一个基于膜板比拟理论的四节点十六自由度的平板壳单元

应用膜板比拟关系,可以避开1c连续性的困难,为板单元的构造提供了一种新的途径,并已成功地构造出一系列相应的板单元。本文提出了一个四节点十六自由度的平板壳单元,该单元由平面四节点理性元RQ4(膜部分)和由膜板比拟理论构造的一个四节点八自由度的板单元(弯曲部分)构成。该单元构造简单,自由度少,数值结果表明具有良好的收敛性和精度。     

一个基于膜板比拟理论的四边形双线性薄板单元

平面弹性与板弯曲的相似性理论为构造薄板单元提供了一条有效的新途径。根据这一理论,现有的平面弹性单元原则上可以转化为板弯曲单元。从平面弹性四节点双线性等参元Q4出发,根据相似性理论构造出一个新的四边形八自由度双线性薄板单元。该单元构造简单,节点自由度少,可以视为最简单的四边形薄板单元。数值结果表明,该单元能通过分片试验,满足坐标不变性,具有良好的收敛性和精度。是一个良好的低阶薄板单元。     

基于平面弹性-板弯曲比拟理论的Wilson型板弯曲单元

应用平面弹性板弯曲比拟关系,可以避开1c连续性的困难,为板单元的构造提供了一种新的途径。这一新方法已成功地将一些平面弹性协调单元转化为新型板弯曲单元。根据比拟理论将著名的平面弹性Wilson元QM6转化为板弯曲单元,从而将新方法应用到平面弹性非协调元。单元构造简单,数值结果表明具有很好的收敛性和精度。     

应用Pian-Sumihara杂交列式的板弯曲模拟元

把典型的平面弹性杂交应力元-Pian-Sumihara 元-转化为板弯曲单元,从而初步探讨了将平面弹性杂交元转化为板弯曲单元的方法。应用板弯曲多类变量变分原理和弯矩函数空间中的Pian-Sumihara 列式,再通过基于平面弹性-板弯曲相似性的单元转化过程,得到一个四节点八自由度板弯曲位移元。该单元为显式单元,计算量少。数值结果表明该单元能通过常曲率分片试验,收敛稳定并具有较好的精度。     

多层与高层建筑中墙的模型

本文基于四边形壳单元提出了一种新的空间墙单元模型，它在平面内是一块模，包括两个平动自由度和绕平面的转动自由度，平面外是一块弯曲板，因而它的每个节点都具有空间全部的六个自由度，由于很好地考虑了平面内和平面外的刚度，这种单元可以很准确地处理墙的空间变形，并且能直接与三维框架的梁，柱及板壳单元连接，算例表明这种单元模型合理，精度高，是一种土建中十分实用有效的单元。     

广义协调平板型三角形壳元

本文构造了一种具有三个角点十八个自由度的平板三角形壳元GST18。其拉伸与弯曲部分分别由含旋转自由度的三角形膜元和薄板弯曲三角形元组成。广义协调方法的采用,使得该单元的收敛性得到保证。在结点上引入了平面内旋转自由度,从根本上克服了单元共面刚度矩阵出现奇异这一困难。对平面膜元采用了缩减积分方案,使该单元不会产生薄膜闭锁现象。数值算例表明,本文提出的GST18薄壳元是计算精度优于同类单元的可靠、实用的单元。     

基于一阶剪切变形理论的新型复合材料层合板单元

基于一阶剪切变形理论(FSDT),本文构造一种新型的20自由度(每结点5个自由度),四边形复合材料层合板单元,适合于任意铺设情形的层合板的计算。它是按如下方式构造的:(1) 单元每边的转角和剪应变由Timoshenko层合厚梁理论来确定;(2) 对单元域内的转角场和剪应变场进行合理的插值;(3) 引入平面内双线性位移场来体现层合板面内与弯曲的耦合作用。本文单元,记为TMQ20,不存在剪切闭锁现象,在计算单层的各向同性板时可以退化为文[1]中优质的中厚板单元TMQ。在文[2]中将给出本文单元对于层合板问题的详细数值算例。     

钢筋混凝土剪力墙非线性分析单元模型

该文基于龙驭球院士研究组创建的带旋转自由度膜元和厚薄通用板单元构造理论,结合修正压场混凝土双轴本构模型,建立了一种新型钢筋混凝土剪力墙非线性有限元分析整体式壳元模型。在整体式壳元模型中,采用钢筋混凝土膜元模拟剪力墙墙板的面内刚度,采用厚薄通用板单元模拟剪力墙墙板的面外刚度,采用纤维梁元模拟剪力墙中的边缘构件。为了验证该模型,将该模型的数值分析结果和钢筋混凝土剪力墙试件的试验结果进行对比。结果表明:整体式壳元模型能够对弯、剪、压共同作用下的钢筋混凝土剪力墙的极限承载力及非线性弯曲、剪切耦合变形进行较为准确的预测。该壳元模型自由度少、单元计算精度高、收敛速度快且总计算量小,适合作为高层建筑结构在地震作用下非线性动力响应分析的钢筋混凝土剪力墙单元模型。     

实体退化板单元及其在板的振动分析中的应用

经典板壳单元是由板壳理论构造出来的,而经典的板壳理论是在空间弹性理论的基础上考虑板壳的基本假定得来的。在空间等参数单元的基础上,直接引入板壳的基本假定,修改空间等参数单元的弹性矩阵,从而构造出适合于厚薄板壳分析的20结点实体退化板单元,并将其应用于开口圆柱薄壳的静力分析和厚薄板的固有振动分析。数值算例表明,该单元收敛快,稳定性好,具有较高的精度。此外,该单元还可以用于曲边变厚度板、壳体及层合板的振动分析。     

新型四边形广义协调层合板单元

基于一阶剪切变形理论（FSDT）,本文采用面积坐标构造一种新型20自由度（每结点5个自由度）,四边形复合材料层合板单元,适合于任意铺设情形的层合板的计算。它是按如下方式构造的：（1）引入平面内双线性位移场来体现层合板面内与弯曲的耦合作用;（2）单元每边的剪应变由Timoshenko层合厚梁理论来确定,对单元域内的剪应变场进行合理的插值;（3）将四边形面积坐标法与广义协调理论相结合,求解单元挠度场。针对位移复合材料板单元提出了一种新型应力杂交化后处理方法来改善单元计算应力的能力,使位移型单元可以简单和正确地预测层合板的应力,特别是层间横向剪应力的解。本文单元,记为TACQ20,不存在剪切闭锁现象,对位移和应力都可以得到高精度的结果。     

Two refined non‐conforming quadrilateral flat shell elements

Two refined quadrilateral flat shell elements named RSQ20 and RSQ24 are constructed in this paper based on the refined non‐conforming element method, and the elements can satisfy the displacement compatibility requirement at the interelement of the non‐planar elements by introducing the common displacements suggested by Chen and Cheung. A refined quadrilateral plate element RPQ4 and a plane quadrilateral isoparametric element are combined to obtain the refined quadrilateral flat shell element RSQ20, and a refined quadrilateral flat shell element RSQ24 is constructed on the basis of a RPQ4 element and a quadrilateral isoparametric element with drilling degrees of freedom. The numerical examples show that the present method can improve the accuracy of shell analysis and that the two new refined quadrilateral flat shell elements are efficient and accurate in the linear analysis of some shell structures. Copyright © 2000 John Wiley & Sons, Ltd.     

A 3‐node flat triangular shell element with corner drilling freedoms and transverse shear correction

The formulation, implementation and testing of simple, efficient and robust shell finite elements have challenged investigators over the past four decades. A new 3‐node flat triangular shell element is developed by combination of a membrane component and a plate bending component. The ANDES‐based membrane component includes rotational degrees of freedom, and the refined nonconforming element method‐based bending component involves a transverse shear correction. Numerical examples are carried out for benchmark tests. The results show that compared with some popular shell elements, the present one is simple but exhibits excellent all‐around properties (for both membrane‐and bending‐dominated situations), such as free of aspect ratio locking, passing the patch test, free of shear locking, good convergence and high suitability for thin to moderately thick plates. The developed element has already been adopted in a warpage simulation package for injection molding. Copyright © 2011 John Wiley & Sons, Ltd.     

Refined non‐conforming triangular elements for analysis of shell structures

Based on the refined non‐conforming element method, simple flat triangular elements with standard nodal displacement parameters are proposed for the analysis of shell structures. For ensuring the convergence of the elements a new coupled continuity condition at the inter‐element has been established in a weaker form. A common displacement for the inter‐element, an explicit expression of refined constant strain matrix, and an adjustable constant are introduced into the formulation, in which the coupled continuity requirement at the inter‐element is satisfied in the average sense. The non‐conforming displacement function of the well‐known triangular plate element BCIZ [1] and the membrane displacement of the constant strain triangular element CST [2] are employed to derive the refined flat shell elements RTS15, and the refined flat shell elements RTS18 is derived by using the element BCIZ and the Allman's triangular plane element [3] with the drilling degrees of freedom. A simple reduced higher‐order membrane strain matrix is proposed to avoid membrane locking of the element RTS18. An alternative new reduced higher‐order strain matrix method is developed to improve the accuracy of the elements RTS15 and RTS18. Numerical examples are given to show that the present methods have improved the accuracy of the shell analysis. Copyright © 1999 John Wiley & Sons, Ltd.     

一种新型厚薄板通用三角形广义协调元

本文提出了一种假设单元剪切应变场的新方法，基于广义协调理论构造了一个只有９个自由度的三角形厚薄板通用单元ＴＣＧＣ Ｔ９。数值算例表明：该单元具有自由度少，精度高，无剪切闭锁现象等特点，适用于从极薄板到厚板较大的范围。     

A family of simple and robust finite elements for linear and geometrically nonlinear analysis of laminated composite plates

A family of simple, displacement-based and shear-flexible triangular and quadrilateral flat plate/shell elements for linear and geometrically nonlinear analysis of thin to moderately thick laminate composite plates are introduced and summarized in this paper.

The developed elements are based on the first-order shear deformation theory (FSDT) and von-Karman’s large deflection theory, and total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from Timoshenko’s laminated composite beam functions, thus convergence can be ensured theoretically for very thin laminates and shear-locking problem is avoided naturally.

The flat triangular plate/shell element is of 3-node, 18-degree-of-freedom, and the plane displacement interpolation functions of the Allman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. The flat quadrilateral plate/shell element is of 4-node, 24-degree-of-freedom, and the linear displacement interpolation functions of a quadrilateral plane element with drilling degrees of freedom are taken as the in-plane displacements.

The developed elements are simple in formulation, free from shear-locking, and include conventional engineering degrees of freedom. Numerical examples demonstrate that the elements are convergent, not sensitive to mesh distortion, accurate and efficient for linear and geometric nonlinear analysis of thin to moderately thick laminates.