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。     

Plastic limit analysis of incompatible finite element method

This paper describes an incompatible finite element model satisfying the consistencycondition of energy to solve the numerical precision problem of finite element solution inperfectly plastic analysis.In this paper the reason and criterion of the application of themodel to plastic limit analysis are discussed,and an algorithm of computing plastic limitload is given.     

A mathematical programming algorithm for limit analysis

This paper deals with the limit analyses of perfect rigid-plastic continua. Based on the kinematic theorem of the limit analysis theory, a mathematical programming finite element formula for determining the upper bound load multiplier has been established, and an iteration algorithm proposed accordingly. In this algorithm the plastic and rigid zones are distinguished for every iteration step, and the goal function is modified gradually. The difficulties caused by the nonsmoothness of the goal function are overcome. Some examples solved by this algorithm are presented. The project supported by National Natural Science Foundation of China.     

Non-local continuum model and its numerical simulation for localization problem

A non-local continuum model for strain-softening simply taking plastic strain or damage variable as a non-local variable is derived by using the additive decomposition principle of finite deformation gradient. At the same time, variational equations, their finite element formulations and numerical convoluted integration algorithm of the model in current configuration usually called co-moving coordinate system are given. Stability and convergence of the model are proven by means of the weak convergence theorem of general function and the convoluted integration theory. Mathematical and physical properties of the characteristic size for material or structure are accounted for within the context of a statistical weighted or kernel function, and way is investigated. Numerical simulation shows that this model is suitable for to analyzing deformation localization problems. The project supported by the National Natural Science Foundation of China (No. 19632030).     

有限变形弹塑性理论及一致性算法

通过对对数应变的引用，成功地将小变形弹塑性理论移植到有限变形之中，形成了一套完整的有限变形弹塑性理论，进一步发展了具有一阶精度的一致性弹塑性算法。最后，给出几个算例以证明此理论的正确性及算法的有效性。     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

非局部模型与变形局部化数值模拟

基于非线性身体场论,建立了材料非局部连续模型、变分方程及相应的实时拖带系大变形有限元数值模型,设计了这一模型的数值卷积算法,由于广义函数弱收敛定理和卷积理论,证明所提出的非局部连续模型具备收敛性和稳定性。并阐明了材料特征尺度数学物理意义,统计加权函数的选择原则,数值结果表明非局部模型描述变形局部化问题是适当的。     

单晶有限变形的热力耦合计算模型

以弹性变形梯度作为基本变量,结合热力学理论构造了单晶有限变形的热、力耦合计算模型。该模型考虑了温度、变温速率以及塑性耗散等条件对单晶有限变形的影响,相对于传统的以弹性变形梯度为基本变量的晶体塑性模型,算法能够体现温度效应的影响。采用隐式的积分方法对建立的控制方程进行计算以保证求解过程的稳定。以1100Al单晶为例计算了不同升温、降温速率,以及不同应变率影响下的材料应力-应变的响应。结果表明,模型能较好地反映变温过程中,单晶各向异性性质的演化以及应力、应变之间关系的变化。     

基于能量等效原理的应变局部化分析:Ⅱ.有限元解法

以非局部塑性理论为基础,应用状态空间理论,通过局部和非局部两个状态空间的塑性能量耗散率等效原理,提出了一种求解应变局部化问题的新方法,以得到与网格无关的数值解.针对二维问题的屈服函数和流动法则导出了求解非局部内变量的一般方程,并提出了在有限元环境中求解应变局部化问题的应力更新算法.为了验证所提出的方法,对1个一维拉杆和3个二维平面应变加载试件进行了有限元分析.数值结果表明,塑性应变的分布和载荷-位移曲线都随着网格的变小而稳定地收敛,应变局部化区域的尺寸只与材料内尺度有关,而对有限元网格的大小不敏感.对于一维问题,当有限元网格尺寸减小时,数值解收敛于解析解.对于二维剪切带局部化问题,数值解随着网格尺寸的减小而稳定地向唯一解收敛.当网格尺寸减小时,剪切带的宽度和方向基本上没有变化.而且得到的塑性应变分布和网格变形是平滑的.这说明,所提方法可以克服经典连续介质力学模型导致的网格相关性问题,从而获得具有物理意义的客观解.此模型只需要单元之间的位移插值函数具有C~0连续性,因而容易在现有的有限元程序中实现而无需对程序作大的修改.     

Stability and extremum principles for post yield analysis of finite plasticity

The post yield behavior of rigid-perfectly plastic solids at the collapse load is studied based on the finite deformation theory. By using the general duality theory developed by Gao-Strang (1989), a global stability criteria is proposed and a pair of dual extremum principles, expressed in terms of displacements, displacement rates and the Kirchhoff stresses are established for plastic collapse analysis. It is proved that under large deformations, the existence of the plastic limit state at the collapse load depends on the directional derivative of a so-called complementary gap function. The application to the nonlinear plastic collapse theory yields a pair of dual bounding theorems for limit loading factor associated with any transient displacement of the deformed body when the global extremum criteria are satisfied. Dedicated to Professor Y.K. Cheung on the occasion of his 60th birthday     

计入膜力塑性耗散效应的矩形板塑性动力响应

从能量的观点在小挠度理论中引入表征膜力塑性耗散效应的修正因子,基于刚性板块的总体平衡给出矩形板大挠度塑性动力响应的完全运动方程组,分析了理想刚塑性简支和固支矩形板在矩形脉冲和冲击载荷下包括移行塑性铰相的完全大挠度响应过程。解决了当矩形板的挠度达到厚度量级时弯矩、膜力的联合作用问题,理论预报的结果在板的挠度为10倍板厚的量级与实验结果符合良好,改进了只考虑弯矩作用的小挠度理论结果和模态近似估计。     

Differential constitutive equations of incompressible media with finite deformations

A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids, and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic deformations of the material and deformations of elements of the medium at the structural level. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009.     

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。     

考虑晶界效应的多晶体有限变形分析

将晶界及其影响区综合考虑，建立了考虑晶界效应的力学模型，结合晶体塑性理论，利用有限变形有限元对多晶体进行数值模拟，数值结果显示了细观层次下晶粒变形场的特点，理论计算同实验定性一致。     

非经典大变形弹塑性本构方程及其算法研究

本文介绍了作者提出的非经典大变形弹塑性木构方程的增量形式，发展了相应的有限元分析方法。由于不采用屈服面的概念及相应的流动规律与加载准则，与传统的算法相比，本文提出的算法不仅简化了计算过程，而且改善了收敛速度和计算精度。作为验证和应用的例子，分析了圆柱试件的大变形拉伸颈缩过程和短圆柱的镦粗过程。与实验结果的比较证明了所发展方法的有效性。     

On a finite strain viscoplastic theory based on a new internal dissipation inequality

This work is focused on the theoretical development and numerical implementation of a viscoplastic law. According to the second law of thermodynamics a dissipation inequality described in the rotated material coordinate system is developed. Based on this dissipation inequality and the principle of maximum dissipation a finite strain viscoplastic model described also in the rotated material coordinate system is formulated. The evolution equations are expressed in terms of the material time derivatives of the rotated elastic logarithmic strain, the accumulated plastic strain and the strain-like tensor conjugate to the rotated back stress. The mathematical structure of this theory is concise and similar to that of the infinitesimal viscoplastic theory. These characteristics make the numerical implementation of this theory easy. The stress integration algorithm and the algorithmic tangent moduli for the infinitesimal theory can be applied to the numerical implementation of the present finite strain theory with a little reformulation. The complicated algorithmic formulations for most of other finite plastic laws can be therefore circumvented. In order to check the effectivity of the present finite strain theory a set of numerical examples under strict deformation conditions are presented. These numerical examples prove the excellent performance of the present viscoplastic material law at describing the finite strain elastoplastic and viscoplastic problems.     

论塑性旋率本构方程的必要性

在有限变形弹塑性理论中,本构方程通常是以率型形式给出的。因此,应变率的分解将是一个十分基本的问题。在当前,较为流行的是基于中间构形的应变率分解,而这其中最有影响的有 Lee,E.H.等人的工作和 Dafalias 等人的工作。然而,本文的研究表明,至少在某些特殊情况下,我们可以得到与微观子结构定向旋率的有关表达式。这就使给出塑性旋率本构方程变得不必要了。显然,本文的结果既不同于 Dafalias 的工作,也不同于 E.H.Lee等人的工作。前者需要通过塑性旋率的本构方程来确定微观子结构定向的旋率,而后者则需要作出附加的隐含假设来避免给出塑性旋率的本构方程。可以相信,本文工作将可能为有限弹塑性变形的本构理论提供一种新的途径。     

形状记忆合金热力学行为的模拟

基于塑性流动法则和马氏体相变动力学 ,引入马氏体体积分数和相变应力间的关系 ,对形状记忆合金的热力学行为进行了模拟 ,算例表明本文提出的形状记忆合金本构模型与实验结果比较吻合 ,且实施起来简单易行 ;最后还用该本构模型进行了有限元分析     

Near crack line elastic-plastic analysis for a finite plate loaded by two pairs of antiplane point forces

I.IntroductionThenearcracklineanalysismethodhasbeengreatlyimprovedbyYill'2].In[l,21,theimprovednearcracklineanalysismethodhasbeenusedtoinvestigateamodeIllcrackinanelastic-perfectlyplasticsolid.Andthesmallscaleyieldingconditionshavebeencompletelyabandoned,andcompletelynewandprecisesolutionsoftheelastic-plasticfieldsofamodeillstationarycrackandamodelillquasi-staticallygrowingcrackwithremotealltiplaneshearinginanelastic-perfectlyplastic'materialhavebeenobtained,respectively.In[3]weanalyzedthene…     

基于均匀化理论韧性复合材料塑性极限分析

运用细观力学中的均匀化方法分析了韧性复合材料的塑性极限承载能力.从反映复合材料细观结构的代表性胞元入手,将均匀化理论运用到塑性极限分析中,计算由理想刚塑性、Mises组分材料构成的复合材料的极限承载能力.运用机动极限方法和有限元技术,最终将上述问题归结为求解一组带等式约束的非线性数学规划问题,并采用一种无搜索直接迭代算法求解.为复合材料的强度分析提供了一个有效手段.