弹性、弹塑性材料显式模拟计算中的准静态加载速度研究
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摘要
动力学显式算法采用时间积分原理,其较静力学隐式算法在强非线性问题中的适用性更广.为将此方法应用到岩土等非线性材料的计算中,考虑到显式算法中动能的影响会导致结果波动,分析动力学显式算法在模拟计算中的准静态加载速度的选取十分必要,如何在缩短模拟消耗时间与结果准确性之间寻求平衡是论文研究重点.研究中提出以加载-位移曲线的波动比来评价准静态计算效果,首先开展弹性材料的平面应变模拟试验以分析弹模、密度、泊松比、围压4个参数对准静态加载速度取值的影响,结果表明:弹模、泊松比、围压的增大会提高准静态加载速度;密度的增大则会减小准静态加载速度.通过对各影响因素与准静态加载速度的相关性分析给出了准静态加载速度取值的经验公式.最后,选取能够反映砂土复杂力学特性的弹塑性本构模型,开展其平面应变模拟试验,对比分析准静态加载速度经验公式在弹性材料与弹塑性材料中的适用性差异,并提出应用建议公式.
The dynamic explicit algorithm is based on the principle of time integration.It is more applicable to nonlinear problems when compared with the static implicit algorithm.To use this method for nonlinear materials including rock and soil,it is extremely necessary to analyze the selection of quasi-static loading rate in the dynamic explicit algorithm during simulation,because the influence of kinetic energy in the explicit algorithm can result in fluctuation of results.To search a balance between the efficiency and accuracy of simulation is emphasized in this study.The fluctuation ratio of the load-displacement curve is proposed in this research to evaluate the effect of quasi-static calculation.First of all,simulations of the plane strain tests on elastic materials are conducted to analyze the effects of elastic modulus,density,Poisson's ratio and confining pressure on the quasi-static loading rate.It is found that the quasi-static loading rate increases with the increase of elastic modulus,Poisson's ratio or confining pressure,but the decrease of density.The correlation analysis between each influence factor and the quasi-static loading rate gives an empirical formula for the latter.At last,the elastic-plastic constitutive model capable of describing the complicated mechanical properties of sandy soil is selected for the simulation of the plane strain test.The applicability of the empirical formula for quasi-static loading rate in elastic materials is compared with that in elastic-plastic materials,and suggestions for formula application are made.
The dynamic explicit algorithm is based on the principle of time integration.It is more applicable to nonlinear problems when compared with the static implicit algorithm.To use this method for nonlinear materials including rock and soil,it is extremely necessary to analyze the selection of quasi-static loading rate in the dynamic explicit algorithm during simulation,because the influence of kinetic energy in the explicit algorithm can result in fluctuation of results.To search a balance between the efficiency and accuracy of simulation is emphasized in this study.The fluctuation ratio of the load-displacement curve is proposed in this research to evaluate the effect of quasi-static calculation.First of all,simulations of the plane strain tests on elastic materials are conducted to analyze the effects of elastic modulus,density,Poisson's ratio and confining pressure on the quasi-static loading rate.It is found that the quasi-static loading rate increases with the increase of elastic modulus,Poisson's ratio or confining pressure,but the decrease of density.The correlation analysis between each influence factor and the quasi-static loading rate gives an empirical formula for the latter.At last,the elastic-plastic constitutive model capable of describing the complicated mechanical properties of sandy soil is selected for the simulation of the plane strain test.The applicability of the empirical formula for quasi-static loading rate in elastic materials is compared with that in elastic-plastic materials,and suggestions for formula application are made.
引文
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[3]Chen C,Ricles J M.Stability analysis of direct integration algorithms applied to nonlinear structural dynamics[J].Journal of Engineering Mechanics,2008,134(134):485-495.
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[9]张伟伟,金先龙.统一格式的显式与隐式任意混合异步算法[J].力学学报,2014,46(3):436-446.(Zhang W W,Jin X L.Unified format of explicit and implicit hybrid asynchronous algorithm[J].Theoretical and Applied Mechanics,2014,46(3):436-446.(in Chinese))
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[18]Shi Y C,Li Z X,Hao H.Mesh size effect in numerical simulation of blast wave propagation and interaction with structures[J].Transactions of Tianjin University,2008,14(6):396-402.
[19]Shayanfar M A,Kheyroddin A,Mirza M S.Element size effects in nonlinear analysis of reinforced concrete members[J].Computers&Structures,1997,62(2):339-352.
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[22]Yao Y P,Sun D A,Matsuoka H.A unified constitutive model for both clay and sand with hardening parameter independent on stress path[J].Computers and Geotechnics,2008,35(2):210-222.
[23]罗汀,姚仰平,侯伟.土的本构关系[M].北京:人民交通出版社,2008.(Luo T,Yao Y P,Hou W.Constitutive Law of Soil[M].Beijing:China Communications Press,2008.(in Chinese))
[24]姚仰平,余亚妮.基于统一硬化参数的砂土临界状态本构模型[J].岩土工程学报,2011,33(12):1827-1832.(Yao Y P,Yu Y N.Extended critical state constitutive model for sand based on unified hardening parameter[J].Chinses Journal of Geomechnical Engineering,2011,33(12):1827-1832.(in Chinese))
[2]Chang S Y.An explicit method with improved stability property[J].International Journal for Numerical Methods in Engineering,2009,77(8):1100-1120.
[3]Chen C,Ricles J M.Stability analysis of direct integration algorithms applied to nonlinear structural dynamics[J].Journal of Engineering Mechanics,2008,134(134):485-495.
[4]Chang S Y.Discussion of paper‘Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation’by Chinmoy Kolay and James M Ricles.Earthquake engineering and structural dynamics2014,43[J].Earthquake Engineering&Structural Dynamics,2015,44(8):1325-1328.
[5]Hughes T J R.The finite element method:Linear static and dynamic finite element analysis[J].Religion,2003,6(2):222.
[6]潘科琪.显式和隐式力学计算方法对比研究[J].现代计算机(专业版),2015,20:20-23.(Pan K Q.Comparative research on the explicit and implicit mechanical calculation method[J].Modern Computer,2015,20:20-23.(in Chinese))
[7]张雄,王天舒,刘岩.计算动力学[M].清华大学出版社,2015.(Zang X,Wang T S,Liu Y.Computational Dynamics[M].Tsinghua University Press.2015.(in Chinese))
[8]Chopra A.Dynamics of Structures:Theory and Applications to Earthquake Engineering/2nded[M].清华大学出版社,2005.
[9]张伟伟,金先龙.统一格式的显式与隐式任意混合异步算法[J].力学学报,2014,46(3):436-446.(Zhang W W,Jin X L.Unified format of explicit and implicit hybrid asynchronous algorithm[J].Theoretical and Applied Mechanics,2014,46(3):436-446.(in Chinese))
[10]吕和祥,于洪洁,裘春航.精细积分的非线性动力学积分方程及其解法[J].固体力学学报,2001,22(3):303-308.(Lv H X,Yu H J,Qiu C H.An integral equation of non-linear dynamics and its solution method[J].Chinese Journal of Solid Mechanics,2001,22(3):303-308.(in Chinese))
[11]黄志辉,陈盛钊,柏友运.显式准静态几种加载方法的讨论[J].武汉理工大学学报,2011,6:122-125.(Huang Z H,Chen S Z,Bai Y Y.Discussion of explicit quasi-static loading methods[J].Journal of Wuhan University of Technology,2011,6:122-125.(in Chinese))
[12]王青春,范子杰.利用Ls-Dyna计算结构准静态压溃的改进方法[J].力学与实践,2003,25(3):20-23.(Wang Q C,Fan Z J.Improvement in analysis of quasi-static collapse with Ls-Dyna[J].Mechanics in Engineering,2003,25(3):20-23.(in Chinese))
[13]陆勇,周国庆,顾欢达.高低压下不同力学特性的砂土统一模型[J].岩土力学,2018,2:614-620.(Lu Y,Zhou G Q,Gu H D.Unified model of sand with different mechanical characteristics under high and low pressures[J].Rock and Soil Mechanics,2018,2:614-620.(in Chinese))
[14]陆勇.高、低压下砂土剪切带及砂土-结构界面层力学行为演化研究[D].徐州:中国矿业大学,2014.(Lu Y.Research on the Mechanical Behavior Evolution of Sand Shear Band and Sand-structure Interface Layer under High and Low Pressure[D].Xuzhou:China University of Minging&Technology,2014.(in Chinese))
[15]周健,池永.土的工程力学性质的颗粒流模拟[J].固体力学学报,2004,25(4):377-382.(Zhou J,Chi Y.Simulating soil properties by particle flow code[J].Chinese Journal of Solid Mechanics,2004,25(4):377-382.(in Chinese))
[16]尚晓江,苏建宇,王化锋.ANSYS/LS-DYNA动力分析方法与工程实例[M].中国水利水电出版社,2008.(Shang X H,Su J Y,Wang H F.ANSYS/LS-DYNA Dynamic Analysis Method and Engineering Example[M].China Water&Power Press,2008.(in Chinese))
[17]王海兵,张海波,田宙,等.岩石动力学计算中的网格效应及机理研究[J].兵工学报,2016,37(10):1828-1836.(Wang H B,Zhang H B,Tian Z,et al.Mesh size effect and its mechanism research in numerical calculation of rock dynamics[J].Acta Armamentarii,2016,37(10):1828-1836.(in Chinese))
[18]Shi Y C,Li Z X,Hao H.Mesh size effect in numerical simulation of blast wave propagation and interaction with structures[J].Transactions of Tianjin University,2008,14(6):396-402.
[19]Shayanfar M A,Kheyroddin A,Mirza M S.Element size effects in nonlinear analysis of reinforced concrete members[J].Computers&Structures,1997,62(2):339-352.
[20]Schofield A,Wroth P.Critical State Soil Mechanics[M].London:McGraw-Hill,1968.
[21]陆勇,周国庆,赖泽金.砂土剪切特性的荷载与粒径效应研究[J].中国矿业大学学报,2014,43(02):195-202.(Lu Y,Zhou G Q,Lai Z J.Effects of normal pressure and particle size on shear properties of sand material[J].Journal of China University of Minging&Technology,2014,43(02):195-202.(in Chinese))
[22]Yao Y P,Sun D A,Matsuoka H.A unified constitutive model for both clay and sand with hardening parameter independent on stress path[J].Computers and Geotechnics,2008,35(2):210-222.
[23]罗汀,姚仰平,侯伟.土的本构关系[M].北京:人民交通出版社,2008.(Luo T,Yao Y P,Hou W.Constitutive Law of Soil[M].Beijing:China Communications Press,2008.(in Chinese))
[24]姚仰平,余亚妮.基于统一硬化参数的砂土临界状态本构模型[J].岩土工程学报,2011,33(12):1827-1832.(Yao Y P,Yu Y N.Extended critical state constitutive model for sand based on unified hardening parameter[J].Chinses Journal of Geomechnical Engineering,2011,33(12):1827-1832.(in Chinese))