大变形硅胶板动力学建模与仿真分析
|
摘要
硅胶材料是一种具有非线性本构关系的不可压缩超弹性材料,与传统的线弹性金属材料相比,硅胶材料不仅要考虑几何非线性,而且要考虑材料非线性。对大变形弯曲的硅胶板进行动力学建模和仿真分析。为了解决体积锁定问题,使用缩减积分法对传统的绝对节点坐标法(ANCF)低阶板单元进行改进。通过引入罚函数,推导了Yeoh模型的弹性力阵及其导数阵,用绝对节点坐标法建立了大变形硅胶板的动力学方程,结合Newmark数值积分方法和Newton-Raphson迭代方法求解二阶微分方程。分别采用传统的ANCF低阶板单元和改进的ANCF低阶板单元,对受重力作用下的悬臂硅胶板和受到球铰约束的硅胶板进行动力学仿真,通过与商业有限元软件ANSYS的仿真结果进行比较,验证了本文建模方法的有效性。最后,对硅胶板中面上的位移云图进行了分析,从另一个角度反映了其位移和构型的变化。
Silicone material is an incompressible hyperelastic material with nonlinear constitutive laws,both the material nonlinearity and the geometric nonlinearity are necessarily taken into consideration for this type of material compared with traditional linear elastic metal materials.Dynamic modeling and simulation analysis of silicone material plates with large bending deformation are investigated in this paper.In order to solve the volumetric locking problem,an improved absolute nodal coordinate formulation(ANCF)lower-order plate element is presented using the selective reduced integration method.The elastic force and its derivative matrices of the Yeoh model are derived by introducing the volumetric energy penalty function.Dynamic equations of motion of a silicone plate with large deformation are established adopting ANCF.Newmark numerical integration method combined with the Newton-Raphson iteration technique are employed to solve second order differential equation.Dynamic simulations of a cantilevered silicone plate and a silicone plate applied with spherical hinge under the action of gravitational force are implemented by employing the conventional ANCF lower-order plate element and the improved ANCF lower-order plate element.Comparison of the simulation results with those obtained by commercial finite element software ANSYS verifies the effectiveness of the present formulations.Finally,the displacement nephograms on the middle surface are analyzed,and the variations of displacements and configurations are reflected from another perspective.
Silicone material is an incompressible hyperelastic material with nonlinear constitutive laws,both the material nonlinearity and the geometric nonlinearity are necessarily taken into consideration for this type of material compared with traditional linear elastic metal materials.Dynamic modeling and simulation analysis of silicone material plates with large bending deformation are investigated in this paper.In order to solve the volumetric locking problem,an improved absolute nodal coordinate formulation(ANCF)lower-order plate element is presented using the selective reduced integration method.The elastic force and its derivative matrices of the Yeoh model are derived by introducing the volumetric energy penalty function.Dynamic equations of motion of a silicone plate with large deformation are established adopting ANCF.Newmark numerical integration method combined with the Newton-Raphson iteration technique are employed to solve second order differential equation.Dynamic simulations of a cantilevered silicone plate and a silicone plate applied with spherical hinge under the action of gravitational force are implemented by employing the conventional ANCF lower-order plate element and the improved ANCF lower-order plate element.Comparison of the simulation results with those obtained by commercial finite element software ANSYS verifies the effectiveness of the present formulations.Finally,the displacement nephograms on the middle surface are analyzed,and the variations of displacements and configurations are reflected from another perspective.
引文
[1]蔡松柏,沈蒲生.大转动平面梁有限元分析的共旋坐标法[J].工程力学,2006,23(A01):69-72.Cai Songbai,Shen Pusheng.Co-rotational procedure for finite element analysis of plane beam under large rotational displacement[J].Engineering Mechanics,2006,23(A01):69-72.
[2]Fleissner F,Gaugele T,Eberhard P.Applications of the discrete element method in mechanical engineering[J].Multibody System Dynamics,2007,18(1):81-94.
[3]Likins P W.Modal method for analysis of free rotations of spacecraft[J].AIAA Journal,1967,5(7):1304-1308.
[4]Likins P W.Dynamic analysis of a system of hingeconnected rigid bodies with non-rigid appendages[J].International Journal of Solids and Structures,1973,9(12):1473-1487.
[5]Gerstmayr J,Sugiyama H,Mikkola A.Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems[J].ASME Journal of Computational and Nonlinear Dynamics,2013,8:031016.
[6]Dufva K,Shabana A A.Analysis of thin plate structures using the absolute nodal coordinate formulation[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-Body Dynamics,2005,219(4):345-355.
[7]Dmitrochenko O,Mikkola A M.Two simple triangular plate elements based on the absolute nodal coordinate formulation[J].ASME Journal of Computational and Nonlinear Dynamics,2008,3(4):041012.
[8]Dmitrochenko O,Pogorelov D Y.Generalization of plate finite elements for absolute nodal coordinate formulation[J].Multibody System Dynamics,2003,10(1):17-43.
[9]Liu C,Tian Q,Hu H Y.Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates[J].Multibody System Dynamics,2011,26(3):283-305.
[10]Mikkola A M,Matikainen M K.Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation[J].ASME Journal of Computational and Nonlinear Dynamics,2006,1(2):103-108.
[11]Ogden R W.Non-Linear Elastic Deformation[M].Dover,New York,1984.
[12]Maqueda L G,Shabana A A.Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams[J].Multibody System Dynamics,2007,18:375-396.
[13]Jung S P,Park T W,Chung W S.Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law[J].Nonlinear Dynamics,2011,63(1-2):149-157.
[14]Luo K,Liu C,Tian Q,et al.Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation[J].Nonlinear Dynamics,2016,85(1):949-971.
[15]Simo J C,Taylor R L.Penalty function formulations for incompressible nonlinear elastostatic[J].Computer Methods in Applied Mechanics and Engineering,1982,35:107-118.
[16]Orzechowski G,Fraczek J.Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF[J].Nonlinear Dynamics,2015,82(1):451-464.
[2]Fleissner F,Gaugele T,Eberhard P.Applications of the discrete element method in mechanical engineering[J].Multibody System Dynamics,2007,18(1):81-94.
[3]Likins P W.Modal method for analysis of free rotations of spacecraft[J].AIAA Journal,1967,5(7):1304-1308.
[4]Likins P W.Dynamic analysis of a system of hingeconnected rigid bodies with non-rigid appendages[J].International Journal of Solids and Structures,1973,9(12):1473-1487.
[5]Gerstmayr J,Sugiyama H,Mikkola A.Review on the absolute nodal coordinate formulation for large deformation analysis of multibody systems[J].ASME Journal of Computational and Nonlinear Dynamics,2013,8:031016.
[6]Dufva K,Shabana A A.Analysis of thin plate structures using the absolute nodal coordinate formulation[J].Proceedings of the Institution of Mechanical Engineers,Part K:Journal of Multi-Body Dynamics,2005,219(4):345-355.
[7]Dmitrochenko O,Mikkola A M.Two simple triangular plate elements based on the absolute nodal coordinate formulation[J].ASME Journal of Computational and Nonlinear Dynamics,2008,3(4):041012.
[8]Dmitrochenko O,Pogorelov D Y.Generalization of plate finite elements for absolute nodal coordinate formulation[J].Multibody System Dynamics,2003,10(1):17-43.
[9]Liu C,Tian Q,Hu H Y.Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates[J].Multibody System Dynamics,2011,26(3):283-305.
[10]Mikkola A M,Matikainen M K.Development of elastic forces for a large deformation plate element based on the absolute nodal coordinate formulation[J].ASME Journal of Computational and Nonlinear Dynamics,2006,1(2):103-108.
[11]Ogden R W.Non-Linear Elastic Deformation[M].Dover,New York,1984.
[12]Maqueda L G,Shabana A A.Poisson modes and general nonlinear constitutive models in the large displacement analysis of beams[J].Multibody System Dynamics,2007,18:375-396.
[13]Jung S P,Park T W,Chung W S.Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law[J].Nonlinear Dynamics,2011,63(1-2):149-157.
[14]Luo K,Liu C,Tian Q,et al.Nonlinear static and dynamic analysis of hyper-elastic thin shells via the absolute nodal coordinate formulation[J].Nonlinear Dynamics,2016,85(1):949-971.
[15]Simo J C,Taylor R L.Penalty function formulations for incompressible nonlinear elastostatic[J].Computer Methods in Applied Mechanics and Engineering,1982,35:107-118.
[16]Orzechowski G,Fraczek J.Nearly incompressible nonlinear material models in the large deformation analysis of beams using ANCF[J].Nonlinear Dynamics,2015,82(1):451-464.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |