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。     

具有旋转自由度的广义协调矩形膜元

本文根据广义协调的思想,在平面应力矩形单元双线性协调位移场中,引入附加广义泡状位移场,构造出一种具有平面内旋转自由度的矩形膜单元,它满足广义协调条件。数值计算结果表明,这种单元有很高的计算精度,而且计算量少,是一种能收敛于精确解的单元。     

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．     

一个有效的厚薄板通用COONS曲面矩形元

本文采用板壳有限元Coons曲面法和挠度位移与转角位移导数相关构造法构造出一个有效的厚薄板通用矩形单元,并直接给出位移场形函数;其推导简单易行,灵活多样,几何意义直观,力学概念清晰,并具有一般性。在薄板极限情况下,本文厚薄板通用单元自动退化为一个性能良好的薄板Coons曲面矩形元,不出现剪切闭锁现象。数值计算表明:本文构造的厚薄板通用单元具有较高的计算精度和良好的收敛性。     

一个三角形广义协调薄板弯曲元

本文采用一点边协调方案^[1,2]构造了一个三角形广义协调薄板弯曲单元。此三角形单元具有自由度少,推导简明,列式简单等优点,且通过分片检验。数值算例表明本文单元是一个较高的精度、并保证收敛的新型薄板弯曲三角形元。可适用于实际工程计算。     

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。     

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。     

一个适合于复合材料层合板分析的应力杂交单元

本文根据修正的余能变分原理构造了一个适合于复合材料层合板特点的三角形单元。此单元能够考虑横向剪切变形的影响和局部扭曲效应。三角形单元的三个顶点取为节点,每个节点具有5个自由度,三个位移自由度,二个转角自由度。文中用此单元计算了几种层合板的固有频率,并将结果与解析解进行了比较。计算表明,此单元计算精度较高,应用方便。     

改进的有限元混合法用于板壳分析

本文从广义变分原理出发,给出了考虑横剪切变形板弯曲混合变分原理的具体形式,在Herrmann 三角形混合单元的基础上,导出了一个挠度按二次多项式、内力矩按线性分布的12个参数的三角形混合板元(×12单元)以及组合平面应力单元的三角形壳元。通过典型结构的分析计算,结果表明×12单元收敛速度快,计算精度高,位移和内力收敛速度比较协调一致,计算剪力方便。     

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。     

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。     

基于多变量小波有限元的一维结构分析

基于区间B样条小波(B-Spline Wavelet on the Interval, BSWI)和多变量广义势能函数,该文构造了二类变量小波有限单元,并用于一维结构的弯曲与振动分析。基于广义变分原理,从多变量广义势能函数出发,推导得到多变量有限元列式,并以区间B样条小波尺度函数作为插值函数对两类广义场变量进行离散。此单元的优势在于可以提高广义力的求解精度,因为在传统有限元中,只有一类广义位移场函数,所以广义力通常是通过对位移的求导得到,而多变量单元中,广义位移和广义力都是作为独立变量处理的,避免了求导运算。此外,区间B样条小波是现有小波中数值逼近性能非常好的小波函数,以它作为插值函数可进一步保证求解精度。转换矩阵的应用,可以将无任何明确物理意义的小波系数转换到相应的物理空间,方便了问题的处理。最后,通过数值算例对Euler梁和平面刚架的分析,验证了此单元的正确性和有效性。     

几何非线性广义协调三角形板单元

本文利用广义协调三角形板单元来分析任意形状弹性薄板的大挠度问题，根据广义协调三角形单元ＴＧＣ－９的位移模式，在Ｔ．Ｌ．．坐标系下给出了其几何非线性切线刚度矩阵的列式，通过对固支及简支方板、固支圆板及椭圆板的大挠度数值分析，验证了几何非线性广义协调板单元具有列式简单、精度高及收敛快的优点．     

Effect of the coupling between stretching and bending in the large displacement analysis of plates

The effect of the rotary inertia on the non-linear dynamics of plates that undergo a large reference displacement is examined in this paper. An assumed displacement field that accounts for the coupling between the stretching and bending of the plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate. Furthermore, the coupling between the stretching and bending of the plate as the result of finite rotation is also considered in this investigation. Based on the assumed displacement field that accounts for the effect of the rotary inertia, a non-linear finite element formulation is developed for the large displacement analysis of plates. The element equations of motion are expressed in terms of a set of element invariants that depend on the assumed displacement field as well as the rotary inertia. The use of the formulation presented in this paper is demonstrated using numerical examples.     

Finite elements with embedded displacement discontinuity: a generalized variable formulation

This paper is intended to bring a contribution towards a satisfactory simulation of those fracture phenomena which result in the appearance and development of discrete cracks. To this purpose, a general mixed finite element formulation is proposed, based on the concept of generalized variables in Prager's sense. The displacement field inside an element is modelled by the sum of two contributions: a regular (continuous) part which is governed by standard shape functions, and a possibly discontinuous one which is introduced soon after a suitable criterion is satisfied. The formulation is first specialized to a one‐dimensional case, then a triangular element for two‐dimensional problems is described in detail. Analytical and numerical examples are presented in order to clarify the formulation and to point out the essential role of inter‐element conformity. Copyright © 2000 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 3‐node C0 triangular element for the modified couple stress theory based on the smoothed finite element method

In this paper, a 3‐node C⁰ triangular element for the modified couple stress theory is proposed. Unlike the classical continuum theory, the second‐order derivative of displacement is included in the weak form of the equilibrium equations. Thus, the first‐order derivative of displacement, such as the rotation, should be approximated by a continuous function. In the proposed element, the derivative of the displacement is defined at a node using the node‐based smoothed finite element method. The derivative fields, continuous between elements and linear in an element, are approximated with the shape functions in element. Both the displacement field and the derivative field of displacement are expressed in terms of the displacement degree of freedom only. The element stiffness matrix is calculated using the newly defined derivative field. The performance of the proposed element is evaluated through various numerical examples.     

Non-singular symmetric boundary element formulation for elastodynamics

In this paper, a non-singular boundary element formulation for 3D-elastostatics and 3D-elastodynamics is presented. The proposed method is based on a generalized variational principle. A weighted superposition of static fundamental solutions is used for the field approximation in the domain, whereas the displacement and stress field on the boundary are interpolated by well-known polynomial shape functions. By separating time- and space-dependence a symmetric equation of motion is derived with time-independent mass and stiffness matrix. The domain integral over inertia terms, leading to the mass matrix, is analytically transformed to the boundary. Thus, a boundary only formulation is derived. Comparing numerical results with analytical solutions clearly shows that the obtained system of equations is well-suited for dynamic problems.