击,2005,25(1)：47-53
[43]贾光辉,黄海.超高速撞击航天器二次碎片云能量特性分析.北京航空航天大学学报,2007,33(3)：257-260
[44]管公顺,张伟,庞宝君,等.铝球弹丸高速正撞击薄铝板穿孔研究.高压物理学报,2005,19(2)：132-138
[45]贾斌,马志涛,庞宝君.含泡沫铝防护结构的超高速撞击数值模拟研究.高压物理学报,2009,23(6)：453-459
[46]徐金中,汤文辉,徐志宏,超高速碰撞碎片云特征的SPH方法数值分析.高压物理学报,2008,22(4)：377-383
[47]Seo S, Min O, Lee J. Application of an improved contact algorithm for penetration analysis in SPH. International Journal of Impact Engineering,2008, 35(6),578-588
[48]Lee M, Yoo Y H. Analysis of ceramic/metal armour systems. International Journal of Impact Engineering,2001,25(9):819-829
[49]张伟,胡德安,韩旭.弹体侵彻运动陶瓷/金属复合装甲SPH模拟.固体力学学报,2010,S1：70-75
[50]Benz W, Asphaug E. Simulations of brittle solids using smooth particle hydrodynamics. Computer Physics Communications,1995,87(1-2):253-265
[51]Bonet J, Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. International Journal for Numerical Method in Engineering,2000,47(6): 1189-1214
[52]Cleary P W, Prakash M, Ha J. Novel applications of smoothed particle hydrodynamics (SPH) in metal forming. Journal of Materials Processing Technology,2006,177(1-3):41-48
[53]Heinstein M, Segalman D. Simulation of orthogonal cutting with smoothed particle hydrodynamics. Report no. SAND97-1961, Sandia National Laboratoties,1997
[54]Limido J, Espinosa C, Salaun M, et al. A new approach of high speed cutting modelling:SPH method. Journal of Physiscs IV,2006,134(1):1195-1200
[55]姜涛,张宪,乔欣,等.基于SPH法的土壤切削刀具三维数值模拟及优化.机电工程,2009,26(6)：44-46
[56]Oger G, Doring M, Alessandrini B, et al. Two-dimensional SPH simulations of wedge water entries. Journal of Computational Physics,2006,213(2):803-822
[57]Gong K. Water entry with of a wedge based on SPH model with an improved boundary treatment. Journal of Hydrodynmics,2009,21(6):750-757
[58]Antoci C, Gallati M, Sibilla S. Numerical simulation of fluid-structure interaction by SPH. Computers & Structures,2007,85(11-14):879-890
[59]Rafiee A, Thiagarajan K P. An SPH projection method for simulating fluid-hypoelastic structure interaction. Computer Methods in Applied Mechanics and Engineering,2009,198(33-36):2785-2795
[60]Muller M, Schirm S, Teschner M. Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics. Technology and Health Care,2004,12(1):25-31
[61]Sinnott M, Cleary P W, Prakash M. An investigation of pulsatile blood flow in a bifurcation artery using a grid-free method. In:Fifth International Conference on CFD in the Process Industries. Melbourne,2006,13-15
[62]Jin Q, Pang W M, Nguyen B P, et al. Particle-based simulation of blood flow and vessel wall interactions in virtual surgery. In:2010 Symposium on Information and Communication Technology. Hanoi,2010,128-133
[63]Tanaka N, Takano T, Masuzawa T.3-dimensional micro-simulation of blood flow with SPH method. Nihon Kikai Gakkai Ryutai Kogaku Bunion Koenkai Koen Ronbunshu (CD-ROM),2004,82:7-12
[64]Tanaka N, Takano T. Microscopic-scale simulation of blood flow uing SPH method. International Journal of Computational Methods,2005,2(4):555-568
[65]Tsubota K, Wada S, Kamada H, et al. A particle method for blood flow simulation, application to flowing red blood cells and platelets. Journal of the Earth Simulator,2006,5:2-7
[66]Bonet J, Lok T-S L. Variational and momentum preservation aspects of smooth particle hydrodynamic formulations. Computer Methods in Applied Mechanics and Engineering,1999,180(1-2):97-115
[67]Bonet J, Kulasegaram S, Rodriguez-Paz M X, et al. Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Computer Methods in Applied Mechanics and Engineering,2004,193(12-14): 1245-1256
[68]Swegle J W, Hicks D L, Attaway S W. Smoothed particle hydrodynamics stability analysis. Journal of Computational Physics 1995,116(1):123-134
[69]Dyka C T, Ingel R P. An approach for tension instability in smoothed particle hydrodynamics. Computers & Structures 1995,57(4):573-580
[70]Dyka C T, Randles P W, Ingel R P. Stress points for tension instability in SPH. International Journal for Numerical Methods in Engineering,1997,40(13): 2325-2341
[71]Randles P W, Libersky L D. Normalized SPH with stress pointss. International Journal for Numerical Method in Engineering,2000,48(10): 1445-1462
[72]Hicks D L, Swegle J W, Attaway S W. Conservative smoothing stabilizes discrete-numerical instabilities in SPH material dynamics computations. Applied Mathematics and Computation,1997,85(2-3):209-226
[73]Monaghan J J. SPH without a tensile instability. Journal of Computational Physics,2000,159(2):290-311
[74]Gray J P, Monaghan J J, Swift R P. SPH elastic dynamics. Computer Methods in Applied Mechanics and Engineering,2001,190(49-50):6641-6662
[75]Sigalotti L D G, Lopez H. Adaptive kernel estimation and SPH tensile instability. Computers & Mathematics with Applications,2008,55(1):23-50
[76]傅学金,强洪夫,杨月诚.固体介质中方法的拉伸不稳定性问题研究进展.力学进展,2007,37(3)：375-388
[77]Campbell P M. Some new algorithms for boundary value problems in smoothed particle hydrodynamics. Report no. DNA-TR-88-286, Mission Research Corporation,1989
[78]Libersky L D, Petschek A G, Carney T C, et al. High strain Lagrangian hydrodynamics:a three-dimensional SPH code for dynamic material response. Journal of Computational Physics,1993,109(1):67-75
[79]Randles P W, Libersky L D. Smoothed particle hydrodynamics:some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering,1996,139(1-4):375-408
[80]Randies P W, Libersky L D.Boundary conditions for a dual particle method. Computers & Structures,2005,83(17-18):1476-1486
[81]Monaghan J J, Kajtar J B. SPH particle boundary forces for arbitrary boundaries. Computer Physics Communications,2009,180(10):1811-1820
[82]Campbell J, Vignjevic R, Libersky L D. A contact algorithm for smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering,2000,184(1):49-65
[83]Seo S, Min O. Axisymmetric SPH simulation of elasto-plastic contact in the low velocity impact. Computer Physics Communications,2006,175(9):583-603
[84]Liu W K, Jun S, Zhang Y F. Reproducing kernel particle methods. International Journal for Numerical Methods in Engineering,1995,20(8-9): 1081-1106
[85]Johnson G R, Beissel S R. Normalized smoothing functions for SPH impact computations. International Journal for Numerical Methods in Engineering, 1996,39(16):2725-2741
[86]Chen J K, Beraun J E, Carney T C. A corrective smoothed particle method for boundary value problems in heat conduction. International Journal for Numerical Methods in Engineering,1999,46(2):231-252
[87]Zhang G M, Batra R C. Modified smoothed particle hydrodynamics method and its application to transient problems. Computational Mechanics,2004, 34(2):137-146
[88]Batra R C, Zhang G M. SSPH basis functions for meshless methods, and comparison of solutions with strong and weak formulations. Computational Mechanics,2008,41(4):527-545
[89]Shintate K, Sekine H. Numerical simulation of hypervelocity impacts of a projectile on laminated composite plate targets by means of improved SPH method. Composites:Part A,2004,35(6):683-692
[90]卞梁,王肖钧,章杰.高速碰撞数值计算中的SPH自适应粒子分布法.爆炸与冲击.2009,29(6)：607-612
[91]Xu F, Chen J S, Huang Q Q. The study of numerical stability in the SPH method. Advanced Materials Research,2008,33-37(1-4):839-844
[92]赵燕,徐绯,李玉龙,陈刘定.一种改进的可阻止SPH数值断裂的方法.爆炸与冲击,2009,29(5)：503-508
[93]Zhao Y, Xu F, Li Y L, et al. A simple method in preventing numerical fractures of SPH computations. Advanced Materials Research,2008, 33-37(1-4):845-850
[94]赵燕,徐绯,李玉龙.一种适用于颗粒非规则分布的阻止SPH数值断裂的方法.航空学报,2009,30(11)：2100-2105
[95]陈刘定,姚磊江,李自山,等.光滑质点流体动力学方法中数值断裂的防止.机械强度,2010,32(1)：148-152
[96]Hernquis L. Some cautionary remarks about smoothed particle hydrodynamics.The Astrophysical Journal.1993,404(2):717-722
[97]Nelson R P, Papalozizou J C B. Variable smoothing lengths and energy conservation in smoothed particle hydrodynamics. Monthly Notices of the Royal Astronomical Society.1994,270(1):1-20
[98]Springel V, Hernquist L. Cosmological smoothed particle hydrodynamics simulations:the entropy equation. Astronomy & Astrophysics.2002,333(3): 649-664
[99]强洪夫,高巍然.修正变光滑长度SPH方法及其应用.解放军理工大学学报.2007,8(5)：419-424
[100]Johnson G R, Beissel S R. SPH for high velocity impact computations. Computer Methods in Applied Mechanics and Engineering,1996,139(1-4): 347-373
[101]Johnson G R. Linking of Lagrangian particle methods to standard finite element methods for high velocity impact simulations. Nuclear Engineering and Design,1994,150(2-3):265-274
[102]Attaway S W, Heinstein M W, Swegle J W. Coupling of Smooth particle hydrodynamic with finite element method. Nuclear Engineering and Design, 1994,150(2-3):199-205
[103]De Vuyst T, Vignjevic R, Campbell J C. Coupling between meshless and finite element methods. International Journal of Impact Engineering,2005,31(8): 1054-1064
[104]Sauer M. Adaptive Kopplung des Netzfreien SPH-Verfahrens mit Finiten Elementen zur Berechnung von Impaktvorgangen:[dissertation]. Munich: Universitat der Bundeswehr Munchen,2000
[105]Xiao Y H, Han X, Hu D A. A coupling algorithm of finite element method and smoothed particle hydrodynamics for impact computations. Computers, Materials & Continua,2011,23(1):9-34
[106]王吉,王肖钧,卞梁.光滑粒子法与有限元的耦合算法及其在冲击动力学中的应用.爆炸与冲击,2007,27(6)：522-528
[107]张志春,强洪夫,高巍然.一种光滑粒子流体动力学-有限元法转换算法及其在冲击动力学中的应用.西安交通大学学报,2011,45(1)：105-110
[108]Fernandez-Mendez S, Bonet J, Huerta A. Continuous blending of SPH with finite elements. Computers and Structures,2005,83(17-18):1448-1458
[109]Rabczuk T, Xiao S P, Sauer M. Coupling of mesh-free method with finite elements:basic concepts and test results. Communications for Numerical Methods in Engineering,2006,22(10):1031-1065
[110]Johnson G R, Stryk R A, Stephen R, et al. An algorithm to automatically convert distorted finite elements into meshless particles during dynamic deformation. International Journal of Impact Engineering,2002,27(10): 997-1013
[111]Johnson G R, Stryk R A. Conversion of 3D distorted elements into meshless particles during dynamic deformation durinh dynamic deformation. International Journal of Impact Engineering,2003,28(9):947-966
[112]Beissel S R, Gerlach C A, Johnson G R. Hypervelocity impact computations with finite elements and meshfree particles. International Journal of Impact Engineering,2006,33(1-12):80-90
[113]Johnson G R. Numerical algorithms and material models for high-velocity impact computations. International Journal of Impact Engineering,2011,38(6): 456-472
[114]Johnson G R, Petersen E H, Stryk R A. Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations. International Journal of Impact Engineering,1993,14(1-4):385-394
[115]Sauer M. Simulation of high velocity impact in fluid-filled containers using finite elements with adaptive coupling to smoothed particle hydrodynamics. International Journal of Impact Engineering,2011,38(6):511-520
[116]Caleyron F, Chuzel-Marmot Y, Combescure A. Modeling of reinforced concrete through SPH-FE coupling and its application to the simulation of a projectile's impact onto a slab. International Journal for Numerical Methods in Biomedical Engineering,2009,27(6):882-898
[117]Lu Y, Wang Z Q, Chong K. A comparative study of buried structure in soil subjected to blast load using 2D and 3D numerical simulations. Soil Dynamics and Earthquake Engineering,2005,25(4):275-288
[118]蔡清裕,崔伟峰,向东,等.模拟刚性动能弹丸侵彻混凝土的FE-SPH方法.国防科学技术大学学报,2003,25(6)：87-90
[119]纪冲,龙源,方向.基于FEM-SPH耦合法的弹丸侵彻钢纤维混凝土数值模拟.振动与冲击,2010,29(7)：69-74
[120]嵇晓宇.弹丸掩击问题的FE-SPH耦合模拟：[中国科学技术大学硕士论文].合肥：中国科学技术大学,2007
[121]宋顺成,才鸿年.模拟战斗部对混凝土侵彻与爆炸耦合作用的计算.弹道学报,2004,16(4)：23-28
[122]Xu J X, Liu X L. Analysis of structural response under blast loads using the coupled SPH-FEM approach. Journal of Zhejiang University SCIENCE A,2008, 9(9):1184-1192
[123]张忠,陈卫东,陈浩FEM/SPH耦合算法的射弹冲击起爆仿真.系统仿真学报,2009,21(22)：7080-7083
[124]武玉玉,何远航,李金柱.耦合方法在超高速碰撞数值模拟中的应用.高压物理学报,2005,19(4)：385-389
[125]冷冰林,许金余,邵宁.等.刚性弹丸侵彻金属靶体的FEM-SPH耦合计算.弹箭与制导学报,2008,28(5)：105-108
[126]卞梁,王肖钧,章杰SPH/FEM耦合算法在陶瓷复合靶抗侵彻数值模拟中的应用.高压物理学报,2010,24(3)：161-167
[127]张洪涛,赵美英,任磊,等.SPH和FEM耦合方法分析机翼前缘鸟撞的响应问题.科学技术工程,2009,9(7)：1802-1806
[128]宿崇,唐亮,侯俊铭,等.基于FEM与SPH耦合算法的金属切削仿真研究.系统仿真学报,2009,21(16)：5002-5005
[129]刘飞宏,王建明,余丰,等.基于SPH耦合有限元法的喷丸残余应力场数值模拟.山东大学学报,2010,40(6)：67-71
[130]王建明,余丰,刘飞宏,等.SPH和FEM耦合法模拟磨料水射流中单磨粒加速过程.山东大学学报,2011,41(5)：114-119
[131]马利,陶伟明,郭乙木,等.SPH耦合有限元方法的水射流弹塑性碰撞模拟.浙江大学学报,2008,42(2)：259-263
[132]Fourey G, Oger G, Le Touze D, et al. Violent fluid-structure interaction simulations using a coupled SPH/FEM method. IOP Conference Series:Materials Science and Engineering,2010,10(1)
[133]Groenenboom P H L, Cartwright B K. Hydrodynamics and fluid-structure interaction by coupled SPH-FE method. Journal of Hydraulic Research,2010, 48(S1):61-73
[134]许庆新,沈荣瀛.充液容器跌落过程的SPH模拟方法.振动与冲击,2007,27(6)：13-16
[135]Johnson G R, Stryk S R, Beissel S R. Interface effects for SPH impact computations. Structures under shock and impact IV,1996:285-294
[136]Liu G R, Liu M B. Smoothed particle hydrodynamics:a meshfree particle method. Singapore:World Scientific,2003
[137]杨刚.光滑粒子法的改进及其若干典型应用：[湖南大学博士论文].长沙：湖南大学,2011,42-45
[138]Belytschko T, O. Neal M. Contact-impact by the pinball algorithm with penalty and lagrangian methods. International Journal for Numerical Methods in Engineering,1991,31(3):547-572
[139]Sulsky, D. The material point method for large deformation solid mechanics. In:Third US Congress on Computational Mechanics. Dallas,1995,214
[140]Dilts G A. Moving least-squares particle hydrodynamics II:conservation and boundaries. International Journal for Numerical Methods in Engineering,2000, 48(10):1503-1524
[141]Haque A, Dilts G A. Three-dimensional boundary detection for particle methods. Journal of Computational Physics,2007,226(2):1710-1730
[142]Piekutowski A J, Forrestal M J, Poormon K L, et al. Perforation of aluminum plates with ogive-nose steel rods at normal and oblique impacts. International Journal of Impact Engineering,1996,18(7-8):877-887
[143]Johnson G R, Cook W H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the Seventh International Symposium on Ballistics. The Hague,1983,541-547
[144]Kmetyk L N, Yarrington P. CTH analyses of steel rod penetration into aluminum and concrete targets with comparison to experiment data. Report No. SAND94-1498, Sandia National Laboratories,1994
[145]Swegle J W. Search Algorithm. Sandia National Laboratories,1992
[146]Swegle J W, Attaway S W, Heinstein M W, et al. An Analysis of Smoothed Particle Hydrodynamics. Report No. SAND93-2513, Sandia National Laboratories,1994
[147]Heinstein M W, Mello F J, Attaway S W, et al. Contact-impact modeling in explicit transient dynamics. Computer Methods in Applied Mechanics and Engineering,2000,187(3-4):621-640
[148]Davis M E, Heinstein M W, Attaway S W, et al. Optimizing the Point-in-Box search algorithm for the Cray Y-MP supercomputer. Report No. SAND93-0933, Sandia National Laboratories,1998
[149]Flanagan D P, Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. International Journal for Numerical Methods in Engineering,1981,17(5):679-706
[150]Johnson G R, Stryk R A. Symmetric contact and sliding interface algorithm for intense impulsive loading computations. Computer Methods in Applied Mechanics and Engineering,2001,190(35-36):4531-4549
[151]Johnson G R, Holmquist T J. Evaluation of cylinder-impact test data for constitutive model constants. Journal of Applied Physics,1988,64(8):3901-3910
[152]B(?)rvik T, Hopperstad O S, Berstad T, et al. Numerical simulation of plugging failure in ballistic penetration. International Journal of solids and structures,2001, 38(34-35):6241-6264
[153]Borvik T, Hopperstad O S, Berstad T, et al. A computational model of viscoplasticity and ductile damage for impact and penetration. European Journal of Mechanics-A/Solids,2001,20(5):685-712
[154]Recht R F, Ipson T W. Ballistic perforation dynamics. Journal of Applied Mechanics,1963,30(3):384-390
[155]Holmquist T J, Johnson G R. A computational constitutive model for concrete subjected to large strains, high strain rates and high pressure. In:14th International Symposium on Ballistics. Quebec,1995,591-600
[156]Hanchak S J, Forrestal M J, Young E R, et al. Perforation of concrete slabs with 48MPa and 140MPa unconfined compressive strenths. International Journal of Impact Engineering,1992,12(1):1-7
[157]蒋莉,沈孟育.求解流体与结构相互作用问题的ALE有限体积方法.水动力学研究与进展,2000,15(2)：148-55
[158]Le Tallec P, Mouro J. Fluid structure interaction with large structural displacements. Computer Methods in Applied Mechanics and Engineering, 2001,190(24-25):3039-3067
[159]Legay A, Chessa J, Belytschko T. An Eulerian-Lagrangian method for fluid-structure interaction based on level sets. Computer Methods in Applied Mechanics and Engineering,2006,195(17-18):2070-2087
[160]Walhorn E, Kolke A, Hubner B, et al. Fluid-structure coupling within a monolithic model involving free surface flows. Computers & Structures,2005, 83(25-26):2100-2111
[161]Idelsohn S R, Marti J, Limache A, et al. Unified Lagrangian formulation for elastic solids and incompressible fluids:Application to fluid-structure interaction problems via the PFEM. Computer Methods in Applied Mechanics and Engineering,2008,197(19-20):1762-1776