弹塑性结构安定下限分析的无网格局部

将基于Voronoi结构的无网格局部Petrov-Galerkin法与减缩基技术相结合,建立了一种安定下限分析的新方法．为了克服移动最小二乘近似难以准确施加本质边界条件的缺点,采用了自然邻近插值构造试函数.通过引入基准载荷域上载荷角点的概念,消除了安定下限分析中由时间参数所引起的求解困难．利用减缩基技术,将安定分析问题化为一系列未知变量较少的非线性规划子问题．在每个非线性规划子问题中,自平衡应力场由一组带有待定系数的自平衡应力场基矢量的线性组合进行模拟,而这些自平衡应力场基矢量可应用弹塑性增量分析中的平衡迭代结果得到．算例结果证明了提出的分析方法的有效性．      

轴对称热冲击SIF过渡过程分析的热权函数法

热权函数法利用温度与热权函数的乘积的积分来直接计算热冲击过程中裂纹尖端的应力强度因子过渡过程。热权函数与时间τ无关,由于免除了对每一时刻τ所需作的有限元或边界元分析,计算过程大大简化,计算效率得到极大提高,本文将热权函数与有限元法直接耦合,给出了基于刚度阵导数法的轴对称问题的热权函数计算格式,实例计算表明,本文给出的热权函数计算格式具有满意的计算精度。     

轴对称热传导有限元格式

分析了目前一些有限元专著中轴对称热传导有限元方法推导中的问题,给出了轴对称热传导有限元格式的正确表达形式。     

旋转壳及附属结构应力分析软件系统

本文概述了近年来旋转壳应力分析软件系统的一些最新发展。它主要是结合电力建设中超大、超高冷却塔设计和施工中提出的壳筒、离散支柱的整体静力分析及抗震研究，不均匀地基及其沉陷，大塔稳定性，离散支柱局部缺断后的壳体应力分布等力学问题，通过新单元的开发和新算法的数值实现两个方面的工作，在文［１］的基础上，开发了一个旋转壳及附属结构应力分析软件系统．近年来这个系统对一些工程的实际应用表明，它是有效可靠的．     

基于自然单元法的轴对称结构极限上限分析

自然单元法是一种以自然邻近插值为试函数的新兴无网格数值方法,其形函数的计算不涉及矩阵求逆,也不需要任何人为参数。为了充分发挥自然单元法的优势,本文基于极限分析上限定理建立了轴对称结构极限上限分析的整套求解算法。轴对称结构的位移场由自然邻近插值构造,并且采用罚函数法处理材料的不可压条件。为了消除目标函数非光滑所引起的数值困难,采用逐步识别刚性区和塑性区,并对两者用不同方法进行处理。数值算例结果表明,本文提出的轴对称结构极限上限分析方法是行之有效的。     

F E M analysis of delamination buckling in composite plates and shells

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A geometrically nonlinear analysis of rotational shells using B-spline function

In this paper, based on the nonlinear thin shell theory, a geometrically nonlinear formulation using the total Lagrangian approach for rotational shells, as well as rotational shells on the Winkler-type elastic foundation, is presented. The displacements of the middle surface are approached by a B-spline function. All nonlinear terms of membrane strains are reserved. Two cases in which the arc length as well as ordinate is used as the coordinate parameter along meridional direction are discussed at the same time.The project supported by National natural Science Foundation of China.     

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。     

New axisymmetric solid elements based on an extended Hellinger-Reissner principle

4-node incompatible axisymmetric hybrid stress elements are developed by a modified rational approach based on an extended Hellinger-Reissner principle. The stress fields are derived by using the constraint conditions that the equilibrium equations of higher order stress terms are imposed in a variational sense through the additional incompatible displacements. The resulting elements enjoy good performance in bending problems and at the nearly incompressible limit. Several examples are given to demonstrate the performance of the new elements. The project supported by the National Natural Science Foundation of China     

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。     

非协调元在复合材料安定下限分析中的应用

采用应力函数法,结合均匀化理论和应变法,在细观层次上研究了复合材料的极限和安定分析,获取复合材料代表性体积元在载荷加载历史未知下的容许承载域。利用8节点非协调等参元离散结构,获取弹性应力场和自平衡残余应力场,建立复合材料在细观层次上安定下限的优化格式。在满足计算精度的同时,大大降低了优化规模。以周期性纤维增强金属基复合材料为例,验证了该单元在安定下限分析中的有效性和可靠性。     

求解轴对称结构侧向冲击响应的一种快速算法

轴对称结构在侧向冲击载荷下的动力响应分析,一般采用解析、半解析法或者直接进行有限元数值模拟,这些方法均有一定的局限性.本文依据线性动力学问题的叠加原理,提出了一种基于有限元分析和线性叠加的快速算法.该方法首先采用多条母线对载荷进行离散,然后采用有限元计算结构在单个"载荷单元"作用下的动力响应,最后采用坐标旋转和线性叠加的方法计算得到结构在复杂分布载荷作用下的响应.算例表明,本文提出的算法是正确、有效的,并且具有快速、简便、灵活的特点.     

A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS‐G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start‐up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd‐B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd.     

极限分析和安定分析的并行算法

本文基于结构极限分析和安定分析的温度参数法，研究了线性规划的并行算法，温度参数法求解的关键是线性规划的求解效率，在分布式布储的多处理机系统上，采用了线性规划的分块单纯形法。对相当于大量工况的结构，子结构是一个很好的并行结构分析方法。     

基于约束函数法的热力耦合有限元分析

分析了滑移接触条件下热力耦合现象,建立了热力耦合的有限元分析连续模型,提出了系统动力学平衡方程和热力学平衡方程。对系统中物体间的接触条件进行了分析,得到了物体间接触条件的数学表达式,在此基础上,用约束函数表示接触约束条件。应用变分原理对约束函数进行变分,与系统平衡方程组成非线性方程组对热力耦合问题进行求解。实例表明,用约束函数法求解热力耦合问题,收敛性较好,算法稳定,计算结果能反映实际。     

基于正交基无单元Galerkin法和非线性规划的安定分析方法

基于安定分析的下限定理,用正交基无单元Galerkin法建立了交交载荷作用下理想弹塑性结构安定分析的下限计算格式.在给定载荷域的载荷角点所对应的载荷作用下,采用正交基无单元Galerkin法计算相应的虚拟弹性应力场.并且利用结构在正交基无单元Galerkin法弹塑性增量分析中平衡迭代结果计算得到自平衡应力场基矢量,然后由这些基矢量的线性组合模拟自平街应力场.安定分析问题最终被归结为一系列未知变量较少的非线性数学规划子问题,通过复合形法求解.算例表明该方法的计算结果是令人满意的,并且对初始复合形顶点和用于构造自平衡应力场基矢量的载荷增量是非常不敏感的.     

A modified basis reduction method for limited kinematic hardening shakedown analysis under complex loads

A novel extension of the basis reduction method for kinematic hardening shakedown problem is presented. Firstly, the basis reduction method is implemented based on the modified Newton–Raphson (N-R) method. Then a new technique for the construction of back stress field is introduced, where the simultaneous influence of multiple load corners in shakedown is taken into consideration. Finally, two typical numerical examples are investigated. The results compared with previous works in literatures demonstrated that the proposed method is accurate and the performance in reducing of computation time is significant.     

A class of Wilson arbitrary quadrilateral elements for an axisymmetric problem

A class of modified Wilson arbitrary quadrilateral nonconforming elements for an axisymmetric problem is proposed. Their convergence is proven by means of the strong patch test. The structure of this finite element class is investigated. Thus a general method of axisymmetric nonconforming elements with convergence properties is presented. Project supported by the Foundation of the Chinese Ministry of Machine-Building Industry     

Initial postbuckling behavior of cylindrical composite shells under axisymmetric deformation

A solution is obtained that describes the postbuckling behavior of cylindrical shells in the case of axisymmetric buckling. The basis for this solution is Koiter’s asymptotic method and the nonlinear equations of the third-order Timoshenko theory of shells. It is shown that the bifurcation point in this case is a symmetrically unstable one. The effect of the initial axisymmetric deflections on the buckling loads is weaker when buckling is axisymmetric. The results obtained by Koiter’s special theory evidence this __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 108–118, April 2006.     

Buckling analysis of cylindrical shells with random geometric imperfections

In this paper the effect of random geometric imperfections on the limit loads of isotropic, thin-walled, cylindrical shells under deterministic axial compression is presented. Therefore, a concept for the numerical prediction of the large scatter in the limit load observed in experiments using direct Monte Carlo simulation technique in context with the Finite Element method is introduced. Geometric imperfections are modeled as a two dimensional, Gaussian stochastic process with prescribed second moment characteristics based on a data bank of measured imperfections. (The initial imperfection data bank at the Delft University of Technology, Part 1. Technical Report LR-290, Department of Aerospace Engineering, Delft University of Technology). In order to generate realizations of geometric imperfections, the estimated covariance kernel is decomposed into an orthogonal series in terms of eigenfunctions with corresponding uncorrelated Gaussian random variables, known as the Karhunen-Loéve expansion. For the determination of the limit load a geometrically non-linear static analysis is carried out using the general purpose code STAGS (STructural Analysis of General Shells, user manual, LMSC P032594, version 3.0, Lockheed Martin Missiles and Space Co., Inc., Palo Alto, CA, USA). As a result of the direct Monte Carlo simulation, second moment characteristics of the limit load are presented. The numerically predicted statistics of the limit load coincide reasonably well with the actual observations, particularly in view of the limited data available, which is reflected in the statistical estimators.