无额外自由度广义有限元的近不可压弹-塑性分析

研究了常规有限元方法在近不可压弹-塑性分析中的体积自锁问题,并在广义有限元框架下引入无额外自由度的强化函数对此问题进行了改进.一方面,插值函数在引入强化函数后获得了更加丰富的近似空间,提高了在体积近似不变约束下正确反映结构变形的能力;另一方面,强化函数的建立不依赖额外自由度,从而消除了传统广义有限元方法中的线性相关性问题.分析并验证了常规有限元在线弹性、超弹性和塑性分析中的体积自锁问题具有不同的触发条件和表现形式.3个典型的数值算例表明,无额外自由广义有限元能有效地缓解体积自锁并得到准确合理的计算结果.     

用力学子单元模型求解与时间有关的各向异性塑性问题

本文介绍了用力学子单元模型摹拟金属各向异性弹-塑性平面应力行为的做法,模型引用的纵向与横向应力-应变曲线,是用几个光滑的短线段来表达的;但为简化起见,把它们当作分段线性线段。模型已纳入粘塑性杂交应力有限元分析程序。     

基于L-D流动法则模糊弹粘塑性的有限变形分析

为了进行岩土材料有限变形的动力分析,采用Green应变和第二类Kirchoff应力描述材料的几何非线性。将隶属度函数引入到屈服函数中,并采用L-D屈服准则,得到了基于L-D流动法则的模糊弹粘塑性本构模型。应用非线性有限元原理,得到了土样动三轴实验有限变形的数值结果,并与小变形的数值结果和土样的动三轴实验结果进行了对比。通过对比发现有限变形的结果更加接近动三轴的实验结果,且模糊弹粘塑性模型能很好地反映循环荷载作用下岩土的动力性质,是岩土动力分析的一种有效方法.     

CVD全离散化的混合有限元解的数值模拟

在已有的对CVD化学方程半离散化和全离散化混合有限元解的存在性及其误差分析的基础上,对其全离散化混合有限元解进行了数值模拟,结果进一步表明了混合有限元解的高精度、易于计算的良好性质.     

波动方程单位分解有限元法及收敛性分析

<正>1引言与问题的提出自黄云清和许进超提出基于单位分解技术的重叠型非匹配网格有限元方法以来,这类方法日益引起人们极大的兴趣.这篇文章将这类有限元方法运用到波动方程当中,分别研究了重叠型非匹配网格波动方程半离散和全离散有限元方法,给出了有限元解及其梯度的误差估计.下面先给出模型问题的简单介绍.     

股票价格波动的塑性性质及模型探讨

首先基于股票价格和成交量，根据股票的量价规律，分析了股价波动的塑性性质；然后使用计量经济学方法建立描述股价波动的塑性模型，包括股价塑性基本模型、基本模型的一阶自回归模型、幂指数模型及幂指数模型的一阶自回归模型，基于12支样本股对这些模型进行参数估计和检验；最后对4种形式的股价塑性模型进行了总结。由4种模型均能够通过经济学检验和统计学检验可知股价波动具有塑性性质，且幂指数模型描述股价塑性较为科学、合理。     

重叠型非匹配网格抛物型方程的有限元法及收敛性分析

基于单位分解技术,本文介绍了重叠型非匹配网格抛物型方程初边值问题的有限元方法,分别给出了半离散有限元、全离散有限元格式和收敛性分析的结果,并给出了数值例子.     

抛物方程初边值问题连续有限元的超收敛性

研究了一类一维抛物方程初边值问题的连续有限元方法.在空间上进行任意m次有限元半离散,在时间方向上进行二次连续有限元后,获得了一个稳定的全离散计算格式.利用单元分析法校正技术的新思想进行理论分析,连续有限元解在剖分网格节点上具有超收敛性.     

固体的统一弹、粘、塑性理论

提出了一个弹、粘、塑性统一理论,可用以计算在任意受力过程下物体各点弹、粘、塑性的变化情况.理论的基础是热力学定律及虚弹性假设.文中导出本构关系以及有关的变分原理,由此容易推导空间-时间的有限元构式.值得指出,适当选取文中的物质常数,可以得出类似于当前习用的塑性本构关系.     

受轴向压缩圆柱壳塑性屈曲的内时分析

采用内时塑性本构方程的增量和全量表达式分析了受轴向压缩圆柱壳的塑性屈曲，得到了塑性屈曲临界应力与圆柱壳特征尺寸间的关系。对ＡＭＦ和铝合金圆柱壳塑性屈曲进行了分析，与实验结果的比较表明：除对于ＡＭＦ圆柱壳由内时塑性本构方程的全量表达式给出了较经典塑性理论全量分析略为保守的结果外，在其它杨合下，内时分析均给出了较经典塑性理论更符合实验数据的结果。     

Plastic zone development in dynamic tear-type test specimens

The J-integral is a fracture criterion, which permits measurement of the fracture toughness of a specimen where fracture occurs in the elastic–plastic regime. An understanding of the ratio of plastic zone size (radius) to the crack tip blunting (stretch zone) is required to determine the upper temperature for transition curves, where elastic–plastic fracture becomes invalid and general yielding occurs. This study endeavors to acquire this ratio using finite element techniques. The development of the plastic zone in dynamic tear (DT) specimens and non-standard three-point bending fracture test specimens was the main focus of the study. The ABAQUS finite element software was used to model the elastic–plastic behaviour of the specimens. The cracks in the specimens were induced by pressing the notch followed by fatigue cracking at 30–40% of the limit loads. The shapes of these cracks were adequately modelled in the finite element analysis. The specimens were made of 350WT steel and 304 stainless steel materials and were loaded until fixed amounts of permanent deformation were recorded. Results were obtained in the form of plots, showing the progression of the plastic zone around the crack tip. For each case, mid-point plastic deflection, stretch zone width and plastic zone radius were computed.     

On finite element methods for plasticity problems

Summary We prove an error estimate for an incremental finite element method for obtaining approximations to the stresses in an elastic-perfectly plastic body. We also comment on the limit load problem.     

An iterative elastic SBFE approach for collapse load analysis of inelastic structures

The paper proposes a novel numerical approach that incorporates the use of a modified elastic compensation method, within a polygon scaled boundary finite element framework, to determine the maximum load capacity of structures at plastic collapse. The distinctive feature of the proposed scheme is its effective computational ability in performing a series of successive elastic analyses by systematically adjusting elastic material properties of structures up to failure. The quadtree structural discretization within a polygon scaled boundary finite element platform enables model construction of sophisticated geometries at modest computing effort and thus the effective analysis of large-scale structures. The approach overcomes the challenges associated with stress singularity and locking phenomena under incompressibility conditions, even in the presence of high-order nonlinear yield loci. The robustness and accuracy of the proposed scheme are validated through a number of benchmarks and available practical engineering applications in 2D and 3D spaces. These illustrate the influences of some key algorithmic parameters, and the satisfaction of a lower-bound limit given by the present analysis method for a sufficiently fine discretization.     

Formulation of hybrid Trefftz finite element method for elastoplasticity

The present investigation provides a hybrid Trefftz finite element approach for analysing elastoplastic problems. A dual variational functional is constructed and used to derive hybrid Trefftz finite element formulation for elastoplasticity of bulky solids. The formulation is applicable to either strain hardening or elastic-perfectly plastic materials. A solution algorithm based on initial stress formulation is introduced into the new element model. The performance of the proposed element model is assessed by three examples and comparison is made with results obtained by other approaches. The hybrid Trefftz finite element approach is demonstrated to be particularly suited for nonlinear analysis of two-dimensional elastoplastic problems.     

Recent advances in the numerical modeling of constitutive relations

In this paper we present an overview of the recent developments in the area of numerical and finite element modeling of nonlinear constitutive relations. The paper discusses elastic, hyperelastic, elastoplastic and anisotropic plastic material models. In the hyperelastic model an emphasis is given to the method by which the incompressibility constraint is applied. A systematic and general procedure for the numerical treatment of hyperelastic model is presented. In the elastoplastic model both infinitesimal and large strain cases are discussed. Various concerns and implications in extending infinitesimal theories into large strain case are pointed out. In the anisotropic elastoplastic case, emphasis is given to the practicality of proposed theories and its feasible and economical use in the finite element environment.     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

裂纹尖端场弹塑性分析的加权残数法及塑性应力强度因子的计算

本文以幂强化材料,平面应变情形为例,系统地提出了裂纹尖端场弹塑性分析的加权残数法,并根据此法,得出了裂纹尖端场的解析式弹塑性近似解.在此基础上.对整个裂纹区域,构造了弹塑性解叠加非线性有限元计算塑性应力强度因子的方法,从而为裂纹尖端场和整个裂纹体的分析和计算,提供了一个方法.     

Three-dimensional simulation of flat rolling through a combined finite element–boundary element approach

This paper presents an innovative approach for analysing three-dimensional flat rolling. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the rigid–plastic numerical modelling of the workpiece allowing the estimation of the roll separating force, rolling torque and contact pressure along the surface of the rolls. The boundary element method is applied for computing the elastic deformation of the rolls. The combination of the two numerical methods is made using the finite element solution of the contact pressure along the surface of the rolls to define the boundary conditions to be applied on the elastic analysis of the rolls. The validity of the proposed approach is discussed by comparing the theoretical predictions with experimental data found in the literature.     

A method for calculating static transmission errors of plastic spur gears using FEM evaluation

There are many ways to calculate the static transmission errors of steel gears, but none is developed for plastic gears. Since the Young's modulus of the plastic material is lower than that of steel by two orders, the effects of large tooth deflection on the static transmission errors of plastic gears become significant. A multi-tooth contact analysis using finite element method for calculating the static transmission errors of plastic spur gears is established to compare with the existing method for steel spur gears. According to the comparison results, a modification of the existing method is proposed for plastic spur gears and verified by the same finite element contact analysis.     

Analysis of adiabatic shear bands in thermo-elasto-viscoplastic materials by using piece-wise discontinuous basis functions

An adiabatic shear band (ASB) is a narrow region of intense plastic deformation that forms when some metallic alloys and some polymers are deformed at high strain rates and there is not enough time for the heat generated by plastic deformations to diffuse away. The study of ASBs is important because an ASB is a precursor to shear/ductile fractures. Initial-boundary-value problems simulating the initiation and propagation of an ASB have been analyzed usually using the finite element method (FEM). Because of the large plastic strains involved, the FE mesh needs to be refined several times to delineate the ASB width. Each refinement requires, in turn, interpolation of data from the previous mesh to the new one which causes a smoothening of the sharp gradients of the deformation fields, and affects characteristics of the ASB. In this paper, we propose the application of the finite element method with piecewise discontinuous basis functions for studying the occurrence of ASBs in simple shearing deformations of a body composed of an isotropic and homogeneous thermo-elastoviscoplastic material. The mathematical model of the problem is defined by a system of coupled nonlinear partial differential equations and an inequality constraint associated with the plastic strain rates admissibility.