壳体结构非线性分析的扁壳有限元法

用单位纵横向曲条条带法构造了扁壳单元的空间位移模式,依据拖带坐标描述去Ｓ－Ｒ分解定理,志出扁壳结构几何非线性分析的有限单元Ｕ．Ｃ．（ｕｐｄａｔｅｄ ｃｏ－ｍｏｖｉｎｇ ｃｏｏｒｄｉｎａｔｅ）列式,算例表明,该计算方法精度高,收敛性好。     

板壳非线性问题的曲壳有限单元法

本文基于总体Lagrange坐标描述法,采用Kirchhoff应力张量定义和Green应变张量定义,导出了分析板壳非线性问题的曲壳有限单元法。通过引入新的单元几何非线性关系,本文方法可用于分析板壳的大挠度大转角情况。由于采用了材料本构关系的修正子增量形式,提高了有限单元的分析计算精度。本文采用增量—拟牛顿—子增量迭代技术求解板壳的荷载一位移曲线,与传统迭代方法相比大大提高了计算效率。此外,对于板壳任意边界条件的形成和任意初始形状的考虑问题,本文分别导出了罚单元法和局部坐标转换法予以处理。经计算比较,证明本文方法可以有效地用于板壳的弯曲、屈曲及屈曲后性态和极限强度等问题的非线性分析。     

一种有效的厚薄板壳单元

对于厚薄板壳分析提出了一种有效的拟协调位移型三角型单元。采用Ｍｉｎｄｌｉｎ变形假定，在横向剪切刚度项中引入特殊的罚函数，有效地解除了剪切闭锁和抑制了零能模式，并扩大了对跨厚比的适用范围，计算精度也明显提高。文中给出了各种材料和形状板壳的线性和非线性分析。     

基于混合变量的脱层壳屈曲分析

提出一种分析脱层圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于一阶剪切理论，通过定义广义位移变量和对应的广义力变量，建立壳的改进的混合变量能量泛函；然后引入条形单元，对混合变量在环向进行离散，从而导出超级壳单元的混合变量能量泛函，由变分原理得到控制方程，采用传递函数方法得到其形式解；最后，将含环向贯穿脱层的复合材料层合壳作为超级壳单元的组合体，得到脱层壳的屈曲方程。给出了脱层大小和深度以及脱层壳边界条件对屈曲载荷的影响。     

四节点二十四自由度平板壳单元几何刚度矩阵显式解析式的推演算法研究

几何刚度矩阵的推演是结构几何非线性有限元分析的重点和难点之一。推导几何刚度矩阵显式解析表达式成为简化非线性有限元列式,提高分析效率的关键。本文在协同转动法框架下,基于刚体运动法则对四节点二十四自由度的平板壳单元几何刚度矩阵显式解析式进行了推导和讨论;分析了悬臂梁大转动、不同壁厚条件下简支圆柱形屋顶空间大变位两个经典算例。研究结果表明：（1）几何刚度矩阵的显式计算公式不仅为板壳结构几何非线性列式提供了方便而且具有良好的精度;（2）推导的几何刚度矩阵适用于各类型四边形二十四自由度平板壳单元模型;（3）与数值积分相比,采用解析形式的几何刚度矩阵可以显著提高非线性响应计算效率。     

基于混合变量条形传递函数方法的圆柱壳屈曲分析

提出了一种分析交各向异性圆柱壳和阶梯圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Fluegge薄壳理论，通过定义广义位移变量和对应的广义力变量，建立了圆柱壳混合变量能量泛函；然后通过引入条形单元，定义混合状态变量和采用传递函数方法对超级壳单元求解，得到具有多种边界条件圆柱壳屈曲问题的半解析解；最后通过位移连续和力平衡条件，可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。     

基于渐近传递函数解的截锥壳单元

普通截锥壳单元是分析旋转壳结构的常用单元,但应力计算的精度较差;而渐近传递函数解在圆锥壳的应力分析方面具有很高的计算精度。本文针对一般截锥壳单元应力计算精度不高的缺点,将传递函数法与有限元法进行结合,以圆锥壳的渐近传递函数解为插值函数,直接构造了一种高精度的截锥壳单元,该单元位移插值模式满足相容性和完备性要求,并具有力学概念清楚、计算精度高等特点。数值算例表明,采用该单元进行圆锥壳的内力和自由振动     

板壳有限变形精确理论及有限元列式

以位移型退化壳理论为基础,提出了板壳模型的有限变形精确理论,该理论引入转动伪矢量概念,充分发挥刚性线段的运动学模型和有限转动矩和作用,精确表达非线性位移－应变关系,抛弃以往的小位移、小应变、小转动增量乃至小加载小长等各种简化假设,并严格遵循能量共轭关系建立有限元平衡方程,能够可靠和有效地用于板壳结构的大位移、大转动分析。算例表明,该文列式在弹性范围内具明显的平方收敛效率,并且计算结果与加载步长无关。由于不受小加载步长、小转动增量等的限制,实现了板壳几何非线性问题的大步长加载。     

几何非线性对旋转园柱壳振动特性的影响

本文动用有限元法，采用九结点超参数壳单元计算放置园柱壳的振动特性，考虑了横向剪切以及轴向变形的影响。对于旋转园柱壳达到平衡位置以前的状态，用大变形非线笥板壳理论处理，并假设园柱壳在平衡位置附近作微振动，建模中考虑了科氏力，离心力，初应力以及由大变形引起的几何非线性的影响，通过对一个一固定一端自由的旋转园柱壳在考虑和不考虑大变形几何非线性这两种情况下的比较，阐明了在高速时大变形下几何一性对旋转壳的固     

曲厚壳单元在斜板拱桥分析中的应用

介绍了利用曲厚壳单元对斜板拱桥进行空间受力分析,并将曲厚壳单元所得结果与采用实体单元分析的结果和模型实验所得结果进行了比较,证明利用曲厚壳单元来分析斜板拱桥是行之有效的。     

On the stability analysis of plates and shells using a quadrilateral, 16-degrees of freedom plat shell element DKQ16

The linear buckling problems of plates and shells were analysed using a recently developped quadrilateral, 16-degrees of freedom flat shell element ( called DKQ16 ). The geometrical stiffness matrix was established. Comparison of the numerical results for several typical problems shows that the DKQ16 element has a very good precision for the linear buckling problems of plates and shells.     

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。     

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.     

Phenomenological invariants and their application to geometrically nonlinear formulation of triangular finite elements of shear deformable shells

A phenomenological definition of classical invariants of strain and stress tensors is considered. Based on this definition, the strain and stress invariants of a shell obeying the assumptions of the Reissner–Mindlin plate theory are determined using only three normal components of the corresponding tensors associated with three independent directions at the shell middle surface. The relations obtained for the invariants are employed to formulate a 15-dof curved triangular finite element for geometrically nonlinear analysis of thin and moderately thick elastic transversely isotropic shells undergoing arbitrarily large displacements and rotations. The question of improving nonlinear capabilities of the finite element without increasing the number of degrees of freedom is solved by assuming that the element sides are extensible planar nearly circular arcs. The shear locking is eliminated by approximating the curvature changes and transverse shear strains based on the solution of the Timoshenko beam equations. The performance of the finite element is studied using geometrically linear and nonlinear benchmark problems of plates and shells.     

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.     

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。     

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.     

Nonlinear Dynamics of Shells: Theory,Finite Element Formulation,and Integration Schemes

The paper is concerned with a dynamical formulation of a recently established shell theory capable to catch finite deformations and falls within the class of geometrically exact shell theories. A basic aspect is the design of time integration schemes which preserve specific features of the continuous system such as conservation of momentum, angular momentum, and energy when the applied forces allow to. The integration method differs from the one recently proposed by Simo and Tarnow in being applicable without modifications to shell formulations with linear as well as nonlinear configuration spaces and in being independent of the nonlinearities involved in the strain-displacement relations. A finite element formulation is presented and various examples of nonlinear shell dynamics including large overall and chaotic motions are considered.