叠加型A-F类随动强化模型塑性应变的数值计算法

以Chaboche随动强化模型为例,在M isses屈服准则及正交流动准则的前提下,推导了叠加型A rm-strong-F rederick(A-F)类随动强化模型塑性应变的数值计算法,联合利用四阶龙格-库塔法与径向返回法实现数值计算中的内部平衡迭代。同时推导了统一切向矩阵以便确定每一平衡迭代后的试算应变。利用AN SY S提供的U PF s将算法嵌入到AN SY S有限元程序,实现了叠加型A-F类随动强化模型塑性应变的数值计算,并利用四边形单元模拟了单轴循环加载时的棘轮应变,计算结果能够很好地与实验值吻合。     

一类加权全局迭代参数卡尔曼滤波算法

结合参数卡尔曼滤波算法和全局迭代推广卡尔曼滤波算法本文提出了加权全局迭代参数卡尔曼滤波算法。参数卡尔曼滤波算法可避免系统参数和状态变量之间的非线性耦合 ,同时通过带有目标函数的全局迭代算法保证能够获取到稳定、收敛的识别结果。分别针对线性结构模型和随动强化双线性结构模型进行了仿真参数识别。结果显示 ,不加权的全局迭代参数卡尔曼滤波算法对线性系统是有效的 ,而对非线性系统必须使用加权的全局迭代参数卡尔曼滤波算法。当信噪比较大 ,迭代无法得到收敛的结果时 ,目标函数保证了较好识别结果的获得     

残损航空器搬移拖车悬臂的拓扑优化

首先,采用导重准则法对在固定载荷下以位移为约束的拓扑优化问题进行计算,运用一种新的插值模型推导了在单工况作用下的最小质量拓扑优化迭代算法,并通过一个算例验证了该算法的可行性。然后,将该算法应用于残损航空器搬移拖车悬臂的拓扑优化设计中,将由此获得的悬臂的拓扑形貌与结构优化软件Optistruct得到的拓扑结果进行对比。结果表明,二者的迭代速度差别不大,且导重准则法的优化效果更好。作为概念设计,所得的拓扑形貌为以后悬臂结构的优化设计提供了有效参考。     

残损航空器搬移拖车悬臂的拓扑优化

首先,采用导重准则法对在固定载荷下以位移为约束的拓扑优化问题进行计算,运用一种新的插值模型推导了在单工况作用下的最小质量拓扑优化迭代算法,并通过一个算例验证了该算法的可行性。然后,将该算法应用于残损航空器搬移拖车悬臂的拓扑优化设计中,将由此获得的悬臂的拓扑形貌与结构优化软件Optistruct得到的拓扑结果进行对比。结果表明,二者的迭代速度差别不大,且导重准则法的优化效果更好。作为概念设计,所得的拓扑形貌为以后悬臂结构的优化设计提供了有效参考。     

迭代学习型瞬时最优控制及其收敛性分析

将传统的瞬时最优化控制和智能算法中的迭代学习控制相结合,提出了基于最优化控制算法和智能控制算法的迭代学习型瞬时最优化控制算法.该方法以线性系统为模型,以系统的响应与期望响应的差值为反馈,以二次型性能泛函为目标函数,通过迭代学习修正主动控制器的控制信号,提高主动控制的效果.针对迭代学习型瞬时最优化控制算法迭代的特性,本文采用范数方法给出了该方法收敛的充分条件.为验证方法的有效性,选取第二代基准模型作为计算模型,埃尔森特罗地震波南北分量作为输入载荷,数值仿真结果表明,迭代学习型瞬时最优控制算法较传统的瞬时最优控制算法有更好的控制效果.     

传热结构的多目标拓扑优化设计研究

深入分析了传热结构多目标拓扑优化设计中的几个关键问题。提出了基于结构柔度最小化和结构散热弱度最小化的多目标拓扑优化设计方法,建立了传热结构的多目标拓扑优化设计模型,推导了传热结构多目标拓扑优化中用于迭代分析求解的优化准则算法和敏度分析方程。通过数值计算验证了理论和算法的有效性。     

结构柔顺度拓扑优化的倒变量准则

针对在工程中广泛应用于最大化结构刚度设计的最小化结构柔顺度拓扑优化问题,应用连续体拓扑优化SIMP法,基于倒变量建立了优化模型;应用K-T条件建立了相应的优化准则,并提出了柔顺度过滤方法消除棋盘格现象及网格依赖等数值问题。应用不同的网格,与原准则法及MMA法进行了算法效率比较,与敏度过滤法及密度过滤法进行了优化求解结果及效率的比较。所附MATLAB程序测试表明:所提方法迭代次数最少、运行时间最短,随问题规模增大迭代次数不会增加;与原准则法相比,不用设置运动极限参数,适合求解大规模工程问题。     

混凝土的一种标量损伤弹塑性本构模型

荷载作用下材料性能的劣化是混凝土结构的微观损伤机理,其宏观表现为结构刚度的折减和承载力的降低。论文推导了基于不可逆热力学过程的弹塑性标量损伤本构,给出时间离散的屈服准则。采用基于向后Euler法的应力更新算法——两步图形返回的最近点投影法,推导了满足迭代结果收敛假设的塑性参数及算法刚度张量,给出了空间梁单元本构积分算法的Jacobi矩阵。将模型用于混凝土简支梁的承载力试验模拟,与计算数据对比表明了模型和算法的合理性和有效性。     

基于D-P准则的压力相关材料结构拓扑优化

基于描述材料力学行为的Drucker-Prager(D-P)屈服准则, 研究了压力相关材料连续体结构拓扑优化设计问题的数学模型和数值算法. 以单元材料人工密度为设计变量, 结合SIMP惩罚模型和多孔微结构局部应力插值模型, 建立了以材料体积最小化为目标、考虑材料D-P屈服条件约束的优化问题数学模型. 利用\varepsilon-松弛方法消除奇异解现象, 采用伴随法有效推导约束函数灵敏度计算公式, 运用基于梯度的连续变量优化算法迭代求解优化问题. 数值算例验证了优化模型的正确性及数值算法的有效性, 并通过与von Mises应力约束优化结果的比较, 说明了材料的压力相关特性会对结构最优拓扑产生重要影响. 该方法设计出的最优拓扑由于充分利用了压力相关材料的抗压能力, 因而更为合理和实际.      

最优化算法的收敛准则

收敛准则是最优化算法的重要组成部分，其选择得好与坏将直接影响到算法的成功与否以及收敛得快与慢。现有常用的收敛准则基本上是建立在前后迭代点的逼近和它们相应函数值的逼近是否达到一定的精度要求以及迭代点处函数梯度是否接近于零的基础上的。它们各自有自己的适用范围。但它们的共同特点是对迭代终止点的性质不能做出判断。本文在总结和分析现有算法收敛准则的基础上，借助于正定矩阵、一维优化方法中对分法和黄金分割法，提出了新的算法收敛准则。算例结果表明，这些收敛准则是有效实用的。     

Thermodynamic based model for the evolution equation of the backstress in cyclic plasticity

A nonlinear kinematic hardening rule is developed here within the framework of thermodynamic principles. The derived kinematic hardening evolution equation has three distinct terms: two strain hardening terms and a dynamic recovery term that operates at all times. The proposed hardening rule, which is referred in this paper as the FAPC (Fredrick and Armstrong–Phillips–Chaboche) kinematic hardening rule, shows a combined form of the Frederick and Armstrong backstress evolution equation, Phillips evolution equation, and Chaboche series rule. A new term is incorporated into the Frederick and Armstrong evolution equation that appears to have agreement with the experimental observations that show the motion of the center of the yield surface in the stress space is directed between the gradient to the surface at the stress point and the stress rate direction at that point. The model is further modified in order to simulate nonproportional cyclic hardening by proposing a measure representing the degree of nonproportionality of loading. This measure represents the topology of the incremental stress path. Numerically, it represents the angle between the current stress increment and the previous stress increment, which is interpreted through the material constants of the kinematic hardening evolution equation. This new kinematic hardening rule is incorporated in a material constitutive model based on the von Mises plasticity type and the Chaboche isotropic hardening type. Numerical integration of the incremental elasto-plastic constitutive equations is based on a simple semi-implicit return-mapping algorithm and the full Newton–Raphson iterative method is used to solve the resulting nonlinear equations. Experimental simulations are conducted for proportional and non-proportional cyclic loadings. The model shows good correlation with the experimental results.     

Constitutive modeling of strain range dependent cyclic hardening

In this paper, a new approach for constitutive modeling of strain range dependent cyclic hardening is proposed by extending the kinematic hardening model based on the critical state of dynamic recovery. It is assumed that isotropic, as well as kinematic, hardening consists of several parts, and that each part of isotropic hardening evolves when the corresponding part of kinematic hardening is in the critical state of dynamic recovery. The extended model is capable of simulating the cyclic hardening behavior in which different characteristics of cyclic hardening appear depending on strain range. The model is verified by simulating the relatively large cyclic straining tests of 304 stainless steel at ambient temperature, in which cyclic hardening does not stabilize before rupture if strain range exceeds a certain value. The model is further verified by predicting the history dependence of cyclic hardening under incremental cyclic loading and the maximum plastic strain dependence of strain hardening in cyclic tension.     

A two-surface model describing ratchetting behaviors and transient hardening under nonproportional loading

A new superposed rule of Mroz's kinematic hardening rule and Ziegler's kinematic hardening rule based on two-surface model is proposed in the paper. Some experimental results on ratchetting of 2014-T6 aluminum alloy are predicted very well under multiaxial loading. In addition the conformability of the model is discussed for transient cyclic hardening under two kinds of nonproportional cyclic loading paths, i.e. square and rhombic path. The project supported by the National Natural Science Foundation of China     

一类新的超弹性-循环塑性本构模型

目前,很多经典的超弹性-有限塑性本构模型已被提出,但由于超弹性理论中中间构型的引入使得随动硬化法则相对复杂,故多数文献均采用的是经典的Armstrong-Frederick(A-F)随动硬化法则.本文基于已有的本构理论,利用多机制过程的概念拓展了Lion塑性变形分解理论,明确提出了多重中间构型的概念,并在此基础上,对经典理论中客观性的定义进行了概念上的推广,使其更好地适用于超弹性本构理论分析,同时提出了一类新的超弹性-有限塑性本构模型.这类本构模型满足热动力学法则,且可融合多种小变形循环塑性理论中常用的随动硬化法则(如经典的A-F模型,Chaboche模型,Ohno-Wang(O-W)模型以及Karim-Ohno(K-O)模型等),使得小变形理论中背应力的加法分解性质及其演化的临界面阶跃特性在大变形领域中均有所体现,故本文提出的本构理论可看作是小变形循环塑性模型在大变形理论中的扩展.本文最后以K-O模型为例,对推荐模型进行了详细探讨,并与相应的次弹性模型进行了对比.      

A three-invariant cap model with isotropic–kinematic hardening rule and associated plasticity for granular materials

In this paper, a three-invariant cap model is developed for the isotropic–kinematic hardening and associated plasticity of granular materials. The model is based on the concepts of elasticity and plasticity theories together with an associated flow rule and a work hardening law for plastic deformations of granulars. The hardening rule is defined by its decomposition into the isotropic and kinematic material functions. The constitutive elasto-plastic matrix and its components are derived by using the definition of yield surface, material functions and non-linear elastic behavior, as function of hardening parameters. The model assessment and procedure for determination of material parameters are described. Finally, the applicability of proposed plasticity model is demonstrated in numerical simulation of several triaxial and confining pressure tests on different granular materials, including: wheat, rape, synthetic granulate and sand.     

循环硬化材料本构模型的隐式应力积分和有限元实现

针对新发展的、能够描述循环硬化行为应变幅值依赖性的粘塑性本构模型,讨论了它的数值实现方法。首先,为了能够对材料的循环棘轮行为（Ratcheting）和循环应力松弛现象进行描述,对已有的本构模型进行了改进;然后,在改进模型的基础上,建立了一个新的、全隐式应力积分算法,进而推导了相应的一致切线刚度（Consistent Tangent Modulus）矩阵的表达式;最后,通过ABAQUS用户材料子程序UMAT将上述本构模型进行了有限元实现,并通过一些算例对一些构件的循环变形行为进行了有限元数值模拟,讨论了该类本构模型有限元实现的必要性和合理性。     

Application of corotational rates of the logarithmic strain in constitutive modeling of hardening materials at finite deformations

In this paper a finite deformation constitutive model for rigid plastic hardening materials based on the logarithmic strain tensor is introduced. The flow rule of this constitutive model relates the corotational rate of the logarithmic strain tensor to the difference of the deviatoric Cauchy stress and the back stress tensors. The evolution equation for the kinematic hardening of this model relates the corotational rate of the back stress tensor to the corotational rate of the logarithmic strain tensor. Using Jaumann, Green–Naghdi, Eulerian and logarithmic corotational rates in the proposed constitutive model, stress–strain responses and subsequent yield surfaces are determined for rigid plastic kinematic and isotropic hardening materials in the simple shear problem at finite deformations.     

Stress integration method for a nonlinear kinematic/isotropic hardening model and its characterization based on polycrystal plasticity

Sheet metal forming processes generally involve non-proportional strain paths including springback, leading to the Bauschinger effect, transient hardening, and permanent softening behavior, that can be possibly modeled by kinematic hardening laws. In this work, a stress integration procedure based on the backward-Euler method was newly derived for a nonlinear combined isotropic/kinematic hardening model based on the two-yield’s surfaces approach. The backward-Euler method can be combined with general non-quadratic anisotropic yield functions and thus it can predict accurately the behavior of aluminum alloy sheets for sheet metal forming processes. In order to characterize the material coefficients, including the Bauschinger ratio for the kinematic hardening model, one element tension–compression simulations were newly tried based on a polycrystal plasticity approach, which compensates extensive tension and compression experiments. The developed model was applied for a springback prediction of the NUMISHEET’93 2D draw bend benchmark example.     

Performance of the MLPG method for static shakedown analysis for bounded kinematic hardening structures

Shakedown analysis is an extension of plastic limit analysis to the case of variable repeated loads and plays a significant role in safety assessment and structural design. This paper presents a solution procedure based on the meshless local Petrov–Galerkin (MLPG) method for lower-bound shakedown analysis of bounded kinematic hardening structures. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the targeted domain. Moreover, the natural neighbour interpolation (NNI) is employed to construct trial functions for simplifying the imposition of essential boundary conditions. The kinematic hardening behaviour is simulated by an overlay model and the numerical difficulties caused by the time parameter are overcome by introducing the conception of load corner. The reduced-basis technique is applied to solve the mathematical programming iteratively through a sequence of reduced residual stress subspaces with very low dimensions and the resulting non-linear programming sub-problems are solved via the Complex method. Numerical examples demonstrate that the proposed solution procedure is feasible and effective to determine the shakedown loads of bounded kinematic hardening structures as well as unbounded kinematic hardening structures.