一种提高四边形四节点平面壳单元计算精度的新方法

发布时间：2017-12-27 05:30

  本文关键词：一种提高四边形四节点平面壳单元计算精度的新方法　出处：《计算力学学报》2017年02期 　论文类型：期刊论文

  更多相关文章： 平面壳单元 高斯积分点 单元局部坐标系 形函数对局部坐标的导数 曲面壳体

【摘要】：平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。
[Abstract]:The planar shell element is composed of planar stress element and plate bending element. It has a simple theoretical expression, but it has large error when calculating the shell structure. In order to further improve the calculation precision of the plane shell element, a new method for calculating the stiffness matrix of the plane shell element is proposed in this paper. By means of this method, multiple element local coordinate systems are established at Gauss integration points, and each local coordinate system is located at the tangent plane at the Gauss point, so that it can effectively adapt to the shape of the surface shell, and further improve the accuracy of the calculation of the shell element. In order to calculate the element stiffness matrix in the new coordinate system, gives the derivative, solving the shape functions of the local coordinates to local natural coordinates conversion, Jacobi integral and local to the new calculation method of the transfer matrix in the global coordinate system. Through these new coordinates and a new calculation method is applied to the plane shell element in DKQ24, can effectively improve the plane shell element especially in the calculation of the precision of curved surface shell. The calculation results show that the combination of this method and the plane shell element not only has a simple theoretical expression of the plane shell element, but also has a satisfactory precision. Besides, this method can also be applied to other types of shell elements. It provides a new way and idea for improving the accuracy of other types of shell elements, and has broad application prospects.
【作者单位】： 大连理工大学工业装备结构分析国家重点实验室航空航天学院;
【基金】：国家自然科学基金(11172055,11202045,11302040) 大连科技之星(2014年称号)资助项目
【分类号】：O302
【正文快照】： 1 引言 目前工程中提出了很多种壳体单元[1-6],应用到三维空间的壳单元,一般分为平面壳元和曲面壳元[7]。曲面壳元可以很好地描述壳体形状,并且在单元内考虑了膜弯耦合,具有较好的计算精度,但是由于难以恰当表达刚体运动来避免剪切和膜闭锁,使得曲面壳元的构造变得困难和复杂，

本文编号：1340464