基于绝对节点坐标法的高次插值梁单元建模
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摘要
针对传统绝对节点坐标平面梁单元存在泊松闭锁的问题,研究平面高次插值梁单元.在多项式位移模式中,基于帕斯卡三角形理论,采用与x2项共用系数的方法引入y2项,建立含有y2项的绝对节点坐标高次插值梁单元模型.实例计算结果与传统绝对节点坐标平面梁单元的计算结果比较说明,在泊松比不为零的情况下,绝对节点坐标高次插值梁单元的计算结果明显好于传统绝对节点坐标平面梁单元.因此,含y2项的绝对节点坐标平面梁单元可有效缓解传统绝对节点坐标平面梁单元的泊松闭锁问题.
For Poisson locking in problem traditional absolute node coordinate beam element,the highorder shear beam element was studied.In the polynomial displacement mode,based on the Pascal triangle theory,the y2 item was included by sharing coefficient with the x2 item and the higher-order interpolation beam element was established.When the Poisson′s ratio is not zero,the results of the example calculations indicate that the absolute node coordinate high-order interpolation beam element is obviously better than the traditional absolute node coordinate beam element.Therefore,the absolute node coordinate beam element contains y2 item can effectively alleviate the Poisson locking problem in traditional absolute node coordinate beam element.
For Poisson locking in problem traditional absolute node coordinate beam element,the highorder shear beam element was studied.In the polynomial displacement mode,based on the Pascal triangle theory,the y2 item was included by sharing coefficient with the x2 item and the higher-order interpolation beam element was established.When the Poisson′s ratio is not zero,the results of the example calculations indicate that the absolute node coordinate high-order interpolation beam element is obviously better than the traditional absolute node coordinate beam element.Therefore,the absolute node coordinate beam element contains y2 item can effectively alleviate the Poisson locking problem in traditional absolute node coordinate beam element.
引文
[1]田强,张云清,陈立平,等.柔性多体系统动力学绝对节点坐标方法研究进展[J].力学进展,2010(2):189-202.
[2] ORZECHOWSKI G,SHABANA A A.Analysis of warping deformation modes using higher order ANCF beam element[J].Journal of Sound and Virbration,2016,363:428-445.
[3]沈振兴,刘铖,田强.一种基于绝对节点坐标方法的高阶梁单元[C]//第十届全国多体动力学与控制暨第五届全国航天动力学与控制学术会议论文摘要集.青岛:中国力学学会动力学与控制专业委员会多体动力学与控制专业组,中国力学学会动力学与控制专业委员会航天动力学与控制专业组,2017.
[4] LI P F,GANTOI F M,SHABANA A A.Higher order representation of the beam cross section deformation in large displacement finite element analysis[J].Journal of Sound and Virbration,2011,330(26):6495-6508.
[5] OMAR M A,SHABANA A A.A two-dimensional shear deformable beam for large rotation and deformation problems[J].Journal of Sound and Virbration,2001,243(3):565-576.
[6] GARCA-VALLEJO D, MIKKOLAAM,ESEALONA J L.A new locking free shear deformable finite element based on absolute nodal coordinates[J].Nonlinear Dynamics,2007,50(1/2):249-264.
[7]张大羽,罗建军,郑银环,等.基于旋转场曲率的二维剪切梁单元建模[J].物理学报,2017,66(11):204-218.
[2] ORZECHOWSKI G,SHABANA A A.Analysis of warping deformation modes using higher order ANCF beam element[J].Journal of Sound and Virbration,2016,363:428-445.
[3]沈振兴,刘铖,田强.一种基于绝对节点坐标方法的高阶梁单元[C]//第十届全国多体动力学与控制暨第五届全国航天动力学与控制学术会议论文摘要集.青岛:中国力学学会动力学与控制专业委员会多体动力学与控制专业组,中国力学学会动力学与控制专业委员会航天动力学与控制专业组,2017.
[4] LI P F,GANTOI F M,SHABANA A A.Higher order representation of the beam cross section deformation in large displacement finite element analysis[J].Journal of Sound and Virbration,2011,330(26):6495-6508.
[5] OMAR M A,SHABANA A A.A two-dimensional shear deformable beam for large rotation and deformation problems[J].Journal of Sound and Virbration,2001,243(3):565-576.
[6] GARCA-VALLEJO D, MIKKOLAAM,ESEALONA J L.A new locking free shear deformable finite element based on absolute nodal coordinates[J].Nonlinear Dynamics,2007,50(1/2):249-264.
[7]张大羽,罗建军,郑银环,等.基于旋转场曲率的二维剪切梁单元建模[J].物理学报,2017,66(11):204-218.