牛顿迭代一致性算法及其在板弹塑性有限元分析中的应用

本文简略讨论了有限载荷增量弹塑性有限元分析中传统切线刚度法丧失精度和牛顿迭代平方收敛速度的原因,并提出保持牛顿迭代平方收敛速度、保证一阶精度和无条件稳定性的一致性算法.一致性算法具备以下两个特征:1)采用路径无关计算格式;2)采用一致弹塑性切线模量。根据一致性算法构造出以弯矩和曲率为基本变量的弹塑性板弯曲有限元NIDKQ元。数值结果表明NIDKQ元具有令人满意的精度,同时验证了有限载荷增量下牛顿迭代一致性算法的平方收敛率特性,而传统切线刚度法随着塑性区的扩展将大大降低收敛速度。     

牛顿迭代一致性算法及其在板弹塑性有限元分析中的应用

本文简略讨论了有限载荷增量弹塑性有限元分析中传统切线刚度法丧失精度和牛顿迭代平方收敛速度的原因,并提出保持牛顿迭代平方收敛速度、保证一阶精度和无条件稳定性的一致性算法.一致性算法具备以下两个特征:1)采用路径无关计算格式;2)采用一致弹塑性切线模量。根据一致性算法构造出以弯矩和曲率为基本变量的弹塑性板弯曲有限元NIDKQ元。数值结果表明NIDKQ元具有令人满意的精度,同时验证了有限载荷增量下牛顿迭代一致性算法的平方收敛率特性,而传统切线刚度法随着塑性区的扩展将大大降低收敛速度。     

弹塑性有限元增量分析的自动选择步长和用予测本步刚度阵求解

本文利用本步刚度参数(current stiffness parameter)概念,对改进弹塑性有限元增量分析的效率和精度提出了两个具体措施。 1.自动选择每个增量步的步长,可在保证精度的前提下大量缩减总的增量步数,并有效地解决了计算结构极限载荷的问题。 2.用予测获得的本步刚度阵代替现行的起点切线刚度阵求解本步载荷增量,可大量缩减每个步长的迭代次数,提高收敛速度。     

岩土弹塑性有限元分析的隐式积分弹性刚度法

本文提出了用于岩土弹塑性有限元分析的隐式积分弹性刚度算法。该算法既具有隐式积分法精度好、效率高、无条件稳定等优点，也具有弹性刚度法中刚度矩阵正定、对称的特点，更重要的是它避免了传统切线刚度法在处理岩土非相关联塑性流动和屈服面“角点”所遇到的非对称性和奇异性计算问题。通过算例分析了该算法的精度、效率     

岩土弹塑性有限元分析的隐式积分弹性刚度法

本文提出了用于岩土弹塑性有限元分析的隐式积分弹性刚度算法。该算法既具有隐式积分法精度好，效率高，无条件稳定等优点，也具有弹性刚度矩阵正定、对称的特点，更重要的是它避免了传统切线刚度法在处理岩土非相关联塑性流动和屈服面“角角”所遇到的非对称性和奇异性计算问题。通过算例分析了该算法的精度、效率。     

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。     

一种高效率弹塑性有限元分析新方法：增量杂交／混合修正弦线模量法

本文在文献[1]给出的放松应力增量平衡约束的修正余能广义变分原理基础上,提出一种高效率的弹塑性有限元分析的新方法——增量杂交/混合修正弦线模量法。该法保持了文[1]方法的全部优点,而在迭代过程中,依据材料的单向拉伸应力—应变关系,不断改变过渡区和塑性区单元柔度矩阵和塑性矩阵中的弹性模量;并在体积压缩模量不变假设下,相应地改变过渡区单元矩阵中的泊松系数。从而大大降低了迭代收敛次数和单刚计算量,提高了多类变量弹塑性有限元分析的计算效率和收敛精度。     

两种弹塑性算法的比较

分析了弹塑性一致切线模量算法与径向返回算法，发现一致切线模量算法并不如有关文献报道的那样，比径向返回算法有快得多的收敛速度，两个算例表明了这一点。这使对一致切线模量算法有比较全面的看法。     

基于逆迭代法的结构动力缩聚技术

有限元模型的动力缩聚法已被广泛地应用到大阶系统的特征分析、试验－分析模型的相关分析等领域中。本文从逆迭代法出发,导出了一种有限元模型动力缩聚迭代方法。该方法具有三个显著的优点：其一是收敛速度远远超过现有的动力缩聚迭代法;若干是该迭代法收敛的可以从理论上得到保证,其三是由于没有必要的在每次迭代中都去计算降阶系数的刚度矩阵、质量矩阵和特征问题,因而可减少计算工作量,尤其在主自由度数较大的情况下。     

三维材料非线性问题的分区混合元法

本文构造了用于空间弹塑性分析的杂交混合元。导出了增量形式的分区混合变分原理,由此构造了用于空间弹塑性分析的分区混合元,并提出了一个加速求解非线性有限元方程组的修正的牛顿-拉夫森法迭代收敛的-维搜索格式。文中算例表明:杂交混合元用于空间弹塑性分析可以得到比位移元和杂交元更好的精度;分区混合元兼有较好的精度和算时较省的长处,适用于非线性问题的数值分析;并验证了该一维搜索法是一个有效地加速迭代收敛的方法。     

Comparison of different implementation algorithms for HiSS constitutive models in fem

Relative accuracy, stability and efficiency of four popular algorithms to implement elasto-plastic constitutive models in non-linear finite element procedures have been compared. Elastic Predictor–Plastic Corrector (EP–PC) method, Plastic Predictor–Plastic Corrector (PP–PC) method, Implicit Integration (Implicit) method and Modified Euler (ME) method wereused to implement Hierarchical Single Surface (HiSS) δ₀1 model into the general purpose finite element program ABAQUS. First, these algorithms were used outside the finite element program to simulate various triaxial stress paths. After that, they were used in ABAQUS to simulate two strip footings: (a) displacement controlled rigid footing and (b) load controlled flexible footing. The effect of the sub-strain increment size on the accuracy, stability and efficiency of each algorithm during these simulations have been compared. Implicit Method and ME performed well for some problems but performed poorly on others. EP–PC and PP–PC methods performed equally well for all the problems. This also showed the importance of testing algorithms under various stress paths and boundary value problems to assess their relative performance.     

相变传热问题的灵敏度分析与优化设计方法

研究了相变传热问题的优化设计及其灵敏度分析方法. 在有限元-时间差分和等效热容 法求解相变温度场的基础上,提出了相变温度场对设计变量一阶灵敏度的计算方法,给出直 接法和伴随法两种计算格式并分析了它们的特点,建立了相变温度场优化的模型和算法,在有限元分析与优化设计软件JIFEX中实现了该方法. 数值算例表明了灵敏度计算的精度和优 化方法的有效性.     

A weakly compressible MPS method for modeling of open‐boundary free‐surface flow

A mesh‐free particle method, based on the moving particle semi‐implicit (MPS) interaction model, has been developed for the simulation of two‐dimensional open‐boundary free‐surface flows. The incompressibility model in the original MPS has been replaced with a weakly incompressible model. The effect of this replacement on the efficiency and accuracy of the model has been investigated. The new inflow–outflow boundary conditions along with the particle recycling strategy proposed in this study extend the application of the model to open‐boundary problems. The final model is able to simulate open‐boundary free surface flow in cases of large deformation and fragmentation of free surface. The models and proposed algorithms have been validated and applied to sample problems. The results confirm the model's efficiency and accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

弱不连续问题高阶有限元离散系统的GAMG法

弱不连续问题(如含夹杂问题)是固体力学计算中的一类重要问题。高阶有限元方法由于其具有更好的逼近效果,是确保数值解在界面保持较高精度的计算方法之一。但与线性元相比,高阶单元需要更多的计算机存储单元,具有更高的计算复杂性。本文利用两水平算法的思想,将高阶有限元离散系统化归于线性元离散系统的求解,为弱不连续问题高阶有限元离散系统设计了一种新的基于几何与分析信息的代数多重网格(GAMG)法,并应用于圆形求解域含单夹杂问题的高阶有限元离散系统的求解。数值试验结果表明,相比于常用GAMG法,新方法的迭代次数基本不依赖于问题规模、单元阶次以及杨氏模量的间断性,CPU计算时间得到明显改善,具有更好的计算效率和鲁棒性,可大大提高弱不连续问题有限元分析的整体效率。     

域外奇点法在弹性力学中的应用

本文将域外奇点法推广应用于弹性力学问题,求解了扭转问题,平面弹性问题和平面弯曲问题.计算表明,这种方法简单,计算时间短,精度高。     

Entropy generation due to natural convection in a partially heated cavity by local RBF-DQ method

The Local Radial Basis Function-Differential Quadrature (RBF-DQ) method is applied to two-dimensional incompressible Navier-Stokes equations in primitive form. Numerical results of heatlines and entropy generation due to heat transfer and fluid friction have been obtained for laminar natural convection. The variations of the entropy generation for different Rayleigh numbers are also investigated. Comparison between the present results and previous works demonstrated excellent agreements which verify the accuracy and flexibility of the method in simulating the fluid mechanics and heat transfer problems.     

Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov–Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.     

基于辛弹性力学解析本征函数的有限元应力磨平方法

在实际工程结构的结构强度与优化等力学数值分析中,应力计算结果的精度是非常重要的。有限元法是得到最广泛应用的一类数值方法,并形成了众多通用的有限元程序系统。这些程序系统采用的几乎都是基于最小总势能的位移法,虽然其分析给出的有限元位移场具有较高的精度,但所得到的有限元应力场的精度较位移场大大降低。基于极坐标辛对偶体系所提供的平面弹性力学的解析辛本征展开解,并借用有限元程序系统所得到的节点位移,本文提出了一个应力分析的改进方法。数值结果表明,本方法给出的应力分析精度得到大幅提高,并具有良好的数值稳定性,可用于有限元程序系统的后处理,以提高应力尤其是关键区域应力的分析精度。     

无网格稳定配点法及其在弹性力学中的应用

伽辽金型无网格法具有精度高、稳定性好的优点,但是实现高阶准确积分过程复杂,计算效率低.配点型无网格法的计算效率高,但是其在求解复杂问题时往往会出现精度和稳定性较差的结果.本文介绍一种新的无网格法-无网格稳定配点法,采用重构核近似作为近似函数,在规则子域内非常容易实现高阶准确积分,既保留了配点型无网格法效率高的特点,又具...     

A perturbation technique for solving boundary value problems arising in the electrodynamics of conducting bodies

The electrodynamics of wave reflection from conducting media lead to difficult mathematical problems because of the matching conditions which must be met at the interface between conductors and nonconductors. Simplified boundary conditions have been proposed by Leontovitch and others which considerably simplify certain of the mathematical problems. We discuss the Leontovitch condition together with certain of its shortcomings and present a new method which overcomes some of the difficulties of the Leontovitch condition. The new method is a perturbation away from infinite conductivity which allows the solution of electrodynamics problems to be calculated to any order of accuracy in the quantity (ωε/σ)^1/2 for some important cases. An instance in which the perturbation method fails is also discussed.