采用SemiLoof型约束条件的薄板矩形广义协调元

本文采用SemiLoof型约束条件,建立一个十二自由度的薄板矩形广义协调元。单元自由度只含角点位移,不含Loof结点位移、单元间的协调条件全部采用点型协调条件,不采用积分型协调条件。此单元吸取广义协调元和SemiLoof元的双重优点,消除其缺点,成为同类低阶薄板单元中的最优单元。     

采用广义协调条件构造具有旋转自由度的四边形膜元

本文根据广义协调的概念,通过引进单元结点刚体转角,提出两种具有平面内旋转自由度的四边形膜元。单元列式简单,是能通过任意四边形分片检验的收敛单元。数值计算表明这两种单元无论是位移还是应力都有很高的计算精度。     

用广义协调方法推导的平面四节点等参单元

对平面四节点Q4单元采用优选的广义协调条件进行推导,将广义协调理论的应用拓展到最基本的平面问题单元。基于Q6以及QM6中基于内部参数的二次附加位移场,在Q4单元基础上增加满足广义协调条件的内参位移场,从而构造了一个满足广义协调条件的平面四节点等参元GQM6。数值算例表明,虽然采用了相同次数的位移场,但GQM6单元中采用的广义协调条件较QM6中采用的数值积分方法,可以进一步放松单元边界的约束,从而使单元的性能进一步提高,尤其在抗网格畸变能力方面。研究表明,将广义协调理论与一些传统单元进行深入融合仍然有着重要价值。     

引入广义泡状型位移场影响的厚板矩形单元

本文提出了在已有的无闭锁现象的广义协调厚板矩形单元的基础之上，引入广义泡状型位移场的影响，构造厚薄板通用的优质单元的一般方法．应用此法构造出新的单元．数值算例表明，在引入适当的广义泡状位移影响后，单元的计算结果显著得到改善，精度进一步提高．     

引入泡状位移含旋转自由度的广义协调三角形膜元

本文通过在单元位移场上增加含内参的广义泡状位移方法,构造了一个具有旋转自由度的三角形膜元。由于直接从完全多项式中应用广义协调方法确定附加位移,有效地扩大了单元位移场的解空间,所构造的单元具有计算精度高、对计算网格畸变不敏感的优良特性。本文为改善位移元世态提供了一个简单有效的方法。     

广义协调六结点平面曲边单元研究

主要运用广义协调原理,针对计算平面曲边单元的有限元算法进行了研究,并且利用点、周混合协调条件构造了三种高性能六结点曲边单元。第一、二种单元在平面直角坐标内分别采用解析试函数和完全三次多项式构造,第三种单元在六结点等参单元Q6的基础上附加广义协调泡状位移而成。这三种单元均能通过强式分片试验,并且显示了良好的计算精度和抗畸变能力。     

含纯弯场的平面四结点矩形广义协调膜元

本文以点移场（３个刚体位移场，３个常应变场，２个纯弯场）作为单元内插值函数的基底，并通过组合型点协调条件直接求得广义位移参数由结点位移表示的显式关系式，从而避免了大量的矩阵求逆运算，提高了计算的效率。     

扁壳广义协调曲面矩形元

本文从修正的扁壳胡海昌-鹫律原理泛函出发,引入两方面的广义协调条件(单元边界位移的积分型协调条件,膜应变与位移之间的积分型协调条件),使泛函退化为扁壳势能原理泛函,在此基础上导出一个具有二十个自由度的扁壳曲面矩形元。此单元对厚扁壳和薄扁壳都通用,不出现剪切闭锁和薄膜闭锁现象,具有良好的性能。     

采用面积坐标和基于假设转角的薄板元

采用四边形面积坐标方法,从假设转角位移场入手构造了两个广义协调四边形4结点薄板单元AΨQ-I和AΨQ-II。通过采用边界协调条件一次项与二次项分别协调使转角场实现了三次完备。与DKQ等同类单元相比,单元的精度和抗网格畸变能力都有很大提高。     

用简单高效的矩形广义协调元分析薄板的振动

本文介绍一种在薄板振动分析中很简单,而且很实用的广义协调矩形元,将其应用于薄板固有振动分析中,求解前几阶的固有频率。文中算例表明,该单元简易,程序通用,且精度高。同时,它还可以与平面应力单元组合,构成平板型壳单元,用以分析某些壳体(如柱壳、折板等)的振动,同样简单实用。     

A new wavelet-based thin plate element using B-spline wavelet on the interval

By interacting and synchronizing wavelet theory in mathematics and variational principle in finite element method, a class of wavelet-based plate element is constructed. In the construction of wavelet-based plate element, the element displacement field represented by the coefficients of wavelet expansions in wavelet space is transformed into the physical degree of freedoms in finite element space via the corresponding two-dimensional C₁ type transformation matrix. Then, based on the associated generalized function of potential energy of thin plate bending and vibration problems, the scaling functions of B-spline wavelet on the interval (BSWI) at different scale are employed directly to form the multi-scale finite element approximation basis so as to construct BSWI plate element via variational principle. BSWI plate element combines the accuracy of B-spline functions approximation and various wavelet-based elements for structural analysis. Some static and dynamic numerical examples are studied to demonstrate the performances of the present element.     

基于解析试函数的内参型广义协调膜元

利用解析试函数法构造一个内参型四结点八自由度广义协调膜元。根据弹性力学平面问题的控制方程和艾雷应力函数,求出问题完备的基本解析解,然后用其作为试函数并采用广义协调条件来构造单元:ATF-GCQ4X。该单元采用了14个解析试函数构造了应变二次完备的内部场,同时引入6个附加边界位移模式,采用平衡力系为权函数构造相应的广义协调条件。数值算例表明,该类内参型单元能在不提高单元结点自由度的情况下提高单元精度,并显示出良好的收敛特性。     

带旋转自由度的广义协调三角形膜元

应用广义协调元理论,通过增加内参位移的方法,构造了两个具有旋转自由度的三角形膜元。本文单元能通过任意三角形分片检验,符合连续介质力学关于旋转自由度的定义,并且没有引入刚性转角假设。数值算例表明其具有较高的计算精度。     

A new finite element for thick laminates and sandwich structures using a generalized and unified plate theory

The contribution of this work is the implementation of a new elastic solution method for thick laminated composites and sandwich structures based on a generalized unified formulation using finite elements. A quadrilateral four‐node element was developed and evaluated using an in‐house finite element program. The C‐1 continuity requirements are fulfilled for the transversal displacement field variable. This method is tagged as Caliri's generalized formulation. The results employing the proposed solution method yielded coherent results with deviations as low as 0.05% for a static simply supported symmetric laminate and 0.5% for the modal analyses of a soft core sandwich structure. Copyright © 2016 John Wiley & Sons, Ltd.     

A new drilling quadrilateral membrane element with high coarse-mesh accuracy using a modified Hu-Washizu principle

By utilizing a modified Hu-Washizu principle, a new mixed variational framework and a corresponding high-performing four-node membrane element with drilling degrees of freedom, named as GCMQ element, are proposed. In this work, the generalized conforming concept, which is originally proposed within a displacement-based formulation, is extended to a mixed formulation. The new element is able to handle higher-order displacement, strain, and stress distributions. The interpolations are complete up to second order for stress and strain. The enhanced strain field is optimized so that a complete cubic displacement field can be represented. For numerical integration, a five-point scheme is proposed to minimize computational cost. Compared to other four-node elements in existing literature, numerical examples show that the proposed element has a better performance regarding predictions of both displacements and internal forces, particularly with coarse meshes. The new element is also free from shear locking and volumetric locking. Due to the nature of the mixed framework, GCMQ can be directly used in elastoplastic applications.     

A robust refined quadrilateral plane element

Based on a rational choice of the internal incompatible displacement function and a special formulation of the a priori elimination of the internal non-conforming displacement parameters, a new refined quadrilateral plane element RQ₄ has been developed. The present element can be shown to be computationally efficient, accurate and free from locking, and is better than other elements such as the Plan's element HS, the generalized hybrid element Q_CS6, and the refined hybrid element RGH₄, etc. Several numerical examples are given to show the superior performances of the present element RQ₄.     

Anomalous behavior of bilinear quadrilateral finite elements for modeling cohesive cracks with XFEM/GFEM

The performance of partition‐of‐unity based methods such as the generalized finite element method or the extended finite element method is studied for the simulation of cohesive cracking. The focus of investigation is on the performance of bilinear quadrilateral finite elements using these methods. In particular, the approximation of the displacement jump field, representing cohesive cracks, by extended finite element method/generalized finite element method and its effect on the overall behavior at element and structural level is investigated. A single element test is performed with two different integration schemes, namely the Newton‐Cotes/Lobatto and the Gauss integration schemes, for the cracked interface contribution. It was found that cohesive crack segments subjected to a nonuniform opening in unstructured meshes (or an inclined crack in a structured finite element mesh) result in an unrealistic crack opening. The reasons for such behavior and its effect on the response at element level are discussed. Furthermore, a mesh refinement study is performed to analyze the overall response of a cohesively cracked body in a finite element analysis. Copyright © 2013 John Wiley & Sons, Ltd.