各向异性弹塑性中厚度板壳的有限元分析

本文在文献〔２，３〕的基础上，提出了一个解各向异性弹塑性中厚度板壳问题的有限元方法。考虑材料各向异性的特点，采用了Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应；为了避免“自锁”现象，文中采用了９节点的Ｈｅｔｅｒｏｓｉｓ二次壳单元；特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了确定变形路径的计算效率。几     

板壳弹塑性屈曲的有限元分析

1 拟协调双曲壳单元为解决板壳有限元分析的C~1连续性问题,本文给出三角形拟协调双曲扁壳单元的刚度矩阵.拟协调单元是基于域内假设应变场和边界拟协调位移场,应用最小势能原理所构     

弹塑性板壳结构非线性有限元分析

本文根据塑性流动理论的基本公式，由隐式积分导出了与路径无关的变量更新算法和一致切线模量。采用单元广义应力应变直接离散塑性流动定律，构造了杂交应力单元一致切线刚度矩阵的显式表达式，编制了结构有限元程序ＳＡＦＥ，数值算例表明：本文的计算方法和计算程序是正确可靠的，可用于弹塑性板壳结构的非线性分析，计算结果屈曲临界载荷和极限承载能力。     

正交各向异性板壳的弹塑性分析

用最小二乘配点法对正交各项异性薄板和双曲扁壳的弹性问题进行了分析.文中采用Huber—Mises屈服函数在各向异性问题中的推广形式,把材料的塑性变形作为等效塑性荷载处理,并取双五次样条函数为位移试函数,推出了迭代公式.算例证明,该法精度高、收敛快,所需计算机内存少,是简单、精确、高效的.     

板壳结构弹塑性稳定性的有限元分析

构造了20参数圆柱壳拟协调单元,同时采用分层模型的弹塑性稳定性分析.根据塑性屈曲的Stowell形变理论,用基于切线刚度矩阵的增量法和修正的Newton-Raphson方法,计算屈曲前的弹塑性内力分布,并用逆幂迭代法求解弹塑性屈曲荷载.     

板壳弹塑性分析的加权残数法

本文采用双五次B一样条函数为位移试函数,由最小二乘配点法导出了板和双曲扁壳弹塑性分析的增量形式的基本计算公式,然后用变步长增量加载和初应力法求解,用一系列弹性解的总和来逼近准确解。文中给出了若干算例,计算表明:该法收敛稳定,敛速快,精度高,同时输入数据极少,比有限元法简便、经济、高效,且可以在微机上实现。     

组合壳体的弹塑性有限元分析

本文采用文[1]提出的曲壳单元,根据Prandtl-Reuss塑性流动理论和Mises等向强化屈服准则,建立了壳体的弹塑性有限元格式,同时按照罚单元原理建立了组合壳体的连接条件,编制了相应的计算程序,具体计算了带接管球壳和等径三通等算例,取得了较好的结果。     

考虑损伤效应的正交各向异性板的弹塑性静动力分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程.基于经典Kirchhoff板理论,获得了正交各向异性薄板的增量型运动控制方程,且采用有限差分法和迭代法进行求解.数值算例中,讨论了损伤演化、外载荷参数等因素对正交各向异性薄板弹塑性静动力性质的影响,数值结果表明,考虑结构的损伤和损伤演化时,结构的力学性质将发生显著的变化.     

一种混合变量板壳有限元的新算法

1、介绍本文的工作在于发展了一种计及几何和物理非线性及材料各向异性的9节点Lagrangian 混合变量板壳元,它建立在文[1]推导的广义变分原理基础上.对文[2]提出的处理混合元的方法作改进,提出一种新算法,使得可以理论上较合理地使用统一“减阶”积分法则.考虑到在物理及几何非线性情况下数值积分点减少会很大地减少计算量.因此,本方法的使用使混合元计算量大的缺点有了很大改善.此法被归结为“独立应变补偿”的新概念.它不同于“零能模式约束”或“秩补偿”概念,在理论和实践上都有自己的特点.2、“自然”应变混合变量板壳元的新算法     

应用平板壳单元DKQl6分析板壳结构的几何非线性

应用新近开发的四边形十六自由度离Kirchhoff平板壳单元DKQl6，分析了板壳结构的几何非线性问题，采用Total Lagrange格式，在小应交、中等转动的假定下，建立了该单元几何刚度阵和大位移矩阵．非线性方程采用位移引导或弧长引导的牛顿-拉夫森增量迭代法求解．讨论了网格和加载步效对收敛性的影响，通过对典型算例的计算以及与其它单元的比较，说明了DKQl6单元在板壳结构几何非线性分析中也有良好的精度．     

复合材料层合厚板锯齿理论及有限元分析

对于较厚复合材料弯曲问题,已有锯齿型厚板理论最大误差超过35%。为了合理地分析较厚复合材料弯曲问题,发展了准确高效的锯齿型厚板理论。此理论位移变量个数独立于层合板层数,其面内位移不含有横向位移一阶导数,构造有限元时仅需C0插值函数,故称此理论为C0型锯齿厚板理论。基于发展的锯齿理论,构造了六节点三角形单元并推导了复合材料层合/夹层板弯曲问题有限元列式。为验证C0型锯齿厚板理论性能,分析了复合材料层合/夹层厚板弯曲问题,并与已有C1型锯齿理论对比。结果表明,本文的C0型锯齿厚板理论最大误差15%,比已有锯齿型厚板理论准确高效。     

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.     

A potential-hybrid/mixed finite element scheme for analysis of plates and cylindrical shells

Based on the potential-hybrid/mixed finite element scheme,4-node quadrilateralplate-bending elements MP4,MP4a and cylindrical shell element MCS4 are derived with,the inclusion of splitting rotations.All these elements demonstrate favorable convergencebehavior over the existing counterparts,free from spurious kinematic modes and do notexhibit locking phenomenon in thin plate/shell limit.Inter-connections between the existingmodified variational functionals for the use of formulating C~0-and C~1-continuous elementsare also indicated.Important particularizations of the present scheme include Prathap’sconsistent field formulation,the RIT/SRIT-compatible displacement model and so on.     

General non-linear finite element analysis of thick plates and shells

A non-linear finite element analysis is presented, for the elasto-plastic behavior of thick shells and plates including the effect of large rotations. The shell constitutive equations developed previously by the authors [Voyiadjis, G.Z., Woelke, P., 2004. A refined theory for thick spherical shells. Int. J. Solids Struct. 41, 3747–3769] are adopted here as a base for the formulation. A simple C⁰ quadrilateral, doubly curved shell element developed in the authors’ previous paper [Woelke, P., Voyiadjis, G.Z., submitted for publication. Shell element based on the refined theory for thick spherical shells] is extended here to account for geometric and material non-linearities. The small strain geometric non-linearities are taken into account by means of the updated Lagrangian method. In the treatment of material non-linearities the authors adopt: (i) a non-layered approach and a plastic node method [Ueda, Y., Yao, T., 1982. The plastic node method of plastic analysis. Comput. Methods Appl. Mech. Eng. 34, 1089–1104], (ii) an Iliushin’s yield function expressed in terms of stress resultants and stress couples [Iliushin, A.A., 1956. Plastichnost’. Gostekhizdat, Moscow], modified to investigate the development of plastic deformations across the thickness, as well as the influence of the transverse shear forces on plastic behaviour of plates and shells, (iii) isotropic and kinematic hardening rules with the latter derived on the basis of the Armstrong and Frederick evolution equation of backstress [Armstrong, P.J., Frederick, C.O., 1966. A mathematical representation of the multiaxial Bauschinger effect. (CEGB Report RD/B/N/731). Berkeley Laboratories. R&D Department, California.], and reproducing the Bauschinger effect. By means of a quasi-conforming technique, shear and membrane locking are prevented and the tangent stiffness matrix is given explicitly, i.e., no numerical integration is employed. This makes the current formulation not only mathematically consistent and accurate for a variety of applications, but also computationally extremely efficient and attractive.     

A finite element formulation for analysis of functionally graded plates and shells

Summary A finite element formulation is derived for the thermoelastic analysis of functionally graded (FG) plates and shells. The power-law distribution model is assumed for the composition of the constitutent materials in the thickness direction. The procedure adopted to derive the finite element formulation contains the analytical through-the-thickness integration inherently. Such formulation accounts for the large gradient of the material properties of FG plates and shells through the thickness without using the Gauss points in the thickness direction. The explicit through-the-thickness integration becomes possible due to the proper decomposition of the material properties into the product of a scalar variable and a constant matrix through the thickness. The nonlinear heat-transfer equation is solved for thermal distribution through the thickness by the Rayleigh-Ritz method. According to the results, the formulation accounts for the nonlinear variation in the stress components through the thickness especially for regions with a variation in martial propperties near the free surfaces.     

中厚板统计分析的随机边界元法

本文建立了分析含随机材料参数并具厚度不均匀性的中厚板问题的随机边界元法,基于Taylor级数展开技术,分析和到广义位移的均值和一阶偏差的积分方程,其中将材料参数的随机性和厚度的不均匀性作为等效荷载处理,从而得到广义边界位移或面力的均值和协方差,并进一步求出部点广义位移和内力的均值和协方差,最后用本文方法计算了两个数例,并对所得结果进行了分析,探讨。     

Variational principles of perforated thin plates and finite element method for buckling and post-buckling analysis

On the basis of the general theory of perforated thin plates under large deflections^{[1, 2]}, variational principles with deflectionw and stress functionF as variables are stated in detail. Based on these principles, finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated, owing to the multiple connexity of the region. Project supported by National Natural Science Foundation of China.     

板壳畸变单元的无网格和有限元自动耦合方法

板壳大变形时单元的严重畸变会使计算精度降低。无网格局部Petrov-Galerkin法是一种真正的无网格方法,能够消除网格畸变,但比有限元法计算效率低。根据板壳网格畸变的局部性特点,利用过渡单元法,基于板壳网格质量,建立了板壳的网格严重畸变区域由有限元分析切换为无网格分析的自动耦合算法,实现了有限元法和无网格局部彼得罗夫．迦辽金法的耦合。应用实例表明：通过自适应耦合,既能发挥有限元法计算效率高的特点,又能发挥无网格法适合大变形分析、没有网格畸变造成计算困难的特点。