计算力学中高精度无网格法基础理论研究
|
摘要
?无网格方法是新一代的计算方法,这种方法计算空间导数时不需要借助于事先划定的网格,从而避免了高维拉普拉斯网格法中网格缠结和扭曲等问题。光滑质点流体动力学的方法(SPH)是一种应用广泛的无网格方法,但这种方法存在计算精度低、求解二阶空间导数不稳定、边界条件难以处理等缺点。
当质点分布均匀、对称时,本文证明:线性函数的真实值与SPH近似值的比值为常数;多项式函数的阶导数的真实值与SPH近似值的比值为常数;多项式函数的二阶导数和与SPH近似值的比值为常数。采用上述结论可以得到一种高精度的SPH离散格式。
本文采用移动最小二乘法保证质点分布均匀、对称。如果采用完备性的方法,则可使计算更加简洁。采用完备性方法时,需引进背景函数,但不再需要质点分布均匀、对称。如果采用线性函数作为背景函数,在计算一阶导数时,可得到与Belytschko类似的结论。
借助弹性力学变分公式推导出一种新的SPH离散方法,并提出扩张核函数的概念。利用扩张核函数求空间函数的二阶导数,可降低核函数的可导性要求。
采用高精度的SPH方法推导了计算流体力学和计算固体力学相关公式,并通过算例检验这种方法的精度。其中固体力学的算例精度令人满意,流体力学的算例与经典SPH方法比较,精度提高不明显。主要原因在于流体力学模拟受边界影响较大,而文中所提高精度SPH格式尚无配套的高精度边界条件处理方法。
本文将SPH方法和动力松弛法(D.R.)相结合,利用SPH的特点,提出加速D.R.方法收敛的新技巧。同时,利用扩张核函数的概念处理固体力学边界条件获得成功。
Meshless methods are regarded as next generation of computationalmethods. The key idea of meshless methods is to provide numericalsolutions for integral equations or PDEs with a set of arbitrarilydistributed nodes without using any mesh that provides the connectivityof these nodes. The smoothed particle hydrodynamics (SPH) is a widelyused messless method. However, there are fewer efficient SPH methodsto treat solid‐liquid boundary and the error of SPH approximation couldlead to computational failure in the case that the computation domainincreases or in the case that the derivative order is high.
The dissertation proves three lemmas: When particles in the supportdomain of smoothing kernel function are distributed evenly andsymmetrically, the ratio of the real value of linear function to its SPHapproximation is constant, the ratio of the real value of the nthderivative of the polynomial function P?????? to its SPH approximation isconstant and the ratio of the real value of ????P?? to its SPHapproximation is constant. A new kind of high precision SPH methodbased on the lemmas mentioned above is achieved in this dissertation.
The dissertation introduces the moving least squares method (MLS)which can make particles in the support domain distribute evenly andsymmetrically. However, the computation can be simplified byintroducing background function instead of MLS. If the backgroundfunction is linear function, the formula deduced in this dissertation isequal to that of Belytschko when calculating 1st derivative.
Through the application of SPH approximation to the elasticmechanics equation of variation, it is discovered that the secondderivative of SPH approximation can be obtained by integral action. Bythis method, a new concept of widened‐kernel function is introduced.
In this dissertation, the high accuracy SPH approximation is appliedto the elastic mechanics equations and Navier‐Stokes equations. Thecomparisons between the results computed by ANSYS and the methoddeduced in the present study prove that the present method is accurate.However, the precision improvement is limited in CFD because there isno high precision method to deal with boundary conditions.
Moreover, the combination of SPH and Dynamic Relaxation (D.R.) isinvestigated. Meanwhile, the boundary conditions are dealt with by thewidened‐kernel function.
当质点分布均匀、对称时,本文证明:线性函数的真实值与SPH近似值的比值为常数;多项式函数的阶导数的真实值与SPH近似值的比值为常数;多项式函数的二阶导数和与SPH近似值的比值为常数。采用上述结论可以得到一种高精度的SPH离散格式。
本文采用移动最小二乘法保证质点分布均匀、对称。如果采用完备性的方法,则可使计算更加简洁。采用完备性方法时,需引进背景函数,但不再需要质点分布均匀、对称。如果采用线性函数作为背景函数,在计算一阶导数时,可得到与Belytschko类似的结论。
借助弹性力学变分公式推导出一种新的SPH离散方法,并提出扩张核函数的概念。利用扩张核函数求空间函数的二阶导数,可降低核函数的可导性要求。
采用高精度的SPH方法推导了计算流体力学和计算固体力学相关公式,并通过算例检验这种方法的精度。其中固体力学的算例精度令人满意,流体力学的算例与经典SPH方法比较,精度提高不明显。主要原因在于流体力学模拟受边界影响较大,而文中所提高精度SPH格式尚无配套的高精度边界条件处理方法。
本文将SPH方法和动力松弛法(D.R.)相结合,利用SPH的特点,提出加速D.R.方法收敛的新技巧。同时,利用扩张核函数的概念处理固体力学边界条件获得成功。
Meshless methods are regarded as next generation of computationalmethods. The key idea of meshless methods is to provide numericalsolutions for integral equations or PDEs with a set of arbitrarilydistributed nodes without using any mesh that provides the connectivityof these nodes. The smoothed particle hydrodynamics (SPH) is a widelyused messless method. However, there are fewer efficient SPH methodsto treat solid‐liquid boundary and the error of SPH approximation couldlead to computational failure in the case that the computation domainincreases or in the case that the derivative order is high.
The dissertation proves three lemmas: When particles in the supportdomain of smoothing kernel function are distributed evenly andsymmetrically, the ratio of the real value of linear function to its SPHapproximation is constant, the ratio of the real value of the nthderivative of the polynomial function P?????? to its SPH approximation isconstant and the ratio of the real value of ????P?? to its SPHapproximation is constant. A new kind of high precision SPH methodbased on the lemmas mentioned above is achieved in this dissertation.
The dissertation introduces the moving least squares method (MLS)which can make particles in the support domain distribute evenly andsymmetrically. However, the computation can be simplified byintroducing background function instead of MLS. If the backgroundfunction is linear function, the formula deduced in this dissertation isequal to that of Belytschko when calculating 1st derivative.
Through the application of SPH approximation to the elasticmechanics equation of variation, it is discovered that the secondderivative of SPH approximation can be obtained by integral action. Bythis method, a new concept of widened‐kernel function is introduced.
In this dissertation, the high accuracy SPH approximation is appliedto the elastic mechanics equations and Navier‐Stokes equations. Thecomparisons between the results computed by ANSYS and the methoddeduced in the present study prove that the present method is accurate.However, the precision improvement is limited in CFD because there isno high precision method to deal with boundary conditions.
Moreover, the combination of SPH and Dynamic Relaxation (D.R.) isinvestigated. Meanwhile, the boundary conditions are dealt with by thewidened‐kernel function.
引文
[1] Isaak Rubinstein, Lev Rubinstein,Partial differential equations in classical mathematical physics,世界图书出版公司,北京:2000
[2]吴望一,流体力学,北京大学出版社.北京:1982
[3] H.Schlichting著,徐燕候、徐立功译,边界层理论(Boundary-Layer Theory),科学出版社,北京:1988
[4] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J., 82: 1013-1024 (1977).
[5] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc., 181:375-389(1977).
[6] Benz W., Application of smoothed particle hydrodynamics(SPH) to astrophysical problems, Computer Physics Communications, 48: 97-105(1988).
[7] Benz W., Smoothed particle hydrodynamics: a review, in numerical modeling of non-linear stellar pulsation: problems and prospects, Kluwer Academic, Boston:1990.
[8] Monaghan J.J., Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 30: 543-574(1992).
[9] Frederic A.R., James C.L., Smoothed particle hydrodynamics calculations of stellar interactions, Journal of Computational and Applied Mathematics, 109: 213-230(1999).
[10] Hultman J., Pharayn A., Hierarchical, dissipative formation of elliptical galaxies: is thermal instability the key mechanism? hydrodynamic simulations including supernova feedback multi-phase gas and metal enrichment in cdm: structure and dynamics of elliptical galaxies, Astronomy and Astrophysics, 347: 769-798(1999).
[11] Monaghan J.J., Lattanzio J.C., A simulation of the collapse and fragmentation of cooling molecular clouds, Astrophysical Journal, 375: 177-189(1991).
[12] Berczik P., Kolesnik I.G., Smoothed particle hydrodynamics and its applications to astrophysical problems, Kinematics and Physics of Celestial Bodies, 9: 1-11(1993).
[13] Berczik P., Kolesnik I.G., Gas dynamical model of the triaxial protogalaxy collapse, Astronomy and Astrophysics Transactions, 16: 163-185(1998).
[14] Berczik P., Modeling the star formation in galaxies using the chemo-dynamical SPH code, Astronomy and Astrophysics, 360: 76-84(2000).
[15] Monaghan J.J., Modeling the universe, Proceedings of the Astronomical Society of Australia, 18: 233-237(1990).
[16] Swegle J.W., Report at Sandia National Laboratories(1992).
[17] Morris J.P., Analysis of smoothed particle hydrodynamics with applications, Ph.D. Thesis, Monash University(1996).
[18] Monaghan J.J., Kocharyan A., SPH simulation of multi-phase flow, Computer Physics Communication, 87: 225-235(1995).
[19] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[20] Morris J.P., Fox P.J., Zhu Y., Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136: 214-226(1997).
[21] Monaghan J.J., Simulating gravity currents with SPH lock gates, Applied Mathematics Reports and Preprints, Monash University(1995).
[22] Morris J.P., Zhu Y., Fox P.J., Parallel simulation of pore-scale flow though porous media, Computers and Geotechnics, 25: 227-246(1999).
[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, 23: 881-904(1999).
[24] Monaghan J.J., Heat conduction with discontinuous conductivity, Applied Mathematics Reports and Preprints, Monash University 95/18(1995).
[25] Chen J.K. Beraun J.E., Carney T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Computer Methods in Applied Mechanics and Engineering, 46: 231-252(1999).
[26] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[27] Monaghan J.J., On the problem of penetration in particle methods, J. Comp. Phys., 82: 1-15(1989).
[28] Morris J.P., Monaghan J.J., A switch to reduce SPH viscosity, Journal of Computational Physics, 136: 41-50(1997).
[29] Benz W., Asphaug E., Simulations of brittle solids using smoothed particle hydrodynamics, Computer Physics Communications, 87: 253-265(1995).
[30] Bonet J., Kulasegaram S., Correction and stabilization of smoothed particle hydrodynamics method with applications in metal forming simulation, International Journal for Numerical Methods in Engineering, 47: 1189-1214(2000).
[31] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[32] Randles P.W., Libersky L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Mehtods Appl. Mech. Engrg., 139:375-408(1996).
[33] Randles P.W., Carney T.C., Libersky L.D., Renick J.R., Petschek A.G., Calculation of oblique impact and fracture of tungsten cubes using smoothed particle hydrodynamics, International Journal of Impact Engineering, 17: 661-672(1995).
[34] Johnson G.R., Stryk R.A., Beissel S.R., SPH for high velocity impact computations, Computer Methods in Applied Mechanics and Engineering, 139: 347-373(1996).
[35] Swegle J.W., Attaway S.W., On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations, Computational Mechanics, 17: 151-168(1995).
[36] Liu M.B., Liu G.R., Lam K.Y., Zong Z., Comparative study of the real and artificial detonation models in underwater explosion simulations, Engineering Simulation, 25(1): 113-124(2003).
[37] Liu M.B., Liu G.R., Lam K.Y., Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of computational and Applied Mathematics, 155: 263-284(2003).
[38] Liu M.B., Liu G.R., Lam K.Y., Zong Z., Meshfree particle simulation of the detonation process for high explosives in shaped charge unlined cavity configurations, Shock Waves, 12: 509-520(2003).
[39] Liu M.B., Liu G.R., Zong Z., Lam K.Y., Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology, Computer & Fluids, 32: 305-322(2003).
[40] Liu M.B., Liu G.R., Lam K.Y., A one-dimensional meshfree particle formulation for simulating shock waves, Shock Waves, 13: 201-211(2003).
[41] Liu M.B., Liu G.R., Zong Z., Lam K.Y., Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Computational Mechanics, 30: 106-118(2003).
[42]徐立,孙锦山,一维激波管问题的SPH模拟,计算物理,20(2):153-156(2003).
[43]毛益明,汤文辉,自由表面流动问题的SPH方法数值模拟,解放军理工大学学报(自然科学版),2(5):92-94(2001).
[44]李梅娥,周进雄,不可压流体自由表面流动的SPH数值模拟,机械工程学报,40(3):5-9(2004).
[45]汤文辉,毛益明,Rayleigh-Taylor不稳定性的SPH模拟,国防科技大学学报,26(1):21-23(2004).
[46]贝新源,岳宗五,三维SPH程序及其在斜高速碰撞问题的应用,计算物理,14(2): 155-166(1997).
[47]毛益明,武文远,陈广林,龚艳春,高速碰撞问题的SPH方法模拟,解放军理工大学学报(自然科学版),4(5):84-87(2003).
[48]闫晓军,张玉珠,聂景旭,空间碎片超高速碰撞数值模拟的SPH方法,北京航空航天大学学报,31(3):351-354(2005).
[49]王裴,秦承森,张树道,刘超,SPH方法对金属表面微射流的数值模拟,高压物理学报,18(2):149-156(2004).
[50]王肖钧,张刚明,刘文韬,周钟,弹塑性波计算钟的光滑粒子法,爆炸与冲击,22(2):97-103(2002).
[51]丁桦,龙丽平,伍彦峰,SPH方法在模拟线弹性波传播中的运用,计算力学学报,22(3):320-325(2005).
[52] Monaghan J.J., Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[53] Gingold R.A., Monaghan J.J., Kernel estimates as a basis for general particle method in hydrodynamics, Journal of Computational Physics, 46: 429-453(1982).
[54] Morris J.P., A study of the stability properties of SPH, Applied Mathematics Reports andPreprints, Monash University(1994).
[55] Balsara D.S., von Neumann stability analysis of smoothed particle hydrodynamics-suggestions for optimal algorithms, J. Comp. Phys., 121:357-372(1995).
[56] Ben M.B., Vila J. P., Convergence of SPH method for scalar nonlinear conservation laws, SIAM Journal on Numerical Analysis, 37(3): 863-887(2000).
[57] Fulk D.A., A numerical analysis of smoothed particle hydrodynamics, Ph.D. Thesis, Air Force Institute of Technology(1994).
[58] Swegle J.W., Hicks D.L. and Attaway S.W., Smoothed particle hydrodynamics stability analysis, J. Comp. Phys., 116:123-134(1995).
[59]李声远,平滑粒子流体动力学(SPH)方法的稳定性,2003年度航天第十信息网学术交流会,232-236(2003).
[60] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[61] Dyka C.T., Addressing tension instability in SPH methods, NRL Report NRL/MR/6384(1994).
[62] Dyka C.T. and Ingel R.P., An approach for tension instability in smoothed particle hydrodynamics, Comp. Struct., 57:573-580(1995).
[63] Randles P.W., Libersky L.D., Normalized SPH with stress points, International Journal for Numerical Methods in Engineering, 48: 1445-1462(2000).
[64] Wen Y., Hicks D.L. and Swegle J.W., Stabilizing SPH with conservative smoothing, Sandia Report, SAND94-1932 (1994).
[65] Guenther C., Hicks D.L. and Swegle J.W., Conservative smoothing verses artificial viscosity, Sandia Report, SAND94-1853, Sandia National Lab., Alb. NM 87185 (1994).
[66] Swegle J.W., Attaway S.W., Heinstein M.W., Mello F.J. and Hicks D.L., An analysis of smoothed particle hydrodynamics, Sandia Report, SAND94-2513, Sandia National Lab., Alb. NM 87185 (1994).
[67] Chen J.K. Beraun J.E., Jih C.J., An improvement for tensile instability in smoothed particle hydrodynamics, Computational Mechanics, 23: 279-287(1999).
[68] Chen J.K. Beraun J.E., Jih C.J., Completeness of corrective smoothed particle method for linear elastodynamics, Computational Mechanics, 24: 273-285(1999).
[69]张刚明,王肖钧,胡秀章,周钟,光滑粒子法中的一种新的核函数,爆炸与冲击,23(3):219-224(2003).
[70] Monaghan J.J., Kos A. and Issa N., Fluid motion generated by impact, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 129, No. 6: 250-259(2003).
[71]汤文辉,毛益明,SPH数值模拟中固壁边界的一种处理方法,国防科技大学学报,23(6):54-57(2001).
[72] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[73] Gotoh H., Sakai T., Lagrangian simulation of breaking waves using particle method, Coast.Engng. J., 41(3/4): 303-326(1999).
[74] Edmond Y.M. Lo, Shao S.D., Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Applied Ocean Research, 24: 275-286(2002).
[75] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods, Int. J. Numer. Meth. Fluids 20:1081-1106(1995).
[76] W.K. Liu, Y. Chen, etc. Generalized multiple scale reproducing kernel particle methods, Comput. Methods Appl. Mech. Engrg. 139:91-157(1996)
[77] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods for structural dynamics, Int. J. Numer. Meth. Engng. 38:1655-1679(1995)
[78] J.S. Chen, C. Pan, etc. Reproducing Kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg. 139:195-227(1996)
[79] W.K.Liu &. S.Li, Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143:113-154(1997).
[80] S.Li &. W.K.Liu, Moving least-square reproducing kernel methods (II) Fourier analysis. Comput. Methods Appl. Mech. Engrg. 139:159-193(1996)
[81]邵文蛟,解非线性结构问题的有效方法——动力松弛法,交通部上海船舶运输科学研究所学报,13(1):26-36(1984)
[82]张志宏,董石麟,空间结构分析中动力松弛法若干问题的探讨,建筑结构学报,23(6): 79-84(2002).
[83]毛国栋,孙炳楠,唐志山,控制网格变形的动力松弛法膜结构找形分析,浙江大学学报(工学版),38(5): 598-602(2004).
[84] Barnes MR. Form finding and analysis of pre-stressed nets and membranes. Computer and Structure, 30 (3) : 685-695(1988).
[85] I.P. Pasqualino, S.F. Estefen, A nonlinear analysis of the buckle propagation problem in deepwater pipelines, International Journal of Solids and Structures ,38: 8481-8502(2001)
[86]陈联盟,董石麟,袁行飞,索穹顶结构施工成形理论分析和试验研究,土木工程学报,39(11):33-38(2006)
[87] L. Iannucci, Dynamic Delamination Modelling using interface elements, Computers and Structures 84: 1029-1048(2006)
[88] R.D. Wood,A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes,Computers and Structures,80: 2115–2120 (2002)
[1] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024(1977).
[2] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181: 375-389(1977).
[3] J.J. Monaghan, Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 1992, 30:543-74.
[4] G.A. Sod, A survey of several finite difference methods for systems of hyperbolic conservation laws, Journal of Computational Physics, 27:1-31(1978).
[5] P.W. Randles , L.D. Libersky, Smoothed Particle Hydrodynamics: Some recent improvements and applications, Computer methods in applied mechanics and engineering, 139:375-408(1996).
[6] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[7] J.J. Monaghan, Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[8] T.Belytschko &.Y.Krongauz, etc. Meshless methods: An overview and recent developments, Comput. Methods Appl. Mech. Engrg. 139: 3-47(1996)
[9] D.Kincaid &. W.Cheney, Numerical Analysis Mathematics of Scientific Computing, Published by Brooks/Cole, Thomson Learning : 2002
[10] P.Lancaster &. K.Salkauskas, Surfaces generated by moving least-squares methods, Math. Comput. 37:141-158(1981)
[11] W.K.Liu &. S.Li, Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143:113-154(1997)
[12] S.Li &. W.K.Liu, Moving least-square reproducing kernel methods (II) Fourier analysis. Comput. Methods Appl. Mech. Engrg. 139:159-193(1996)
[13] B.P.Rynne &. M.A.Youngson, Linear Functional Analysis. Springer-Verlag: 2000
[14] W.Cheney &. W.Light, Acouse in Approximation Theory. Published by Brooks/Cole, Thomson Learning: 2002
[15] S.N. Atluri, T.Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Comput. Mech. 22:117-127 (1998)
[16] S.N. Atluri, H.G. Kim, J.Y.Cho, A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods, Comput. Mech. 24:348-372(1999)
[17] S.N. Atluri, T.Zhu, The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics, Comput. Mech. 25:169-179(2000)
[18] J.R. Xiao, Local Heaviside weighted MLPG meshless method for two-dimensional solidsusing compactly supported radial basis functions, Comput. Methods Appl. Mech. Engrg. 193:117-138(2004)
[19] T.Chen, I.S.Raju, A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems, Comput. Methods Appl. Mech. Engrg., 192:4533-4550(2003)
[20] Y.T. Gu, G.R. Liu, A local point interpolation method for static and dynamic analysis of thin beams, Comput. Methods Appl. Mech. Engrg. 190:5515-5528(2001)
[21] T. Belytschko, Y. Krongauz, M. Fleming, etc. Smoothing and accelerated computations in the element free Galerkin method, Journal of Computational and Applied Mathematics, 74:111-126(1996)
[22] Y.T. Gu, G.R. Liu, A coupled element free Galerkin/boundary element method for stress analysis of two-dimensional solids, Comput. Methods Appl. Mech. Engrg., 190:4405-4419(2001)
[23] X.L. Chen, G.R. Liu, S.P.Lim, An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape, Composite Structures, 59:279-289(2003)
[24] Chongjiang Du, An element-free Galerkin method for simulation of stationary two-dimensional shallow water flows in rivers, Comput. Methods Appl. Mech. Engrg., 182:89-107(2000)
[25] L.Gavete, S. Falcon, A. Ruiz, An error indicator for the element free Galerkin method, Eur. J. Mech. A/Solids, 20:327-341(2001)
[26] P. Breitkopf, A. Rassineux, etc. Integration constraint in diffuse element method, Comput. Methods Appl. Mech. Engrg., 193:1203-1220(2004)
[27] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods, Int. J. Numer. Meth. Fluids 20:1081-1106(1995)
[28] W.K. Liu, Y. Chen, etc. Generalized multiple scale reproducing kernel particle methods, Comput. Methods Appl. Mech. Engrg., 139:91-157(1996)
[29] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods for structural dynamics, Int. J. Numer. Meth. Engng., 38:1655-1679(1995)
[30] J.S. Chen, C. Pan, etc. Reproducing Kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg., 139:195-227(1996)
[31] W.K. Liu, Y. Chen, Wavelet and multiple scale reproducing kernel methods, Int. J. Numer. Methods Fluids, 21:901-931(1995)
[32] S. Qian, J. Weiss, Wavelet and the numerical solution of partial differential equations, J. Comput. Phys., 106:155-175(1993)
[33] C.A.M. Duarte, J.T. Oden, An hp adaptive method using clouds, Comput. Methods Appl. Methods Appl. Mech. Engrg., 139:237-262(1996)
[34] C.A.M. Duarte, J.T. Oden, hp clouds– an hp meshless method, Numer. Methods Partial Differential Equations, 12:673-705(1996)
[35] J.J. Monaghan, A. Kocharyan, SPH simulation of multi-phase flow, Computer Physics Communications 87:225-235(1995)
[36] J.P. Gray, J.J. Monaghan, etc., SPH elastic dynamics, Comput. Methods Appl. Mech. Engrg., 190:6641-6662(2001)
[37] V. Roubtsova, R. Kahawita, The SPH technique applied to free surface flows, Computers & Fluids xxx:xxx-xxx(2006)4
[38] Miguel R.P., J. Bonet, A corrected smooth particle hydrodynamics formulation of the shallow-water equations, Computers and Structures 83:1396-1410(2005)
[39] P.W. Cleary, J. Ha, etc., 3D SPH flow predictions and validation for high pressure die casting of automotive components, Applied Mathematical Modelling xxx:xxx-xxx(2006)
[40] T. De Vuyst, R. Vignjevic, etc, Coupling between meshless and finite element methods, International Journal of Impact Engineering 31:1054-1064(2005)
[41]张恭庆,泛函分析讲义,北京大学出版社,北京:1986
[42] A.H.柯尔莫戈洛夫、C.B.佛明著,段虞荣、郑洪深、郭思旭译,函数论与泛函分析初步,高等教育出版社,北京:2006
[1] L. Brookshaw, A Method of Calculating Radiative Heat Diffusion in Particle Simulations, Proc. ASA, 6(2):207-210 (1985)
[2] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024(1977).
[3] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181: 375-389(1977).
[4] G.A. Sod, A survey of several finite difference methods for systems of hyperbolic conservation laws, Journal of Computational Physics, 27:1-31 (1978) .
[5] J. Campbell, R. Vignjevic, A contact algorithm for smoothed particle hydrodynamics, Comput. Methods Appl. Mech. Engrg. 184:49-65 (2000)
[6] J.J. Monaghan, Simulating free surface flows with SPH, J. Comput. Phys. 110:399-406 (1994).
[7] J.J. Monaghan, A. Kos, Solitary Waves on a Cretan Beach, Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(3): 145-154 (1999)
[8] M.B. Liu, G.R. Liu, etc. Investigations into water mitigations using a meshless particle method, Shock Waves 12(3): 181-195 (2002).
[9] M.B. Liu, G.R. Liu, etc. Computer simulation of the high explosive explosion using smoothed particle hydrodynamics methodology, Comput. Fluids 32(3): 305-322 (2003).
[10] P.W. Cleary, Modeling confined multi-material heat and mass flows using SPH, Appl. Math. Modell. 22:981-993 (1998).
[11] J.J. Monaghan, Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 30:543-74(1992).
[12] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[13] Flebbe, S. Münzel, etc. Smoothed Particle Hydrodynamics: Physical Viscosity and the Simulation, The Astrophysical Journal, 431:754-760 (1994).
[14] S.J. Watkins, A.S. Bhattal, etc. A new prescription for viscosity in Smoothed Particle Hydrodynamics, Astron. Astrophys. Suppl. Ser. 119:177-187(1996)
[15] M.B. Liu, G.R. Liu, etc. Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of Computational and Applied Mathematics 155:263-284(2003).
[16] T. Belytschko, Y. Krongauz, J. Dolbow, etc. On the completeness of meshfree particle methods, International Journal for Numerical Methods in Engineering, 43(5): 785-819
[1] R.柯朗&. D.希尔伯特著,钱敏、郭敦仁译,数学物理方法(卷一),科学出版社,北京:1981
[2]鹫津九一郎著,老亮、郝松林译,弹性和塑性力学中的变分法,科学出版社,北京:1984
[3]武际可,力学史,重庆出版社,重庆:2000
[4] L.Lapidus, G.F. Pinder著,孙讷正等译,科学和工程中的偏微分方程数值解法,煤炭出版社,北京:1985
[5]张雄,陆明万等,任意拉格朗日-欧拉描述法研究进展,计算力学学报,1997(14),1
[6] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[7] J.N. Reddy, An Introduction to the Finite Element Method (Third Edition), McGraw-Hill Companies, Inc. 2006.
[8] S.P. Timoshenko &. J.N. Goodier, Theory of Elasticity (Third Edition), McGraw-Hill Companies, Inc. 1970.
[1] Balsara D.S., von Neumann stability analysis of smoothed particle hydrodynamics-suggestions for optimal algorithms, J. Comp. Phys., 121:357-372(1995).
[2] Swegle J.W., Hicks D.L. and Attaway S.W., Smoothed particle hydrodynamics stability analysis, J. Comp. Phys., 116:123-134(1995).
[3] Dyka C.T., Addressing tension instability in SPH methods, NRL Report NRL/MR/6384(1994).
[4] Dyka C.T. and Ingel R.P., An approach for tension instability in smoothed particle hydrodynamics, Comp. Struct., 57:573-580(1995).
[5] Randles P.W., Libersky L.D., Normalized SPH with stress points, International Journal for Numerical Methods in Engineering, 48: 1445-1462(2000).
[6] Swegle J.W., Attaway S.W., Heinstein M.W., Mello F.J. and Hicks D.L., An analysis of smoothed particle hydrodynamics, Sandia Report, SAND94-2513, Sandia National Lab., Alb. NM 87185 (1994).
[7] Wen Y., Hicks D.L. and Swegle J.W., Stabilizing SPH with conservative smoothing, Sandia Report, SAND94-1932 (1994).
[8] Guenther C., Hicks D.L. and Swegle J.W., Conservative smoothing verses artificial viscosity, Sandia Report, SAND94-1853, Sandia National Lab., Alb. NM 87185 (1994).
[9] Chen J.K. Beraun J.E., Carney T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Computer Methods in Applied Mechanics and Engineering, 46: 231-252(1999).
[10] Chen J.K. Beraun J.E., Jih C.J., An improvement for tensile instability in smoothed particle hydrodynamics, Computational Mechanics, 23: 279-287(1999).
[11] Chen J.K. Beraun J.E., Jih C.J., Completeness of corrective smoothed particle method for linear elastodynamics, Computational Mechanics, 24: 273-285(1999).
[12] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[13] Monaghan J.J., Kos A. and Issa N., Fluid motion generated by impact, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 129, No. 6: 250-259(2003).
[14] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[15] Gotoh H., Sakai T., Lagrangian simulation of breaking waves using particle method, Coast. Engng. J., 41(3/4): 303-326(1999).
[16] Randles P.W., Libersky L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Mehtods Appl. Mech. Engrg., 139: 375-408(1996).
[17] Edmond Y.M. Lo, Shao S.D., Simulation of near-shore solitary wave mechanics by anincompressible SPH method, Applied Ocean Research, 24: 275-286(2002).
[18]吴望一,流体力学,北京大学出版社.北京:1982
[19] F.M. White著,魏中磊、甄思淼译,粘性流体动力学(Viscous Fluid Flow),机械工业出版社,北京:1982
[20] G.K.Batchelor著,沈青、贾复译,流体动力学引论(An Introduction to Fluid Dynamics ),科学出版社,北京:1997
[21] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[22] Monaghan J.J., Kos A., Solitary waves on a Cretan beach, Journal of Waterway, Port, Coastal and Ocean Engineering, 125(3): 145-154(1999).
[23] Colagrossi A., Landrini M., Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. Comput. Phys., 191: 448-475(2003).
[24] Monaghan J.J., Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[25] Monaghan J.J., Particle methods for hydrodynamics, Computer Physics Report, 3: 71-124(1985).
[26] Monaghan J.J., An introduction to SPH, Computer Physics Communications, 48: 89-96(1988).
[27] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[28] Chen J.K. Beraun J.E., A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems, Computer Methods in Applied Mechanics and Engineering, 190: 225-239(2000).
[29] Belytschko T., Krongauz Y., Dolbow J., Gerlach C., On the Completeness of Meshfree Particle Methods, International Journal for Numerical Methods in Engineering 43: 785–819(1998).
[30]黄润生,混沌及其应用.武汉大学出版社,武汉:2000
[31]是勋刚,湍流,天津大学出版社,天津:1994
[32] H.Schlichting著,徐燕候、徐立功译,边界层理论(Boundary-Layer Theory),科学出版社,北京:1988
[33]苏铭德,黄素逸,计算流体力学基础,清华大学出版社,北京:1997
[34] von Neumann J., Richtmyer R.D., A method for the numerical calculation of hydrodynamic shocks, Journal of Applied Physics, 21:232-247(1950).
[35] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[36] Balsara D.S., Brandt A., Multilevel methods for fast solution of N-body and hybrid systems, International Series of Numerical Mathematics, 98: 131-142(1991).
[37] Monaghan J.J., Heat conduction with discontinuous conductivity, Applied MathematicsReports and Preprints, Monash University 95/18(1995).
[38] Shao S.D., Ji C.M., Graham D.I., Reeve D.E., James P.W., Chadwick A.J., Simulation of wave overtopping by an incompressible SPH model, Coastal Engineering, 53: 723–735(2006).
[39] Batchelor G.K., Introduction to fluid dynamics, Cambridge Univ. Press, Cambridge, U.K.(1974).
[40] Morris J.P., Fox P.J., Zhu Y., Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136: 214-226(1997).
[41] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[42]朱明善,刘颖,林兆庄等,工程热力学,清华大学出版社,北京:1995
[1] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024 (1977).
[2] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181:375-389 (1977).
[3] Benz W., Application of smoothed particle hydrodynamics(SPH) to astrophysical problems, Computer Physics Communications, 48: 97-105(1988).
[4] Monaghan J.J., Lattanzio J.C., A simulation of the collapse and fragmentation of cooling molecular clouds, Astrophysical Journal, 375: 177-189(1991).
[5] Morris J.P., Analysis of smoothed particle hydrodynamics with applications, Ph.D. Thesis, Monash University(1996).
[6] Monaghan J.J., Kocharyan A., SPH simulation of multi-phase flow, Computer Physics Communication, 87: 225-235(1995).
[7] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[8]毛益明,汤文辉,自由表面流动问题的SPH方法数值模拟,解放军理工大学学报(自然科学版),2(5):92-94(2001).
[9]李梅娥,周进雄,不可压流体自由表面流动的SPH数值模拟,机械工程学报,40(3):5-9(2004).
[10] 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, 23: 881-904(1999).
[11] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[12]徐立,孙锦山,一维激波管问题的SPH模拟,计算物理,20(2):153-156(2003).
[13] Benz W., Asphaug E., Simulations of brittle solids using smoothed particle hydrodynamics, Computer Physics Communications, 87: 253-265(1995).
[14] Bonet J., Kulasegaram S., Correction and stabilization of smoothed particle hydrodynamics method with applications in metal forming simulation, International Journal for Numerical Methods in Engineering, 47: 1189-1214(2000).
[15] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[16] Johnson G.R., Stryk R.A., Beissel S.R., SPH for high velocity impact computations, Computer Methods in Applied Mechanics and Engineering, 139: 347-373(1996).
[17]贝新源,岳宗五,三维SPH程序及其在斜高速碰撞问题的应用,计算物理,14(2): 155-166(1997).
[18]毛益明,武文远,陈广林,龚艳春,高速碰撞问题的SPH方法模拟,解放军理工大学学报(自然科学版),4(5):84-87(2003).
[19]闫晓军,张玉珠,聂景旭,空间碎片超高速碰撞数值模拟的SPH方法,北京航空航天大学学报,31(3):351-354(2005).
[20] Swegle J.W., Attaway S.W., On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations, Computational Mechanics, 17: 151-168(1995).
[21]张锁春,光滑质点流体动力学(SPH)方法(综述),计算物理,13(4): 385-397(1996)
[22] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[23] L. Brookshaw, A Method of Calculating Radiative Heat Diffusion in Particle Simulations, Proc. ASA 6(2) (1985)
[24] S.J. Watkins, A.S. Bhattal, etc. A new prescription for viscosity in Smoothed Particle Hydrodynamics, Astron. Astrophys. Suppl. Ser. 119, 177-187(1996)
[25] S.Timoshenko, J.N.Goodier著,徐芝纶译,弹性理论(Theory of Elasticity),高等教育出版社,北京:1990
[26]张志宏,董石麟,空间结构分析中动力松弛法若干问题的探讨,建筑结构学报,23(6):79-84(2002).
[27]毛国栋,孙炳楠,唐志山,控制网格变形的动力松弛法膜结构找形分析,浙江大学学报(工学版),38(5),2004
[28] Barnes MR. Form finding and analysis of pre-stressed nets and membranes. Computer and Structure, 1988, 30 (3) : 685-695.
[29] I.P. Pasqualino, S.F. Estefen, A nonlinear analysis of the buckle propagation problem in deepwater pipelines, International Journal of Solids and Structures ,38: 8481-8502(2001)
[30]陈联盟,董石麟,袁行飞,索穹顶结构施工成形理论分析和试验研究,土木工程学报,39(11):33-38(2006)
[31] L. Iannucci, Dynamic Delamination Modelling using interface elements, Computers and Structures 84: 1029-1048(2006)
[32] R.D. Wood,A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes,Computers and Structures,80: 2115–2120 (2002)
[33]倪振华,振动力学,西安交通大学出版社,西安:1989
[34]郑兆昌,机械振动,机械工业出版社,北京:1978
[2]吴望一,流体力学,北京大学出版社.北京:1982
[3] H.Schlichting著,徐燕候、徐立功译,边界层理论(Boundary-Layer Theory),科学出版社,北京:1988
[4] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J., 82: 1013-1024 (1977).
[5] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc., 181:375-389(1977).
[6] Benz W., Application of smoothed particle hydrodynamics(SPH) to astrophysical problems, Computer Physics Communications, 48: 97-105(1988).
[7] Benz W., Smoothed particle hydrodynamics: a review, in numerical modeling of non-linear stellar pulsation: problems and prospects, Kluwer Academic, Boston:1990.
[8] Monaghan J.J., Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 30: 543-574(1992).
[9] Frederic A.R., James C.L., Smoothed particle hydrodynamics calculations of stellar interactions, Journal of Computational and Applied Mathematics, 109: 213-230(1999).
[10] Hultman J., Pharayn A., Hierarchical, dissipative formation of elliptical galaxies: is thermal instability the key mechanism? hydrodynamic simulations including supernova feedback multi-phase gas and metal enrichment in cdm: structure and dynamics of elliptical galaxies, Astronomy and Astrophysics, 347: 769-798(1999).
[11] Monaghan J.J., Lattanzio J.C., A simulation of the collapse and fragmentation of cooling molecular clouds, Astrophysical Journal, 375: 177-189(1991).
[12] Berczik P., Kolesnik I.G., Smoothed particle hydrodynamics and its applications to astrophysical problems, Kinematics and Physics of Celestial Bodies, 9: 1-11(1993).
[13] Berczik P., Kolesnik I.G., Gas dynamical model of the triaxial protogalaxy collapse, Astronomy and Astrophysics Transactions, 16: 163-185(1998).
[14] Berczik P., Modeling the star formation in galaxies using the chemo-dynamical SPH code, Astronomy and Astrophysics, 360: 76-84(2000).
[15] Monaghan J.J., Modeling the universe, Proceedings of the Astronomical Society of Australia, 18: 233-237(1990).
[16] Swegle J.W., Report at Sandia National Laboratories(1992).
[17] Morris J.P., Analysis of smoothed particle hydrodynamics with applications, Ph.D. Thesis, Monash University(1996).
[18] Monaghan J.J., Kocharyan A., SPH simulation of multi-phase flow, Computer Physics Communication, 87: 225-235(1995).
[19] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[20] Morris J.P., Fox P.J., Zhu Y., Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136: 214-226(1997).
[21] Monaghan J.J., Simulating gravity currents with SPH lock gates, Applied Mathematics Reports and Preprints, Monash University(1995).
[22] Morris J.P., Zhu Y., Fox P.J., Parallel simulation of pore-scale flow though porous media, Computers and Geotechnics, 25: 227-246(1999).
[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, 23: 881-904(1999).
[24] Monaghan J.J., Heat conduction with discontinuous conductivity, Applied Mathematics Reports and Preprints, Monash University 95/18(1995).
[25] Chen J.K. Beraun J.E., Carney T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Computer Methods in Applied Mechanics and Engineering, 46: 231-252(1999).
[26] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[27] Monaghan J.J., On the problem of penetration in particle methods, J. Comp. Phys., 82: 1-15(1989).
[28] Morris J.P., Monaghan J.J., A switch to reduce SPH viscosity, Journal of Computational Physics, 136: 41-50(1997).
[29] Benz W., Asphaug E., Simulations of brittle solids using smoothed particle hydrodynamics, Computer Physics Communications, 87: 253-265(1995).
[30] Bonet J., Kulasegaram S., Correction and stabilization of smoothed particle hydrodynamics method with applications in metal forming simulation, International Journal for Numerical Methods in Engineering, 47: 1189-1214(2000).
[31] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[32] Randles P.W., Libersky L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Mehtods Appl. Mech. Engrg., 139:375-408(1996).
[33] Randles P.W., Carney T.C., Libersky L.D., Renick J.R., Petschek A.G., Calculation of oblique impact and fracture of tungsten cubes using smoothed particle hydrodynamics, International Journal of Impact Engineering, 17: 661-672(1995).
[34] Johnson G.R., Stryk R.A., Beissel S.R., SPH for high velocity impact computations, Computer Methods in Applied Mechanics and Engineering, 139: 347-373(1996).
[35] Swegle J.W., Attaway S.W., On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations, Computational Mechanics, 17: 151-168(1995).
[36] Liu M.B., Liu G.R., Lam K.Y., Zong Z., Comparative study of the real and artificial detonation models in underwater explosion simulations, Engineering Simulation, 25(1): 113-124(2003).
[37] Liu M.B., Liu G.R., Lam K.Y., Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of computational and Applied Mathematics, 155: 263-284(2003).
[38] Liu M.B., Liu G.R., Lam K.Y., Zong Z., Meshfree particle simulation of the detonation process for high explosives in shaped charge unlined cavity configurations, Shock Waves, 12: 509-520(2003).
[39] Liu M.B., Liu G.R., Zong Z., Lam K.Y., Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology, Computer & Fluids, 32: 305-322(2003).
[40] Liu M.B., Liu G.R., Lam K.Y., A one-dimensional meshfree particle formulation for simulating shock waves, Shock Waves, 13: 201-211(2003).
[41] Liu M.B., Liu G.R., Zong Z., Lam K.Y., Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Computational Mechanics, 30: 106-118(2003).
[42]徐立,孙锦山,一维激波管问题的SPH模拟,计算物理,20(2):153-156(2003).
[43]毛益明,汤文辉,自由表面流动问题的SPH方法数值模拟,解放军理工大学学报(自然科学版),2(5):92-94(2001).
[44]李梅娥,周进雄,不可压流体自由表面流动的SPH数值模拟,机械工程学报,40(3):5-9(2004).
[45]汤文辉,毛益明,Rayleigh-Taylor不稳定性的SPH模拟,国防科技大学学报,26(1):21-23(2004).
[46]贝新源,岳宗五,三维SPH程序及其在斜高速碰撞问题的应用,计算物理,14(2): 155-166(1997).
[47]毛益明,武文远,陈广林,龚艳春,高速碰撞问题的SPH方法模拟,解放军理工大学学报(自然科学版),4(5):84-87(2003).
[48]闫晓军,张玉珠,聂景旭,空间碎片超高速碰撞数值模拟的SPH方法,北京航空航天大学学报,31(3):351-354(2005).
[49]王裴,秦承森,张树道,刘超,SPH方法对金属表面微射流的数值模拟,高压物理学报,18(2):149-156(2004).
[50]王肖钧,张刚明,刘文韬,周钟,弹塑性波计算钟的光滑粒子法,爆炸与冲击,22(2):97-103(2002).
[51]丁桦,龙丽平,伍彦峰,SPH方法在模拟线弹性波传播中的运用,计算力学学报,22(3):320-325(2005).
[52] Monaghan J.J., Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[53] Gingold R.A., Monaghan J.J., Kernel estimates as a basis for general particle method in hydrodynamics, Journal of Computational Physics, 46: 429-453(1982).
[54] Morris J.P., A study of the stability properties of SPH, Applied Mathematics Reports andPreprints, Monash University(1994).
[55] Balsara D.S., von Neumann stability analysis of smoothed particle hydrodynamics-suggestions for optimal algorithms, J. Comp. Phys., 121:357-372(1995).
[56] Ben M.B., Vila J. P., Convergence of SPH method for scalar nonlinear conservation laws, SIAM Journal on Numerical Analysis, 37(3): 863-887(2000).
[57] Fulk D.A., A numerical analysis of smoothed particle hydrodynamics, Ph.D. Thesis, Air Force Institute of Technology(1994).
[58] Swegle J.W., Hicks D.L. and Attaway S.W., Smoothed particle hydrodynamics stability analysis, J. Comp. Phys., 116:123-134(1995).
[59]李声远,平滑粒子流体动力学(SPH)方法的稳定性,2003年度航天第十信息网学术交流会,232-236(2003).
[60] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[61] Dyka C.T., Addressing tension instability in SPH methods, NRL Report NRL/MR/6384(1994).
[62] Dyka C.T. and Ingel R.P., An approach for tension instability in smoothed particle hydrodynamics, Comp. Struct., 57:573-580(1995).
[63] Randles P.W., Libersky L.D., Normalized SPH with stress points, International Journal for Numerical Methods in Engineering, 48: 1445-1462(2000).
[64] Wen Y., Hicks D.L. and Swegle J.W., Stabilizing SPH with conservative smoothing, Sandia Report, SAND94-1932 (1994).
[65] Guenther C., Hicks D.L. and Swegle J.W., Conservative smoothing verses artificial viscosity, Sandia Report, SAND94-1853, Sandia National Lab., Alb. NM 87185 (1994).
[66] Swegle J.W., Attaway S.W., Heinstein M.W., Mello F.J. and Hicks D.L., An analysis of smoothed particle hydrodynamics, Sandia Report, SAND94-2513, Sandia National Lab., Alb. NM 87185 (1994).
[67] Chen J.K. Beraun J.E., Jih C.J., An improvement for tensile instability in smoothed particle hydrodynamics, Computational Mechanics, 23: 279-287(1999).
[68] Chen J.K. Beraun J.E., Jih C.J., Completeness of corrective smoothed particle method for linear elastodynamics, Computational Mechanics, 24: 273-285(1999).
[69]张刚明,王肖钧,胡秀章,周钟,光滑粒子法中的一种新的核函数,爆炸与冲击,23(3):219-224(2003).
[70] Monaghan J.J., Kos A. and Issa N., Fluid motion generated by impact, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 129, No. 6: 250-259(2003).
[71]汤文辉,毛益明,SPH数值模拟中固壁边界的一种处理方法,国防科技大学学报,23(6):54-57(2001).
[72] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[73] Gotoh H., Sakai T., Lagrangian simulation of breaking waves using particle method, Coast.Engng. J., 41(3/4): 303-326(1999).
[74] Edmond Y.M. Lo, Shao S.D., Simulation of near-shore solitary wave mechanics by an incompressible SPH method, Applied Ocean Research, 24: 275-286(2002).
[75] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods, Int. J. Numer. Meth. Fluids 20:1081-1106(1995).
[76] W.K. Liu, Y. Chen, etc. Generalized multiple scale reproducing kernel particle methods, Comput. Methods Appl. Mech. Engrg. 139:91-157(1996)
[77] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods for structural dynamics, Int. J. Numer. Meth. Engng. 38:1655-1679(1995)
[78] J.S. Chen, C. Pan, etc. Reproducing Kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg. 139:195-227(1996)
[79] W.K.Liu &. S.Li, Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143:113-154(1997).
[80] S.Li &. W.K.Liu, Moving least-square reproducing kernel methods (II) Fourier analysis. Comput. Methods Appl. Mech. Engrg. 139:159-193(1996)
[81]邵文蛟,解非线性结构问题的有效方法——动力松弛法,交通部上海船舶运输科学研究所学报,13(1):26-36(1984)
[82]张志宏,董石麟,空间结构分析中动力松弛法若干问题的探讨,建筑结构学报,23(6): 79-84(2002).
[83]毛国栋,孙炳楠,唐志山,控制网格变形的动力松弛法膜结构找形分析,浙江大学学报(工学版),38(5): 598-602(2004).
[84] Barnes MR. Form finding and analysis of pre-stressed nets and membranes. Computer and Structure, 30 (3) : 685-695(1988).
[85] I.P. Pasqualino, S.F. Estefen, A nonlinear analysis of the buckle propagation problem in deepwater pipelines, International Journal of Solids and Structures ,38: 8481-8502(2001)
[86]陈联盟,董石麟,袁行飞,索穹顶结构施工成形理论分析和试验研究,土木工程学报,39(11):33-38(2006)
[87] L. Iannucci, Dynamic Delamination Modelling using interface elements, Computers and Structures 84: 1029-1048(2006)
[88] R.D. Wood,A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes,Computers and Structures,80: 2115–2120 (2002)
[1] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024(1977).
[2] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181: 375-389(1977).
[3] J.J. Monaghan, Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 1992, 30:543-74.
[4] G.A. Sod, A survey of several finite difference methods for systems of hyperbolic conservation laws, Journal of Computational Physics, 27:1-31(1978).
[5] P.W. Randles , L.D. Libersky, Smoothed Particle Hydrodynamics: Some recent improvements and applications, Computer methods in applied mechanics and engineering, 139:375-408(1996).
[6] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[7] J.J. Monaghan, Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[8] T.Belytschko &.Y.Krongauz, etc. Meshless methods: An overview and recent developments, Comput. Methods Appl. Mech. Engrg. 139: 3-47(1996)
[9] D.Kincaid &. W.Cheney, Numerical Analysis Mathematics of Scientific Computing, Published by Brooks/Cole, Thomson Learning : 2002
[10] P.Lancaster &. K.Salkauskas, Surfaces generated by moving least-squares methods, Math. Comput. 37:141-158(1981)
[11] W.K.Liu &. S.Li, Moving least-square reproducing kernel methods (I) Methodology and convergence. Comput. Methods Appl. Mech. Engrg. 143:113-154(1997)
[12] S.Li &. W.K.Liu, Moving least-square reproducing kernel methods (II) Fourier analysis. Comput. Methods Appl. Mech. Engrg. 139:159-193(1996)
[13] B.P.Rynne &. M.A.Youngson, Linear Functional Analysis. Springer-Verlag: 2000
[14] W.Cheney &. W.Light, Acouse in Approximation Theory. Published by Brooks/Cole, Thomson Learning: 2002
[15] S.N. Atluri, T.Zhu, A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics, Comput. Mech. 22:117-127 (1998)
[16] S.N. Atluri, H.G. Kim, J.Y.Cho, A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods, Comput. Mech. 24:348-372(1999)
[17] S.N. Atluri, T.Zhu, The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics, Comput. Mech. 25:169-179(2000)
[18] J.R. Xiao, Local Heaviside weighted MLPG meshless method for two-dimensional solidsusing compactly supported radial basis functions, Comput. Methods Appl. Mech. Engrg. 193:117-138(2004)
[19] T.Chen, I.S.Raju, A coupled finite element and meshless local Petrov-Galerkin method for two-dimensional potential problems, Comput. Methods Appl. Mech. Engrg., 192:4533-4550(2003)
[20] Y.T. Gu, G.R. Liu, A local point interpolation method for static and dynamic analysis of thin beams, Comput. Methods Appl. Mech. Engrg. 190:5515-5528(2001)
[21] T. Belytschko, Y. Krongauz, M. Fleming, etc. Smoothing and accelerated computations in the element free Galerkin method, Journal of Computational and Applied Mathematics, 74:111-126(1996)
[22] Y.T. Gu, G.R. Liu, A coupled element free Galerkin/boundary element method for stress analysis of two-dimensional solids, Comput. Methods Appl. Mech. Engrg., 190:4405-4419(2001)
[23] X.L. Chen, G.R. Liu, S.P.Lim, An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape, Composite Structures, 59:279-289(2003)
[24] Chongjiang Du, An element-free Galerkin method for simulation of stationary two-dimensional shallow water flows in rivers, Comput. Methods Appl. Mech. Engrg., 182:89-107(2000)
[25] L.Gavete, S. Falcon, A. Ruiz, An error indicator for the element free Galerkin method, Eur. J. Mech. A/Solids, 20:327-341(2001)
[26] P. Breitkopf, A. Rassineux, etc. Integration constraint in diffuse element method, Comput. Methods Appl. Mech. Engrg., 193:1203-1220(2004)
[27] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods, Int. J. Numer. Meth. Fluids 20:1081-1106(1995)
[28] W.K. Liu, Y. Chen, etc. Generalized multiple scale reproducing kernel particle methods, Comput. Methods Appl. Mech. Engrg., 139:91-157(1996)
[29] W.K. Liu, S. Jun, etc. Reproducing Kernel particle methods for structural dynamics, Int. J. Numer. Meth. Engng., 38:1655-1679(1995)
[30] J.S. Chen, C. Pan, etc. Reproducing Kernel particle methods for large deformation analysis of non-linear structures, Comput. Methods Appl. Mech. Engrg., 139:195-227(1996)
[31] W.K. Liu, Y. Chen, Wavelet and multiple scale reproducing kernel methods, Int. J. Numer. Methods Fluids, 21:901-931(1995)
[32] S. Qian, J. Weiss, Wavelet and the numerical solution of partial differential equations, J. Comput. Phys., 106:155-175(1993)
[33] C.A.M. Duarte, J.T. Oden, An hp adaptive method using clouds, Comput. Methods Appl. Methods Appl. Mech. Engrg., 139:237-262(1996)
[34] C.A.M. Duarte, J.T. Oden, hp clouds– an hp meshless method, Numer. Methods Partial Differential Equations, 12:673-705(1996)
[35] J.J. Monaghan, A. Kocharyan, SPH simulation of multi-phase flow, Computer Physics Communications 87:225-235(1995)
[36] J.P. Gray, J.J. Monaghan, etc., SPH elastic dynamics, Comput. Methods Appl. Mech. Engrg., 190:6641-6662(2001)
[37] V. Roubtsova, R. Kahawita, The SPH technique applied to free surface flows, Computers & Fluids xxx:xxx-xxx(2006)4
[38] Miguel R.P., J. Bonet, A corrected smooth particle hydrodynamics formulation of the shallow-water equations, Computers and Structures 83:1396-1410(2005)
[39] P.W. Cleary, J. Ha, etc., 3D SPH flow predictions and validation for high pressure die casting of automotive components, Applied Mathematical Modelling xxx:xxx-xxx(2006)
[40] T. De Vuyst, R. Vignjevic, etc, Coupling between meshless and finite element methods, International Journal of Impact Engineering 31:1054-1064(2005)
[41]张恭庆,泛函分析讲义,北京大学出版社,北京:1986
[42] A.H.柯尔莫戈洛夫、C.B.佛明著,段虞荣、郑洪深、郭思旭译,函数论与泛函分析初步,高等教育出版社,北京:2006
[1] L. Brookshaw, A Method of Calculating Radiative Heat Diffusion in Particle Simulations, Proc. ASA, 6(2):207-210 (1985)
[2] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024(1977).
[3] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181: 375-389(1977).
[4] G.A. Sod, A survey of several finite difference methods for systems of hyperbolic conservation laws, Journal of Computational Physics, 27:1-31 (1978) .
[5] J. Campbell, R. Vignjevic, A contact algorithm for smoothed particle hydrodynamics, Comput. Methods Appl. Mech. Engrg. 184:49-65 (2000)
[6] J.J. Monaghan, Simulating free surface flows with SPH, J. Comput. Phys. 110:399-406 (1994).
[7] J.J. Monaghan, A. Kos, Solitary Waves on a Cretan Beach, Journal of Waterway, Port, Coastal, and Ocean Engineering, 125(3): 145-154 (1999)
[8] M.B. Liu, G.R. Liu, etc. Investigations into water mitigations using a meshless particle method, Shock Waves 12(3): 181-195 (2002).
[9] M.B. Liu, G.R. Liu, etc. Computer simulation of the high explosive explosion using smoothed particle hydrodynamics methodology, Comput. Fluids 32(3): 305-322 (2003).
[10] P.W. Cleary, Modeling confined multi-material heat and mass flows using SPH, Appl. Math. Modell. 22:981-993 (1998).
[11] J.J. Monaghan, Smoothed particle hydrodynamics, Annual Review of Astronomical and Astrophysics, 30:543-74(1992).
[12] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[13] Flebbe, S. Münzel, etc. Smoothed Particle Hydrodynamics: Physical Viscosity and the Simulation, The Astrophysical Journal, 431:754-760 (1994).
[14] S.J. Watkins, A.S. Bhattal, etc. A new prescription for viscosity in Smoothed Particle Hydrodynamics, Astron. Astrophys. Suppl. Ser. 119:177-187(1996)
[15] M.B. Liu, G.R. Liu, etc. Constructing smoothing functions in smoothed particle hydrodynamics with applications, Journal of Computational and Applied Mathematics 155:263-284(2003).
[16] T. Belytschko, Y. Krongauz, J. Dolbow, etc. On the completeness of meshfree particle methods, International Journal for Numerical Methods in Engineering, 43(5): 785-819
[1] R.柯朗&. D.希尔伯特著,钱敏、郭敦仁译,数学物理方法(卷一),科学出版社,北京:1981
[2]鹫津九一郎著,老亮、郝松林译,弹性和塑性力学中的变分法,科学出版社,北京:1984
[3]武际可,力学史,重庆出版社,重庆:2000
[4] L.Lapidus, G.F. Pinder著,孙讷正等译,科学和工程中的偏微分方程数值解法,煤炭出版社,北京:1985
[5]张雄,陆明万等,任意拉格朗日-欧拉描述法研究进展,计算力学学报,1997(14),1
[6] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[7] J.N. Reddy, An Introduction to the Finite Element Method (Third Edition), McGraw-Hill Companies, Inc. 2006.
[8] S.P. Timoshenko &. J.N. Goodier, Theory of Elasticity (Third Edition), McGraw-Hill Companies, Inc. 1970.
[1] Balsara D.S., von Neumann stability analysis of smoothed particle hydrodynamics-suggestions for optimal algorithms, J. Comp. Phys., 121:357-372(1995).
[2] Swegle J.W., Hicks D.L. and Attaway S.W., Smoothed particle hydrodynamics stability analysis, J. Comp. Phys., 116:123-134(1995).
[3] Dyka C.T., Addressing tension instability in SPH methods, NRL Report NRL/MR/6384(1994).
[4] Dyka C.T. and Ingel R.P., An approach for tension instability in smoothed particle hydrodynamics, Comp. Struct., 57:573-580(1995).
[5] Randles P.W., Libersky L.D., Normalized SPH with stress points, International Journal for Numerical Methods in Engineering, 48: 1445-1462(2000).
[6] Swegle J.W., Attaway S.W., Heinstein M.W., Mello F.J. and Hicks D.L., An analysis of smoothed particle hydrodynamics, Sandia Report, SAND94-2513, Sandia National Lab., Alb. NM 87185 (1994).
[7] Wen Y., Hicks D.L. and Swegle J.W., Stabilizing SPH with conservative smoothing, Sandia Report, SAND94-1932 (1994).
[8] Guenther C., Hicks D.L. and Swegle J.W., Conservative smoothing verses artificial viscosity, Sandia Report, SAND94-1853, Sandia National Lab., Alb. NM 87185 (1994).
[9] Chen J.K. Beraun J.E., Carney T.C., A corrective smoothed particle method for boundary value problems in heat conduction, Computer Methods in Applied Mechanics and Engineering, 46: 231-252(1999).
[10] Chen J.K. Beraun J.E., Jih C.J., An improvement for tensile instability in smoothed particle hydrodynamics, Computational Mechanics, 23: 279-287(1999).
[11] Chen J.K. Beraun J.E., Jih C.J., Completeness of corrective smoothed particle method for linear elastodynamics, Computational Mechanics, 24: 273-285(1999).
[12] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[13] Monaghan J.J., Kos A. and Issa N., Fluid motion generated by impact, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 129, No. 6: 250-259(2003).
[14] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[15] Gotoh H., Sakai T., Lagrangian simulation of breaking waves using particle method, Coast. Engng. J., 41(3/4): 303-326(1999).
[16] Randles P.W., Libersky L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput. Mehtods Appl. Mech. Engrg., 139: 375-408(1996).
[17] Edmond Y.M. Lo, Shao S.D., Simulation of near-shore solitary wave mechanics by anincompressible SPH method, Applied Ocean Research, 24: 275-286(2002).
[18]吴望一,流体力学,北京大学出版社.北京:1982
[19] F.M. White著,魏中磊、甄思淼译,粘性流体动力学(Viscous Fluid Flow),机械工业出版社,北京:1982
[20] G.K.Batchelor著,沈青、贾复译,流体动力学引论(An Introduction to Fluid Dynamics ),科学出版社,北京:1997
[21] Liu G.R., Liu M.B., Smoothed particle hydrodynamics: a meshfree particle method, World Scientific Pub. Co. Inc., 01 Dec, 2003.
[22] Monaghan J.J., Kos A., Solitary waves on a Cretan beach, Journal of Waterway, Port, Coastal and Ocean Engineering, 125(3): 145-154(1999).
[23] Colagrossi A., Landrini M., Numerical simulation of interfacial flows by smoothed particle hydrodynamics, J. Comput. Phys., 191: 448-475(2003).
[24] Monaghan J.J., Why particle methods work, SIAM Journal on Scientific and Statistical Computing, 3: 422-433(1982).
[25] Monaghan J.J., Particle methods for hydrodynamics, Computer Physics Report, 3: 71-124(1985).
[26] Monaghan J.J., An introduction to SPH, Computer Physics Communications, 48: 89-96(1988).
[27] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[28] Chen J.K. Beraun J.E., A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems, Computer Methods in Applied Mechanics and Engineering, 190: 225-239(2000).
[29] Belytschko T., Krongauz Y., Dolbow J., Gerlach C., On the Completeness of Meshfree Particle Methods, International Journal for Numerical Methods in Engineering 43: 785–819(1998).
[30]黄润生,混沌及其应用.武汉大学出版社,武汉:2000
[31]是勋刚,湍流,天津大学出版社,天津:1994
[32] H.Schlichting著,徐燕候、徐立功译,边界层理论(Boundary-Layer Theory),科学出版社,北京:1988
[33]苏铭德,黄素逸,计算流体力学基础,清华大学出版社,北京:1997
[34] von Neumann J., Richtmyer R.D., A method for the numerical calculation of hydrodynamic shocks, Journal of Applied Physics, 21:232-247(1950).
[35] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[36] Balsara D.S., Brandt A., Multilevel methods for fast solution of N-body and hybrid systems, International Series of Numerical Mathematics, 98: 131-142(1991).
[37] Monaghan J.J., Heat conduction with discontinuous conductivity, Applied MathematicsReports and Preprints, Monash University 95/18(1995).
[38] Shao S.D., Ji C.M., Graham D.I., Reeve D.E., James P.W., Chadwick A.J., Simulation of wave overtopping by an incompressible SPH model, Coastal Engineering, 53: 723–735(2006).
[39] Batchelor G.K., Introduction to fluid dynamics, Cambridge Univ. Press, Cambridge, U.K.(1974).
[40] Morris J.P., Fox P.J., Zhu Y., Modeling low Reynolds number incompressible flows using SPH, Journal of Computational Physics, 136: 214-226(1997).
[41] Gesteira M.G., Dalrymple R.A., Using a three-dimensional smoothed particle hydrodynamics method for wave impact on a tall structure, J. Waterway, Port, Coastal and Ocean Engrg., Vol. 130, No. 2: 63-69(2004).
[42]朱明善,刘颖,林兆庄等,工程热力学,清华大学出版社,北京:1995
[1] L.B. Lucy, A numerical approach to the testing of the fission hypothesis, Astron. J. 82: 1013-1024 (1977).
[2] R.A. Gingold and J.J. Monaghan, Smoothed Particle Hydrodynamics: Theory and application to non-spherical stars, Mon. R. Astr. Soc. 181:375-389 (1977).
[3] Benz W., Application of smoothed particle hydrodynamics(SPH) to astrophysical problems, Computer Physics Communications, 48: 97-105(1988).
[4] Monaghan J.J., Lattanzio J.C., A simulation of the collapse and fragmentation of cooling molecular clouds, Astrophysical Journal, 375: 177-189(1991).
[5] Morris J.P., Analysis of smoothed particle hydrodynamics with applications, Ph.D. Thesis, Monash University(1996).
[6] Monaghan J.J., Kocharyan A., SPH simulation of multi-phase flow, Computer Physics Communication, 87: 225-235(1995).
[7] Monaghan J.J., Simulating free surface flows with SPH, J. Comput. Phys., 110(2):399-406(1994).
[8]毛益明,汤文辉,自由表面流动问题的SPH方法数值模拟,解放军理工大学学报(自然科学版),2(5):92-94(2001).
[9]李梅娥,周进雄,不可压流体自由表面流动的SPH数值模拟,机械工程学报,40(3):5-9(2004).
[10] 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, 23: 881-904(1999).
[11] Monaghan J.J., Gingold R.A., Shock simulation by the particle method sph, J. Comp. Phys., 52: 374-389(1983).
[12]徐立,孙锦山,一维激波管问题的SPH模拟,计算物理,20(2):153-156(2003).
[13] Benz W., Asphaug E., Simulations of brittle solids using smoothed particle hydrodynamics, Computer Physics Communications, 87: 253-265(1995).
[14] Bonet J., Kulasegaram S., Correction and stabilization of smoothed particle hydrodynamics method with applications in metal forming simulation, International Journal for Numerical Methods in Engineering, 47: 1189-1214(2000).
[15] Libersky L.D., Petschek A.G., Carney T.C., Hipp J.R., Allahdadi F.A., High strain Lagrangian hydrodynamics - a three-dimensional SPH code for dynamic material response, Journal of Computational Physics, 109: 67-75(1993).
[16] Johnson G.R., Stryk R.A., Beissel S.R., SPH for high velocity impact computations, Computer Methods in Applied Mechanics and Engineering, 139: 347-373(1996).
[17]贝新源,岳宗五,三维SPH程序及其在斜高速碰撞问题的应用,计算物理,14(2): 155-166(1997).
[18]毛益明,武文远,陈广林,龚艳春,高速碰撞问题的SPH方法模拟,解放军理工大学学报(自然科学版),4(5):84-87(2003).
[19]闫晓军,张玉珠,聂景旭,空间碎片超高速碰撞数值模拟的SPH方法,北京航空航天大学学报,31(3):351-354(2005).
[20] Swegle J.W., Attaway S.W., On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations, Computational Mechanics, 17: 151-168(1995).
[21]张锁春,光滑质点流体动力学(SPH)方法(综述),计算物理,13(4): 385-397(1996)
[22] G.R. Liu &. M.B. Liu, Smoothed Particle Hydrodynamics: A meshfree particle method, World Scientific, 2003.
[23] L. Brookshaw, A Method of Calculating Radiative Heat Diffusion in Particle Simulations, Proc. ASA 6(2) (1985)
[24] S.J. Watkins, A.S. Bhattal, etc. A new prescription for viscosity in Smoothed Particle Hydrodynamics, Astron. Astrophys. Suppl. Ser. 119, 177-187(1996)
[25] S.Timoshenko, J.N.Goodier著,徐芝纶译,弹性理论(Theory of Elasticity),高等教育出版社,北京:1990
[26]张志宏,董石麟,空间结构分析中动力松弛法若干问题的探讨,建筑结构学报,23(6):79-84(2002).
[27]毛国栋,孙炳楠,唐志山,控制网格变形的动力松弛法膜结构找形分析,浙江大学学报(工学版),38(5),2004
[28] Barnes MR. Form finding and analysis of pre-stressed nets and membranes. Computer and Structure, 1988, 30 (3) : 685-695.
[29] I.P. Pasqualino, S.F. Estefen, A nonlinear analysis of the buckle propagation problem in deepwater pipelines, International Journal of Solids and Structures ,38: 8481-8502(2001)
[30]陈联盟,董石麟,袁行飞,索穹顶结构施工成形理论分析和试验研究,土木工程学报,39(11):33-38(2006)
[31] L. Iannucci, Dynamic Delamination Modelling using interface elements, Computers and Structures 84: 1029-1048(2006)
[32] R.D. Wood,A simple technique for controlling element distortion in dynamic relaxation form-finding of tension membranes,Computers and Structures,80: 2115–2120 (2002)
[33]倪振华,振动力学,西安交通大学出版社,西安:1989
[34]郑兆昌,机械振动,机械工业出版社,北京:1978