采用有限质点法的薄壳动力非线性行为分析
|
摘要
基于有限质点法原理和K-L经典薄壳理论,构造具有大位移大转动分析能力的薄壳离散质点模型,推导表述基本控制方程与公式.对于质点位移以及壳元的变形和内力,均按照面内拉压和面外弯扭两部分进行拆分与叠加,并通过物理方式的虚拟运动依次分离出与薄膜刚度和弯曲刚度相关的纯变形,进而在局部变形坐标系下求解面外变形相对应的质点内力和内力矩,建立质点切平面外转角的变步长显式时间积分式,并对质点质量、时间步长、阻尼等关键参数取值给出建议.在此基础上引入材料非线性应力修正算法,实现对薄壳弹塑性大应变动力非线性行为的模拟,并通过典型算例验证方法及程序的有效性和正确性.
A discrete particle model of thin shells with large displacement and large rotation analysis capability was constructed based on the principle of finite particle method and K-L classical thin shell theory, and the fundamental governing equations and formulas were derived. For the particle displacement and the deformation and internal force of the shell element, the two parts corresponding to the in-plane tension and the out-of-plane bending and twisting were split and superimposed, respectively. The pure deformation related with the membrane rigidity and bending rigidity was sequentially separated by using a physical modeling procedure involving fictitious motions. Then in the local deformation coordinate system, the internal forces and moments were solved, and the explicit time integral formula with variable step sizes for calculation of the out-of-plane rotation was established. The determinations of several key parameters were also given, including particle mass, time step and damping. Moreover, an stress correction algorithm for solving material nonlinearity was introduced to simulate the dynamic nonlinear behavior of a thin shell with large elastic-plastic strain. The efficiency and validity of the presented method and the selfdeveloped program are verified by several benchmark examples of nonlinear shell dynamics.
A discrete particle model of thin shells with large displacement and large rotation analysis capability was constructed based on the principle of finite particle method and K-L classical thin shell theory, and the fundamental governing equations and formulas were derived. For the particle displacement and the deformation and internal force of the shell element, the two parts corresponding to the in-plane tension and the out-of-plane bending and twisting were split and superimposed, respectively. The pure deformation related with the membrane rigidity and bending rigidity was sequentially separated by using a physical modeling procedure involving fictitious motions. Then in the local deformation coordinate system, the internal forces and moments were solved, and the explicit time integral formula with variable step sizes for calculation of the out-of-plane rotation was established. The determinations of several key parameters were also given, including particle mass, time step and damping. Moreover, an stress correction algorithm for solving material nonlinearity was introduced to simulate the dynamic nonlinear behavior of a thin shell with large elastic-plastic strain. The efficiency and validity of the presented method and the selfdeveloped program are verified by several benchmark examples of nonlinear shell dynamics.
引文
[1]TIMOSHENKO S,WOINOWSKY-KRIEGER S.Theory of Plates and Shells[M].2nd ed.Singapore:Mcgraw-Hill,1959:107-145.
[2]DOYLE J F.Nonlinear Analysis of Thin-Walled Structures:Statics,Dynamics,and Stability[M].Berlin:Springer,2001.
[3]RAMM E,WALL W A.Shells in advanced computational environment[C]//Proceedings of the5th World Congress on Computational Mechanics.Barcelona:IACM,2002:1-22.
[4]BELYTSCHKO T,LIU W K,MORAN B,et al.Nonlinear Finite Elements for Continua and Structures[M].2nd ed.New York:John Wiley&Son,2014.
[5]BATOZ J L,BATHE K J,HO L W.A Study of threenode triangular bending elements[J].International Journal for Numerical Methods in Engineering,1980,15(12):1771-1812.
[6]BELYTSCHKO T,WONG B L,CHIANG H Y.Advances in one-point quadrature shell elements[J].Computer Methods in Applied Mechanics and Engineering,1992,96(1):93-107.
[7]O?ATE E,CENDOYA P,MIQUEL J.Non-linear explicit dynamic analysis of shells using the BSTrotation-free triangle[J].Engineering Computations,2002,19(6):662-706.
[8]LIU C,TIAN Q,YAN D,et al.Dynamic analysis of membrane systems undergoing overall motions,large deformations and wrinkles via thin shell elements of ANCF[J].Computer Methods in Applied Mechanics and Engineering,2013,258(258):81-95.
[9]HOSSEINI S,REMMERS J J C,VERHOOSEL C V,et al.An isogeometric solid-like shell element for nonlinear analysis[J].International Journal for Numerical Methods in Engineering,2013,95(3):238-256.
[10]DVORKIN E N,BATHE K J.A continuum mechanics based four-node shell element for general non-linear analysis[J].Engineering Computations,1984,1(1):77-88.
[11]HUGHES T J R,LIU W K.Nonlinear finite element analysis of shells:Part I.three-dimensional shells[J].Computer Methods in Applied Mechanics and Engineering,1981,26(3):331-362.
[12]LUIZ B M,KLAUS JüEN B.Higher-order MITCgeneral shell elements[J].International Journal for Numerical Methods in Engineering,2010,36(21):3729-3754.
[13]喻莹.基于有限质点法的空间钢结构连续倒塌破坏研究[D].杭州:浙江大学,2010.YU Ying.Progressive collapse of space steel structures based on the finite particle method[D].Hangzhou:Zhejiang University,2010.
[14]罗尧治,郑延丰,杨超,等.结构复杂行为分析的有限质点法研究综述[J].工程力学,2014,31(8):1-7,23.LUO Yao-zhi,ZHENG Yan-feng,YANG Chao,et al.Review of the finite particle method for complex behaviors of structures[J].Engineering Mechanics,2014,31(8):1-7,23.
[15]郑延丰,罗尧治.基于有限质点法的多尺度精细化分析[J].工程力学,2016,33(9):21-29.ZHENG Yan-feng,LUO Yao-zhi.Multi-scale fine analysis based on the finite particle method[J].Engineering Mechanics,2016,33(9):21-29.
[16]TING E C,WANG C Y,WU T Y,et al.Motion analysis and vector form intrinsic finite element[R].Taiwan:V-5 Research Group,National Central University,2006.
[17]赵阳,王震,胡可.考虑Cowper-Symonds黏塑性材料本构的向量式有限元三角形薄壳单元研究[J].建筑结构学报,2014,35(4):71-77.ZHAO Yang,WANG Zhen,HU Ke.Study on triangular thin-shell element of vector form intrinsic finite element considering Cowper-Symonds viscoplastic constitutive model[J].Journal of Building Structures,2014,35(4):71-77.
[18]王震,赵阳,杨学林.薄壳结构碰撞、断裂和穿透行为的向量式有限元分析[J].建筑结构学报,2016(6):53-59.WANG Zhen,ZHAO Yang,YANG Xue-lin.Collision-contact,crack-fracture and penetration behavior analysis of thin-shell structures based on vector form intrinsic finite element[J].Journal of Building Structures,2016(6):53-59.
[19]YANG C,SHEN Y,LUO Y.An efficient numerical shape analysis for light weight membrane structures[J].Journal of Zhejiang University:SCIENCE A,2014,15(4):255-271.
[20]BAZELEY G P,CHEUNG Y K,IRONS B M,et al.Triangular elements in plate bending,conforming and non-conforming solutions[C]//Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics.Dayton:Wright-Patterson Air Force Base,1965:547-576.
[21]HALL J F.Problems encountered from the use(or misuse)of Rayleigh damping[J].Earthquake Engineering and Structural Dynamics,2006,35(5):525-545.
[22]SIMO J C,HUGHES T J R.Computational Inelasticity[M].New York:Springer-Verlag,1998:120-138.
[23]BATHE K,RAMM E,WILSON E L.Finite element formulations for large deformation dynamic analysis[J].International Journal for Numerical Methods in Engineering,1975,9(2):353-386.
[24]O?ATE E,FLORES F G.Advances in the formulation of the rotation-free basic shell triangle[J].Computer Methods in Applied Mechanics and Engineering,2005,194(21-24):2406-2443.
[25]ARGYRIS J,PAPADRAKAKIS M,MOUROUTIS ZS.Nonlinear dynamic analysis of shells with the triangular element TRIC[J].Computer Methods in Applied Mechanics and Engineering,2003,192(26/27):3005-3038.
[26]WITMER E A,CLARK E N,BALMER H A.Experimental and theoretical studies of explosiveinduced large dynamic and permanent deformations of simple structures[J].Experimental Mechanics,1967,7(2):56-66.
[27]STOLARSKI H,BELYTSCHKO T,CARPENTER N,et al.A simple triangular curved shell element[J].Engineering computations,1984,1(3):210-218.
[28]MACNAY G H.Numerical modelling of tube crush with experimental comparison[C]//Proceedings of the 7th International Conference on Vehicle Structural Mechanics.Warrendale:American Society of Automotive Engineers,1988:123-134.
[29]KIM H C,DONG K S,LEE J J,et al.Crashworthiness of aluminum/CFRP square hollow section beam under axial impact loading for crash box application[J].Composite Structures,2014,112(5):1-10.
[2]DOYLE J F.Nonlinear Analysis of Thin-Walled Structures:Statics,Dynamics,and Stability[M].Berlin:Springer,2001.
[3]RAMM E,WALL W A.Shells in advanced computational environment[C]//Proceedings of the5th World Congress on Computational Mechanics.Barcelona:IACM,2002:1-22.
[4]BELYTSCHKO T,LIU W K,MORAN B,et al.Nonlinear Finite Elements for Continua and Structures[M].2nd ed.New York:John Wiley&Son,2014.
[5]BATOZ J L,BATHE K J,HO L W.A Study of threenode triangular bending elements[J].International Journal for Numerical Methods in Engineering,1980,15(12):1771-1812.
[6]BELYTSCHKO T,WONG B L,CHIANG H Y.Advances in one-point quadrature shell elements[J].Computer Methods in Applied Mechanics and Engineering,1992,96(1):93-107.
[7]O?ATE E,CENDOYA P,MIQUEL J.Non-linear explicit dynamic analysis of shells using the BSTrotation-free triangle[J].Engineering Computations,2002,19(6):662-706.
[8]LIU C,TIAN Q,YAN D,et al.Dynamic analysis of membrane systems undergoing overall motions,large deformations and wrinkles via thin shell elements of ANCF[J].Computer Methods in Applied Mechanics and Engineering,2013,258(258):81-95.
[9]HOSSEINI S,REMMERS J J C,VERHOOSEL C V,et al.An isogeometric solid-like shell element for nonlinear analysis[J].International Journal for Numerical Methods in Engineering,2013,95(3):238-256.
[10]DVORKIN E N,BATHE K J.A continuum mechanics based four-node shell element for general non-linear analysis[J].Engineering Computations,1984,1(1):77-88.
[11]HUGHES T J R,LIU W K.Nonlinear finite element analysis of shells:Part I.three-dimensional shells[J].Computer Methods in Applied Mechanics and Engineering,1981,26(3):331-362.
[12]LUIZ B M,KLAUS JüEN B.Higher-order MITCgeneral shell elements[J].International Journal for Numerical Methods in Engineering,2010,36(21):3729-3754.
[13]喻莹.基于有限质点法的空间钢结构连续倒塌破坏研究[D].杭州:浙江大学,2010.YU Ying.Progressive collapse of space steel structures based on the finite particle method[D].Hangzhou:Zhejiang University,2010.
[14]罗尧治,郑延丰,杨超,等.结构复杂行为分析的有限质点法研究综述[J].工程力学,2014,31(8):1-7,23.LUO Yao-zhi,ZHENG Yan-feng,YANG Chao,et al.Review of the finite particle method for complex behaviors of structures[J].Engineering Mechanics,2014,31(8):1-7,23.
[15]郑延丰,罗尧治.基于有限质点法的多尺度精细化分析[J].工程力学,2016,33(9):21-29.ZHENG Yan-feng,LUO Yao-zhi.Multi-scale fine analysis based on the finite particle method[J].Engineering Mechanics,2016,33(9):21-29.
[16]TING E C,WANG C Y,WU T Y,et al.Motion analysis and vector form intrinsic finite element[R].Taiwan:V-5 Research Group,National Central University,2006.
[17]赵阳,王震,胡可.考虑Cowper-Symonds黏塑性材料本构的向量式有限元三角形薄壳单元研究[J].建筑结构学报,2014,35(4):71-77.ZHAO Yang,WANG Zhen,HU Ke.Study on triangular thin-shell element of vector form intrinsic finite element considering Cowper-Symonds viscoplastic constitutive model[J].Journal of Building Structures,2014,35(4):71-77.
[18]王震,赵阳,杨学林.薄壳结构碰撞、断裂和穿透行为的向量式有限元分析[J].建筑结构学报,2016(6):53-59.WANG Zhen,ZHAO Yang,YANG Xue-lin.Collision-contact,crack-fracture and penetration behavior analysis of thin-shell structures based on vector form intrinsic finite element[J].Journal of Building Structures,2016(6):53-59.
[19]YANG C,SHEN Y,LUO Y.An efficient numerical shape analysis for light weight membrane structures[J].Journal of Zhejiang University:SCIENCE A,2014,15(4):255-271.
[20]BAZELEY G P,CHEUNG Y K,IRONS B M,et al.Triangular elements in plate bending,conforming and non-conforming solutions[C]//Proceedings of the 1st Conference on Matrix Methods in Structural Mechanics.Dayton:Wright-Patterson Air Force Base,1965:547-576.
[21]HALL J F.Problems encountered from the use(or misuse)of Rayleigh damping[J].Earthquake Engineering and Structural Dynamics,2006,35(5):525-545.
[22]SIMO J C,HUGHES T J R.Computational Inelasticity[M].New York:Springer-Verlag,1998:120-138.
[23]BATHE K,RAMM E,WILSON E L.Finite element formulations for large deformation dynamic analysis[J].International Journal for Numerical Methods in Engineering,1975,9(2):353-386.
[24]O?ATE E,FLORES F G.Advances in the formulation of the rotation-free basic shell triangle[J].Computer Methods in Applied Mechanics and Engineering,2005,194(21-24):2406-2443.
[25]ARGYRIS J,PAPADRAKAKIS M,MOUROUTIS ZS.Nonlinear dynamic analysis of shells with the triangular element TRIC[J].Computer Methods in Applied Mechanics and Engineering,2003,192(26/27):3005-3038.
[26]WITMER E A,CLARK E N,BALMER H A.Experimental and theoretical studies of explosiveinduced large dynamic and permanent deformations of simple structures[J].Experimental Mechanics,1967,7(2):56-66.
[27]STOLARSKI H,BELYTSCHKO T,CARPENTER N,et al.A simple triangular curved shell element[J].Engineering computations,1984,1(3):210-218.
[28]MACNAY G H.Numerical modelling of tube crush with experimental comparison[C]//Proceedings of the 7th International Conference on Vehicle Structural Mechanics.Warrendale:American Society of Automotive Engineers,1988:123-134.
[29]KIM H C,DONG K S,LEE J J,et al.Crashworthiness of aluminum/CFRP square hollow section beam under axial impact loading for crash box application[J].Composite Structures,2014,112(5):1-10.