一种带有沙漏控制的新型EAS实体壳单元

基于 Hu-Washizu 变分原理推导了一种带有沙漏控制的实体壳单元的显式有限元列式;采用面内单点积分方案,提高了计算效率;同时引入沙漏控制力,抑制了沙漏现象.基于缩减积分方案,采用 B-bar 法消除体积自锁,并通过添加七个改善拟应变参数解决了泊松自锁和剪切自锁.采用改善拟应变法消除剪切自锁,使得表达式简洁.利用这种显式实体壳单元模型对3个非线性变形的标准算例进行了计算,并与相关参考文献和有限元软件 ABAQUS 的计算结果进行了比较.结果表明:该实体壳单元具有较高的计算精度,可有效地解决板壳非线性大变形分析问题,具有很好的工程应用前景.     

A URI 4-Node quadrilateral element by assumed strain

In this paper one-point quadrature ““““assumed strain““““ mixed element formulation based on the Hu-Washizu variational principle is presented. Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking. The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection, while the implementation of the proposed URI scheme is straightforward to suppress hourglass modes. In order to treat geometric nonlinearities simply and efficiently, a corotational coordinate system is used. Several numerical examples are given to demonstrate the performance of the suggested formulation, including nonlinear static/dynamic mechanical problems.     

适用于壳体h型自适应有限元分析的一组新单元

推导出一组适用于h型自适应分析的四边形蜕化壳元。对于大多数壳体结构,壳单元的刚度矩阵可分为薄膜、弯曲和剪切三部分。对薄膜部分本文采用杂交应力元方法进行设计,独立假设薄膜应力场以改善其精度;弯曲部分的刚度矩阵则依然由基于位移的应变来获得;而剪切部分则采用假设自然应变的方法来获得能克服薄壳下剪切自锁的新剪应变并用于计算此部...     

New mixed plate-bending elements with shear strain interpolations

This paper is concerned with two mixed plate-bending elements with shear strain interpolations, a quadrilateral element and an 8-node serendipity-type element based on discussions on the element proposed in Ref.[1]. The shear strains and inner-forces in the natural coordinates are interpolated in an element and then transformed into Cartesian coordinates in accordance with covariant and contravariant tensor transformations, respectively. The quadrilateral element coincides with the element in Ref.[1] when it is rectangular. Numerical examples show that the two new elements are free from shear locking and spurious kinematic modes under regular and irregular meshes and have the advantages of being insensitive to element distortion and able to give fairly accurate results.The Project supported by National Natural Science Foundation of China.     

带旋转自由度C^0类任意四边形板（壳）单元

基于Ｒｅｉｓｓｎｅｒ－Ｍｉｎｄｉｌｉｎ板弯曲理论和Ｖｏｎ－Ｋａｒｍａｎ大挠度理论,采用单元域内和边界位移插值一致性的概念,将四节点等参弯曲单元与Ａｌｌｍａｎ膜变形二次插值模式相结合,对层合板壳的大挠度分析提供了一种实用的带旋转自由度的四节点Ｃ＾０类板单元。大量算例表明：该单元对板壳结构的线性强度、稳定性和后屈曲分析都表现出良好的收敛性和足够的工程精度。     

一个不闭锁和抗畸变的四边形厚板元

构造一个彻底消除剪切闭锁现象并且对网格畸变不敏感的四边形厚薄板通用单元RPAQ。在方法上有三个特点：第一,在厚板挠度和转角的试函数中,采用了合理匹配方案,从而在源头上彻底消除了剪切闭锁现象;第二,采用四边形面积坐标,以代替通常的等参坐标,从而使网格畸变时仍然保持高精度;第三,采用广义协调元做法,使协调条件的采用灵活多样,并保证单元的收敛性。进行了一系列数值例题测试,表明单元RPAQ能自动消除闭锁现象,在由薄板到厚板的不同情况下,在各种网格畸变的情况下,都能体现出良好的精度和数值稳定性。     

一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发,并假设横向剪切应变在单元内线性变化,提出了一种考虑横向剪切变形的具有15个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度,计算效率高,可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

Geometrically non-linear analysis of laminated composite structures using a 4-node co-rotational shell element with enhanced strains

To demonstrate the solutions of linear and geometrically non-linear analysis of laminated composite plates and shells, the co-rotational non-linear formulation of the shell element is presented. The combinations of an enhanced assumed strain (EAS) in the membrane strains and assumed natural strains (ANS) in the shear strains improve the behavior of 4-node shell element. To secure computational efficiency in the incremental non-linear analysis, the present element uses the form of the resultant forces pre-integrated through the thickness. The transverse shear stiffness of the laminates is defined by an equilibrium approach instead of the shear correction factor. Numerical examples of this study show very good agreement with the references.     

Novel shear deformation model for moderately thick and deep laminated composite conoidal shell

This article presents a novel mathematical model for moderately thick and deep laminated composite conoidal shell. The zero transverse shear stress at top and bottom of conoidal shell conditions is applied. Novelty in the present formulation is the inclusion of curvature effect in displacement field and cross curvature effect in strain field. This present model is suitable for deep and moderately thick conoidal shell. The peculiarity in the conoidal shell is that due to its complex geometry, its peak value of transverse deflection is not at its center like other shells. The C¹ continuity requirement associated with the present model has been suitably circumvented. A nine-node curved quadratic isoparametric element with seven nodal unknowns per node is used in finite element formulation of the proposed mathematical model. The present model results are compared with experimental, elasticity, and numerical results available in the literature. This is the first effort to solve the problem of moderately thick and deep laminated composite conoidal shell using parabolic transverse shear strain deformation across the thickness of conoidal shell. Many new numerical problems are solved for the static study of moderately thick and deep laminated composite conoidal shell considering 10 different practical boundary conditions, four types of loadings, six different hl/hh (minimum rise/maximum rise) ratios, and four different laminations.     

一种考虑剪切变形的平行四边形厚/薄板通用单元

根据Timoshenko二广义位移梁理论，构造了深梁位移场的插值函数。利用斜坐标系与直角坐标系的变换关系、有限条带思想和深梁位移插值函数，构造了一种考虑剪切变形的平行四边形厚／薄板弯曲通用单元的位移(曲率、剪应变、转角、横向位移)插值函数，导出了刚度矩阵和非结点荷载等效力。并对简支阍支方板、Razzaque斜板、四边简支斜交板弯曲进行了数值计算。算例表明此单元有较好的精度，对于薄板不出现剪切闭锁，可适应于目前桥梁建设中大量采用的斜交板桥结构分析。     

基于有限条带的厚/薄板矩形通用单元

基于两广义位移梁理论,利用解析试函数来建立厚／薄梁单元的横向位移、转角位移、曲率、剪应变等位移模式,构造出厚／薄梁通用单元．应用有限条带,将厚／薄梁单元的位移模式应用于厚／薄板矩形弯曲单元,直接构造出单元的横向位移、转角、曲率、剪应变,导出了单元的刚度矩阵和结点等效力,编制了计算程序,进行了数值计算和比较,结果表明,所研究的单元不出现剪切闭锁且精度较好．     

Modified Mindlin plate theory and shear locking-free finite element formulation

The basic equations of the Mindlin theory are specified as starting point for its modification in which total deflection and rotations are split into pure bending deflection and shear deflection with bending angles of rotation, and in-plane shear angles. The equilibrium equations of the former displacement field are split into one partial differential equation for flexural vibrations. In the latter case two differential equations for in-plane shear vibrations are obtained, which are similar to the well-known membrane equations. Rectangular shear locking-free finite element for flexural vibrations is developed. For in-plane shear vibrations ordinary membrane finite elements can be used. Application of the modified Mindlin theory is illustrated in a case of simply supported square plate. Problems are solved analytically and by FEM and the obtained results are compared with the relevant ones available in the literature.     

饱和多孔介质中的混合有限元法和有限应变下应变局部化分析

对基于Biot理论的饱和多孔介质中动力-渗流耦合分析提出了一个耦合场混合元．固相位移、应变和有效应力以及流相压力、压力梯度和Darcy速度在单元内均处理为独立变量分别插值．基于胡海昌-Washizu三变量广义变分原理给出的饱和多孔介质动力-渗流耦合问题控制方程的单元弱形式,导出了单元公式．进一步导出了考虑压力相关非关联塑性的非线性单元公式和发展了相应的一致性算法．对几何非线性分析,采用了共旋公式途径．数值结果例题显示所发展耦合场混合元模拟大应变下由应变软化引起以应变局部化为特征的渐进破坏现象的性能．     

Some results for approximate strain and rotation tensor formulations in geometrically non-linear Reissner-Mindlin plate theory

Finite element deflection and stress results are presented for four flat plate configurations and are computed using kinematically approximate (rotation tensor, strain tensor or both) non-linear Reissner-Mindlin plate models. The finite element model is based on a mixed variational principle and has both displacement and force field variables. High order interpolation of the field variables is possible through p-type discretization. Results for some of the higher order approximate models are given for what appears to be the first time. It is found that for the class of example problems examined, exact strain tensor but approximate rotation tensor theories can significantly improve the solution over approximate strain tensor models such as the von Kármán and moderate rotation models when moderate deflections/rotations are present. However, for each of the problems examined (with the exception of a postbuckling problem) the von Kármán and moderate rotation model results compared favorably with the higher order models for deflection magnitudes which could be reasonably expected in typical aeroelastic configurations.