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Wasim Barham Amjad Aref Gary Dargush 《International Journal of Solids and Structures》2008,45(22-23):5688-5704
This paper presents the extension of a flexibility-based large increment method (LIM) for the case of cyclic loading. In the last few years, LIM has been successfully tested for solving a range of non-linear structural problems involving elastoplastic material models under monotonic loading. In these analyses, the force-based LIM algorithm provided robust solutions and significant computational savings compared to the displacement-based finite element approach by using fewer elements and integration points. Although in cyclic analysis a step-by-step solution procedure has to be adopted to account for the plastic history, LIM will still have many advantages over the traditional finite element method. Before going into the basic idea of this extension, a brief discussion regarding LIM governing equations is presented followed by the proposed solution procedure. Next, the formulation is specified for the treatment of the elastic perfectly plastic beam element. The local stage for the beam behavior is discussed in detail and the required improvement for the LIM methodology is described. Illustrative truss and beam examples are presented for different non-linear material models. The results are compared with those obtained from a standard displacement method and again highlight the potential benefits of the proposed flexibility-based approach. 相似文献
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S. Kaliszky 《基于设计的结构力学与机械力学》2013,41(1):39-50
ABSTRACT This paper presents solution methods for elastoplastic and shakedown analysis of linearly elastic, perfectly plastic bodies for which the conventional classical formulations of these problems are completed by constraints on overall plastic deformation and elastoplastic displacement. The methods are described in terms of nonlinear mathematical programming and provide solutions when the plastic reserves of the body are not fully exhausted, and the plastic performance and the plastic deformations are controlled. Application of the method is illustrated by an example. 相似文献
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材料构型力学主要研究材料中的缺陷(夹杂、空穴、位错、裂纹、塑性区等)的构型(形状、尺寸和位置)改变时,所引起的系统自由能的变化。本研究将基于数字散斑相关技术,实验测量材料试件的位移场分布,随后通过材料构型力的定义式,计算求得弹塑性材料中缺陷构型力的分布。其方法概括如下:位移场通过数字图像相关技术测得;应变及位移梯度场利用三次样条拟合获得;线弹性材料应力通过简单线弹性本构方程获取,而塑性材料的表面应力场通过Ramberg-Osgood本构方程计算求得;弹塑性应变能密度分布则由应力-应变曲线数值积分获得。该方法对普通弹性材料或者弹塑性材料均适用,可以用于各种不同的缺陷及缺陷群的材料构型力测量。 相似文献
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目前框架结构体系可靠度分析大多是在荷载完全相关的假定下完成的,对于非完全相关荷载作用下的体系可靠度研究则鲜有涉及,对于非理想弹塑性或弹脆性的结构尤其如此.本文在随机系统分析的概率密度演化理论的基础上,结合结构非线性全过程分析的位移控制算法,推导了基于归一化位移参数的结构非线性发展概率密度演化方程和承载力裕度的概率密度演化方程.采用纤维梁柱单元进行非线性分析,研究了钢筋混凝土框架结构在非完全相关荷载下的体系可靠度,并与Monte Carlo法进行了对比分析,证明了文中建议方法的可行性.基于文中方法,分析了荷载相关性对可靠度的影响,计算结果表明,荷载相关性对体系可靠度有比较明显的影响. 相似文献
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等效静态载荷法是目前解决动态拓扑优化问题的一种有效方法,但是由于未考虑塑性变形中应力应变关系的时效性,会导致等效载荷偏大和载荷方向偏差,因此无法有效处理材料的非线性问题.据此,提出一种基于模量比率因子的等效静态载荷计算方法.首先,根据结构应力、应变和杨氏模量之间的函数关系,计算各时刻的计算杨氏模量;然后,得到各时刻的模量比率因子,根据位移等效原则计算修正等效静态载荷,进而进行多工况静态拓扑优化,并更新设计变量再次进行动力学分析,重复直至收敛.数值算例表明,修正后的等效静态载荷法能够解决弹塑性材料的非线性问题,在提高等效精度的同时拓展了在非线性材料方面的应用边界.工程算例表明,在相同约束下,采用基于模量比率因子的等效静态载荷法在轻量化的同时能得到更小的塑性应变. 相似文献
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将无额外自由度的广义有限元法由线弹性分析扩展到弹塑性大变形分析.局部强化函数的构建依赖于已有节点,不引入额外自由度,避免了线性相关性问题.在更新拉格朗日框架下,通过控制方程弱形式的线性化推导得到了节点内力的率形式,并分为材料和几何两部分.考虑超弹性和亚弹-塑性两种材料模型,采用Newton-Raphson迭代求解,给出了相关的一致切线刚度阵.三个典型算例的数值结果表明,本文发展的非线性无额外自由度广义有限元方法不仅能够准确求解超弹性和弹塑性大变形问题,同时相比于传统的线性有限元方法具有更高的精度.本文工作进一步拓宽了无额外自由度广义有限元方法的应用领域. 相似文献
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N. A. Abrosimov N. A. Novosel’tseva 《Journal of Applied Mechanics and Technical Physics》2015,56(6):937-944
A method for identification of material parameters of the constitutive relations of elastoplastic and viscoelastic deformation of isotropic and composite materials is developed. The method is based on minimizing the functional of the residue of results of numerical and experimental analysis of unsteady deformation of structural elements made of examined materials. The method is tested, and prospects of its application for determining material parameters of viscoelastic and elastoplastic models of nonlinear deformation of cylindrical metal–plastic shells under explosive loading are demonstrated. 相似文献
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具有有限差分法特征的虚单元法,可视为是有限元法向任意多边形单元的扩展。在材料细观力学性能表征、非均质材料力学分析等非线性问题方面,传统的弹塑性有限元法具有网格数目多、效率低下等不足之处,而虚单元法使网格划分更加灵活,为材料的弹塑性力学分析等非线性问题提供了新的思路。基于增量法弹塑性力学原理和双线性投影算子,建立了弹塑性力学问题的虚单元法求解技术,提出了弹塑性力学问题虚单元法的应力更新方案,研究了弹性力学问题虚单元法的精度和收敛性,讨论了虚单元法求解弹塑性力学问题的网格依赖性。同时,开展了任意多边形和凹多边形单元的数值试验研究,结果表明,虚单元法无须分割多边形,仅需节点自由度便可求得单元刚度矩阵和应力等效荷载,程序实现简单,计算精度高,改善了传统有限元的网格依赖性和塑性区的网格奇异性。 相似文献
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Jeoung-Heum Yeon Sung-Kie Youn 《International Journal of Solids and Structures》2008,45(17):4709-4724
A variational multiscale method has been presented for efficient analysis of elastoplastic deformation problems. Severe deformation occurs in plastic region and leads to high gradient displacement. Therefore, solution needs to be refined to properly capture local deformation in plastic region. In this work, scale decomposition based on variational formulation is presented. A coarse scale and a fine scale are introduced to represent global and local behavior, respectively. The displacement is decomposed into a coarse and a fine scale. Subsequently the problem is also decomposed into a coarse and a fine scale from the variational formulation. Each scale variable is approximated using meshfree method. Adaptivity can easily and nicely be implemented in meshfree method. As a method of increasing resolution, extrinsic enrichment of partition of unity is used. Each scale problem is solved iteratively and conversed results are obtained consequently. Iteration procedure is indispensable for the elastoplastic deformation analysis. Therefore iterative solution procedure of each scale problem is naturally adequate. The proposed method is applied to the Prandtl’s punch test and shear band problem. The results are compared with those of other methods and the validity of the proposed method is demonstrated. 相似文献
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基于修正的拉格朗日法,建立非线性有限元平衡方程,介绍了空间梁单元非线性刚度矩阵。针对此类结构在形态分析及设计中的难点问题,提出利用定力单元、定形单元和微调单元建立数值模型。采用AutoCAD二次开发工具ObjectARX编制有限元软件,能够进行考虑支承的大跨度索膜结构整体分析与设计。以芜湖体育场为工程背景,进行了形态分析和长期荷载组合下的反应。计算结果表明,本文所提方法和有限元软件显著地提高了设计工作的效率,并能准确地获得满足设计要求的结构初始形态及受力分析数据,便于实际工程的设计应用。 相似文献
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Multi-scale dual-phase cyclic plasticity with quantitative transitions and size effects of layered structures 总被引:1,自引:0,他引:1
A method is developed for cyclic elastoplastic analysis across micro/meso/macro scales which is effective for the quantitative
transition of physical variables and for evaluating the size effects of microstructures. By using the improved self-consistent
scheme proposed by Fan[1] and carrying out a delicate mesoscopic analysis based on a shear-lag model, the size effects including the thickness of hard
and soft layers relative to the inclusion dimension are obtained on the overall elastoplastic responses of materials up to
50 cycles. The dominant characteristics of the analysis are that the characteristic dimensions of a microstructure such as
the thickness of the layers and the inclusion dimension can be explicitly incorporated into the formulation. Results of numerical
analysis using only 4 plastic constants show that the thicker the layer relative to the inclusion size, the softer the material
in producing more plastic strain values for a given applied stress amplitude. This is in agreement with the well-known experimental
rule that the yield strength of layered structures is inversely proportional to the square root of the spacing between layers.
It is found that ratcheting depends very much on the size of the layered-structure and that the thinner the relative thickness
of the layer the less the ratcheting displacement. This finding may be used to explain why phenomenological models on ratcheting
are not quite successful so far, indicating the significance of across scale analysis in understanding issues which have existed
for a long time. 相似文献
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薄板结构仅在较小的荷载下就能产生较大的位移、旋转,甚至引发结构产生裂纹并扩展,进而发生结构整体断裂,因此,建立薄板结构在大变形过程中的裂纹扩展及断裂仿真模型,具有重要的工程实际意义.文章建立了用于薄板结构几何大变形和断裂分析的近场动力学(PD)和连续介质力学(CCM)耦合模型.首先基于冯·卡门假设,采用更新的拉格朗日法得到薄板在几何大变形增量步下的虚应变能密度增量公式,并利用虚功原理和均质化假设求出几何大变形微梁键的本构模型参数;接着分别建立几何大变形薄板PD模型与CCM模型的虚应变能密度增量,并建立了薄板几何大变形PD-CCM耦合模型;最后模拟了薄板结构在横向变形作用下的渐进断裂过程,得到与实验结果高度一致的仿真结果,验证了所提出的几何非线性PD-CCM耦合模型的精度.结果表明:本文所提出的薄板PD-CCM耦合模型具有简单高效,无需考虑材料参数限制和边界效应的特点,可以很好地用于预测薄板结构在几何大变形过程中的局部损伤和结构断裂,有利于薄板结构的断裂安全评价和理论发展. 相似文献
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《力学快报》2020,10(1):46-56
This research, for the first time, predicts theoretically static stability response of a curved carbon nanotube(CCNT) under an elastoplastic behavior with several boundary conditions. The CCNT is exposed to axial compressive loads. The equilibrium equations are extracted regarding the Euler–Bernoulli displacement field by means of the principle of minimizing total potential energy.The elastoplastic stress-strain is concerned with Ramberg–Osgood law on the basis of deformation and flow theories of plasticity. To seize the nano-mechanical behavior of the CCNT, the nonlocal strain gradient elasticity theory is taken into account. The obtained differential equations are solved using the Rayleigh–Ritz method based on a new admissible shape function which is able to analyze stability problems. To authorize the solution, some comparisons are illustrated which show a very good agreement with the published works. Conclusively, the best findings confirm that a plastic analysis is crucial in predicting the mechanical strength of CCNTs. 相似文献
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一种典型的半解析数值方法——线法被引入功能梯度材料的结构分析。首先推导了功能梯度材料位移形式的平衡方程和边界条件,然后阐述了线法功能梯度材料结构分析的基本步骤和数值原理。该方法的基本思想是通过有限差分将问题的控制方程半离散为定义在沿梯度方向离散节线上的常微分方程组,然后应用B样条函数Gauss配点法求解该常微分方程组得到问题的解答。为演示线法在功能梯度材料结构分析中的应用,给出了线性梯度和指数梯度功能梯度材料板分别受恒定位移、均匀拉伸载荷和弯曲载荷作用的数值算例。与相应问题解析解和其他数值方法的比较表明,线法的计算结果具有很高的精度,而且不需要任何特殊的考虑就能够有效模拟材料内部物性参数的连续变化,也无需事先选取满足特定条件的待定场函数,是一种非常适合功能梯度材料结构形式和材料特点的半解析数值方法。 相似文献
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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。 相似文献