一种薄壳厚壳通用的轴对称曲壳单元

有限元法分析轴对称壳体时，常需区分薄壳和厚壳并选用不同的单元，给计算带来不便．为此，通过对现有的轴对称壳体单元的研究，基于加权残值法，将广义协调条件引入剪应变场，构造了一种挠度和转角各自独立的新型轴对称曲壳单元．算例结果表明，新单元具有很高的精度，既可用于厚壳，也可用于薄壳．该单元可用于轴对称壳体结构的计算分析．     

复合材料回转壳的有限元级数解

本文用有限元法和Fourier级数展开技术求解复合材料回转壳体在各种荷载作用下的弯曲问题,文中利用回转壳在几何上的轴对称性质,将各物理量在环向展开为Fourei级数,而在母线和壳厚方向分割单元,所采用的单元为6节点18自由度等参元,它考虑了剪切变形和挤压变形的影响,能计算厚度方向的挤压应力,数值算例表明,本文提出的单元性能优良,算法稳定收敛。     

用正交曲线坐标系中的曲壳单元分析旋转壳的自由振动

本文采用正交曲线坐标系中考虑横向剪切变形的双曲旋转壳单元,对几种不同类型的旋转壳的自由振动进行了分析。为了计算封闭和半封闭的旋转壳,本文用半解析法,由位移连续条件导出旋转壳顶点的两类位移限制条件,并通过结圆自由度的变换,将其转换为齐次形式。当壳体的经线有折角时,我们采用模态综合法分析它的固有振动特性。     

一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

正交曲线坐标中的曲壳单元

本文建立了正交曲线坐标中的曲壳单元。采用这种单元不仅使程序简化,使输入输出方便,而且由于能较好地拟合壳体曲面的真实形状,并在厚度方向直接积分,从而节省了机时并能提高精度。     

线性变厚度圆锥壳扭转振动的弹性力学理论解

本文给出线性变厚度圆锥壳轴对称扭转振动的弹性力学理论解,探讨壳体的无剪扭振和剪切扭振,揭示了圆锥壳在厚度方向剪切、母线方向扭转的耦合振动特性。这些性质用经典壳理论是无法反映的。文末算例用许多数据表和曲线图描述变厚度圆锥壳的周有频率和振型。     

双曲率壳的力学研究进展

双曲率壳是飞机、汽车以及船舶上常见的薄壁结构，其中性面可看作是一条动曲线沿着另一条曲线扫掠所形成的曲面．双曲率壳的非线性理论不断更新推动着双曲率壳力学行为的研究．随着工程实际应用的不断改进，如功能梯度材料(FGM)，加筋壳，弹性地基模型等的引入，双曲率壳在强度、变形和稳定性等方面的研究得到了进一步促进．本文首先回顾了双曲率壳结构非线性力学基本理论发展过程，主要阐述了经典的二维板壳理论，如Donnell 薄壳理论，一阶剪切变形壳理论，高阶剪切变形壳理论，和三维板壳理论的理论体系及基本公式，并对几种理论之间的联系和应用进行了总结和讨论，简述了近几十年来国内外学者在双曲率壳非线性弯曲、稳定性和振动等方面的最新研究成果，最后对双曲率壳体研究目前的局限性和未来的研究方向进行了探讨．     

宏纤维压电层合壳结构非线性屈曲分析

以纤维压电MFC （Micro-Fiber Composite）层合圆柱壳为例,研究了其在准静态屈曲下的非线性振动响应。基于Reissner-Mindlin一阶剪切变形假设,采用大转角几何全非线性理论,建立了带有纤维角度的MFC层合壳结构的非线性屈曲与振动分析模型。采用全拉格朗日方程（Total Lagrange Formulation）对非线性模型进行线性化处理,并结合Riks-Wempner弦长控制迭代法进行准静态求解,然后在每个解点进行自由振动分析。通过与文献数据对比验证了所建模型的准确性。并用该计算模型对MFC-d31层合圆柱壳进行屈曲及自由振动分析,研究了几何参数（曲率、厚度、纤维角度和不同外加电压）对频率的影响。结果表明,厚度、曲率和纤维增强角度对结构的临界载荷有显著的影响,且结构的临界载荷随着上述参数的增大而增大;电场强度可对不同纤维角度壳体的自振频率进行调节,能够提高结构的临界载荷;纤维角度越大,电压对结构自振频率调节的效果越明显。     

复合材料层合圆柱壳的有限元分析

本文根据Reissner-Mindlin型的全局位移场(一阶和三阶)，应用有限元预测一修正法，数值计算和分析了机械载荷作用下复合材料层合圆柱壳的挠度和横向剪应力。首先按照一般的有限元分析过程(没有引入剪切修正系数)计算出层合圆柱壳的挠度预测值；然后利用Lagrange插值构造横向剪应力的一般形式，使得满足层间连续和表面上为零的条件，通过最小二乘法拟合三维应力平衡方程获得横向剪应力；最后在单元上计算和引入剪切修正系数，再经过有限元分析计算出层合圆柱壳的挠度修正值。数值计算结果与三维线弹性解的比较表明，挠度修正值和横向剪应力的精度是十分满意的。     

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.     

Three dimensional degenerated shell theory and assumed strain shell elements

In this paper Reissner-Mindlin plate theory is extended to cater for curved shell structures. It can be considered as Reissner-Mindlin type shell theory. From this theory, the C(O) continuity formulation of shell elements of taking account the transverse shear deformation could be derived directly. These degenerated shell elements have been widely employed. To overcome the locking of shear and membrane and avoid zero energy modes the author proposed the formulation of the new elements with assumed strains. A wide range of numerical tests was conducted and the results illustrate that the assumed strain elements possess high accuracy and good performance.     

Triangular elements for Reissner-Mindlin plate

I-IntroductionInrecentyearsmuchresearchefforthasbeenspentonthedevel0pmentofreliableandefficientplateelementsbasedonReissner-Mindlintheory.Adifficultyisthelockingbehaviorexhibitedasl- 0(tisthethicknessoftheplate)forlowerorderc'elements.BasedonTaylorexpendi…     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures

The first-order shear deformation moderate rotation shell theory of Schmidt and Reddy [R. Schmidt and J. N. Reddy, J. Appl. Mech. 55, 611–617 (1988)] is used as a basis for the development of finite element models for the analysis of the static, geometrically non-linear response of anisotropic and laminated structures. The incremental, total Lagrangian formulation of the theory is developed, and numerical solutions are obtained by using the isoparametric Lagrangian 9-node and Serendipity 8-node shell finite elements. Various integration schemes (full, selective reduced, and uniformly reduced integration) are applied in order to detect and to overcome the effects of shear and membrane locking on the predicted structural response. A number of sample problems of isotropic, orthotropic, and multi-layered structures are presented to show the accuracy of the present theory. The von Kármán-type first-order shear deformation shell theory and continuum 2D theory are used for comparative analyses.     

十六结点四十自由度相对位移板壳单元

本文从三维弹性理论出发,构造了一个新的能很好反映横向剪切变形影响的十六结点四十自由度等参板壳元。为克服直接引用三维公式系统所造成的数值方面的困难,引入了相对位移。对于曲壳单元,采用正交曲线坐标系,大大加快了计算速度。算例表明,新单元与八结点四十自由度厚壳单元有相同的精度。由于新单元由三维单元退化而成,它便于与三维单元连接,便于计算变厚度壳。     

用于超弹性分析的高效杂交应变--EAS固体壳单元的研究

提出了一个用于橡胶材料分析的弱变分方程，基于一个可压缩Neo—Hookean模型，将EAS模式和杂交元法有机地结合起来，推导了一个高效、稳定的杂交应变——EAS固体壳单元，通过巧妙地选择应交插值函数和本文中提出的一个精化措施，克服了橡胶材料所表现出的大应变超弹性本构为杂交元正交化法的实施所带来的困难，保证了整个单元列式都仅采用低阶高斯积分，显著提高了计算效率，确保橡胶材料不可压缩性计算的顺利进行，并克服了固体壳元的厚度自锁问题。     

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。     

Locking-Free Degenerated Isoparametric Shell Element

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A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates

A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap(DSG) method, is formulated based on the global coordinate for analysis of Reissner–Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices,which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner–Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.     

Large rotations in first-order shear deformation FE analysis of laminated shells

The paper deals with the geometrically non-linear analysis of laminated composite beams, plates and shells in the framework of the first-order transverse shear deformation (FOSD) theory. A central point of the present paper is the discussion of the relevance of five- and six-parameter variants, respectively, of the FOSD hypothesis for large rotation plate and shell problems. In particular, it is shown that the assumption of constant through-thickness distribution of the transverse normal displacements is acceptable only for small and moderate rotation problems. Implications inherent in this assumption that are incompatible with large rotations are discussed from the point of view of the transverse normal strain-displacement relations as well as in the light of an enhanced, accurate large rotation formulation based on the use of Euler angles. The latter one is implemented as an updating process within a Total Lagrangian formulation of the six-parameter FOSD large rotation plate and shell theory. Numerical solutions are obtained by using isoparametric eight-node Serendipity-type shell finite elements with reduced integration. The Riks-Wempner-Ramm arc-length control method is used to trace primary and secondary equilibrium paths in the pre- and post-buckling range of deformation. A number of sample problems of non-linear, large rotation response of composite laminated plate and shell structures are presented including symmetric and asymmetric snap-through and snap-back problems.