摘要
在板的有限元分析中 ,构造协调和无剪切闭锁现象的中厚板单元一直是人们所关注的问题和难题。文献[2 ,3 ] 提出了一种假设剪切应变场的方法 ,基于广义协调理论成功地构造出厚板薄板通用的三角形和四边形单元 ,但这类单元并不具有完备性和真正的C1阶连接性。为此 ,文献[1] 构造出了具有完备和真正C1阶协调的薄板矩形单元 ,为构造这类单元的构造提供了一个有效的新途径。本文首先从Mindin厚板理论出发 ,导出单元各边的剪应变和节点剪应变公式 ,进行合理插值导出单元的剪应变场 ,当板的厚度变小时 ,厚板理论理论自动退化为薄板理论 ,各边剪应变以及单元剪应变插值函数自动退化为零 ,厚板单元自动退化为薄板单元 ,彻底消除了剪切闭锁现象。然后根据转角场、挠度场和剪应变场的关系 ,通过反复试算构造出一个具有 12个自由度的厚板薄板通用协调矩形单元 ,通过理论证明该厚板薄板通用单元具有完备性、C1阶连续性和无剪切闭锁现象 ,从而较好地解决了厚板薄板能单元的C1阶连续性和无剪切闭锁现象的难题。为了验证该协调单元的正确性 ,对不同厚距比 (h/l)的四边简支和固定方形板在均布载荷作用下的中心挠度和弯矩进行分析。数值算例表明 :该单元精度高 ,原理简明 ,列式简单 ,自由度少 ,收敛速度快 ;
The structure coordination and shear unlocking middle thick plate element is a problem to which people pay close attention in the finite element analysis of plate.A supposed shear strain field is presented in the documents [2,3] and a generalized triangle and quadrangle element for thick and thin plates is developed by generalized coordination theory.But this kind of element is not perfect and harmonized in deed.Therefore,a coordinating and harmonized rectangle elements for thin plate is constructed in the document [1] ,and it provides a new valid way for constructing this kind of element. Firstly,the variation function of shear strain along each side and at node of the element are determined based on the Mindin thick plate theory,and the shear strain fields in the domain of the element are detemined with improved interpolation in this paper.When thickness of plate become small,the thick theory is automatically degenerated the thin theory,and shear strain along each side of element and the variation function of shear strain of element are automatically shear locking.Secondly,based on the relation of the rotation,flexivity and strain fields in the domain of the elements,a generalized coordinating twelve freedom rectangle element for thick and thin plates is developed by repeated trying.It is proved by theory that the elements are perfect,harmonized and free of shear locking.The C repeated continuity and shear locking problem of element for thick and thin plate is solved preferably. In order to validate the correctness of the coordinating element,center flexivity and bending moments of square plate are analyzed in this paper and the plate is supported simply and fixed at four sides in different ratio of thickness to span and is acted on equispared load.The convergence velocity of the calculated result by this coordinating plate element is faster and the precision is higher than the average,and the principle and formula is more simple,and the freedom degree of the element is fewer.The element is degenerated coordinating thin plate element and is free of shear locking in the case of thin plate.The result calculated by the coordinating element is very near to that of Mindin middle thick plates in the case of near to thick plate,and the coordinating element can be used to different thickness plates and is a fine element.
出处
《中国铁道科学》
EI
CAS
CSCD
北大核心
2001年第2期96-100,共5页
China Railway Science
关键词
厚板薄板通用
协调矩形单元
理论证明
有限元
Thick and thin plate
A generalized coordinating rectangle element
Theoretical identification
