岑松, 龙驭球. 采用面积坐标的四边形厚薄板通用单元[J]. 工程力学, 1999, 16(2): 1-15.
引用本文: 岑松, 龙驭球. 采用面积坐标的四边形厚薄板通用单元[J]. 工程力学, 1999, 16(2): 1-15.
CEN Song, LONG Yu-qiu. A QUADRILATERAL THIN-THICK PLATE BENDING ELEMENT BY USING AREA COORDINATE METHOD[J]. Engineering Mechanics, 1999, 16(2): 1-15.
Citation: CEN Song, LONG Yu-qiu. A QUADRILATERAL THIN-THICK PLATE BENDING ELEMENT BY USING AREA COORDINATE METHOD[J]. Engineering Mechanics, 1999, 16(2): 1-15.

采用面积坐标的四边形厚薄板通用单元

A QUADRILATERAL THIN-THICK PLATE BENDING ELEMENT BY USING AREA COORDINATE METHOD

  • 摘要: 本文采用四边形面积坐标,利用假设剪切应变场方法和广义协调理论构造出一个具有12个自由度的四边形厚薄板通用弯曲单元TACQ。基本思路如下:首先从Mindlin厚板理论出发,独立假设剪应变场和挠度场,而转角场则由挠度场和剪应变场导出;其次,单元剪应变场是先按Timoshenko厚梁理论确定单元各边剪应变,然后在单元内进行合理插值导出;第三,单元挠度场是根据单元角点处挠度的点协调条件以及单元各边挠度和法向转角的平均协调条件导出。这个方法有两个特点,(1)由于满足点协调和边协调的广义协调条件,故能保证收敛;(2)由于在薄板情况剪应变退化为零,故不出现剪切闭锁现象。数值算例表明:该单元具有精度高,收敛性和可靠性好,对网格畸变不敏感,无剪切闭锁现象等优点;适用于从极薄板到厚板较大的范围。

     

    Abstract: In this paper,a new quadrilateral thin-thick plate bending element with only 12 degrees of freedom, TACQ,is developed by using the area coordinate method.The basic idea of above approach is as follows. Firstly, on the basis of Mindlin thick plate theory, deflection and shear strain fields are assumed independently. Then the rotation fields are derived from the shear strain and the deflection fields. Secondly, the shear strain along each side of the element is determined based on Timoshenko beam theory. Then the shear strain fields in the domain of the element are determined with rational interpolation. Thirdly, the deflection field of the element is obtained by using the point compatibility conditions of the deflection at the element nodes, and the side average compatibility conditions of the deflection and the normal rotation along each side.This approach has two characteristics. (1) The convergence is ensured because the point and side-average generalized compatibility conditions are satisfied. (2) The shear strain fields are degenerated to be zero under the thin plate situation, so there is no shear locking phenomenon. Numerical examples show that this element is effective for a large range of thickness-span ratio from very thin plate to thick plate.

     

/

返回文章
返回