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A new method to improve the calculation accuracy of 4-node quadrilateral flat shell element[J].计算力学学报,2017,(2):206~212

A new method to improve the calculation accuracy of 4-node quadrilateral flat shell element
A new method to improve the calculation accuracy of 4-node quadrilateral flat shell element

DOI：10.7511/jslx201702012

 作者 单位 E-mail 刘云飞 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 大连 116024 吕军 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 大连 116024 高效伟 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 大连 116024 xwgao@dlut.edu.cn

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。

The flat shell element is composed of the plane stress element and plate bending element, which have the simple theoretical expressions. But when the curvature of the element surface is large, the numerical results of the flat shell element are not very accurate. In order to improve the performance of the flat shell element, a new method to calculate the element stiffness matrix of the flat shell element is proposed in this paper. By establishing the local Cartesian coordinate systems on each Gauss point over the tangent plane to the surface, the local Cartesian coordinate systems can adapt to the curved element surface better. In order to compute the element stiffness matrix of the flat shell element in these local Cartesian coordinate systems, the corresponding techniques to calculate the derivatives of the shape functions with respect to the local coordinates, the transformation matrix from the Local to the Global Coordinate Systems and Jacobian are also provided in this paper. The 4-node flat shell element DKQ24 based on the theories of the plane stress element and DKQ plate bending element with this new method can achieve higher precision results than the traditional ways, especially for the curved shell structure. The numerical results demonstrate that the flat shell element with this new method not only has simple theoretical expressions but also can obtain satisfactory results. Furthermore, this new method presented in this paper offers a new approach for other flat shell element to improve the computing accuracy.