平面应变和反平面应变复合型裂纹尖端的各向异性塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下,利用平衡方程,各向异性塑性应力应变率关系、相容方程和Hill各向异性屈服条件,本文导出了平面应变和反平面应变复合型裂纹尖端的各向异性塑性应力场的一般解析表达式.将这些一般解析表达式用于复合型裂纹,我们就可以得到Ⅰ-Ⅲ、Ⅱ-Ⅲ及Ⅰ-Ⅱ-Ⅲ复合型裂纹尖端的各向异性塑性应力场的解析表达式.     

Ti-6242S钛合金高温循环粘塑性行为有限元模拟

采用ANSYS提供的粘塑性流动准则下的双线性各向同性硬化本构模型,考虑材料参数的温度相关性,通过单个单元有限模型对4种温度下施加相同平均应力和不同应力幅值的应力循环工况进行有限元模拟。实验与模拟结果的对比表明,该模型能够较好的地模拟高温450℃以下Ti-6242S钛合金粘塑性变形的循环累积。此外,由于该模型没有考虑循环过程中背应力的演化,对滞回环的预测不够理想,且过高预测了520℃下的粘塑性累积变形。     

平面应变和反平面应变复合型裂纹尖端的理想塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的条件下.利用平衡方程.应力应变率关系、相容方程和屈服条件,本文导出了平面应变和反平面应变复合型裂纹尖端的理想塑性应力场的一般解析表达式.将这些一般解析表达式用于复合型裂纹.我们就可以得到Ⅰ-Ⅲ、Ⅱ-Ⅲ及Ⅰ-Ⅱ-Ⅲ复合型裂纹尖端的理想塑性应力场的解析表达式.     

不同类型高强钢轨道轮轨接触下塑性变形分析

基于ABAQUS有限元软件建立三维轮轨接触模型,采用用户材料子程序定义的非线性随动硬化模型和任意Lagrange-Euler(拉格朗日-欧拉)算法,研究碳含量不同的3种高强轨道钢稳态滚动接触时接触区应力和塑性应变分布。结果表明:累积塑性变形最大值发生在轨道次表面2 mm处,随着碳含量的增加,轨道接触斑中间相同深度的累积塑性应变逐渐增大。研究结果对于高强轨道钢的选材有一定参考意义。     

对于正交异性材料屈服与流动的探讨

假定正交异性材料的屈服准则与各向同性材料的Huber-Mises准则同构,提出了无量纲应力屈服准则,进而推导了与之相关的塑性流动规则.用不同的简单应力状态下的应力-应变试验曲线,可以得到不同的广义等效应力-应变关系.     

简单剪切振荡现象及弹塑性本构的限制条件

基于在真应力空间刻划弹塑性物质的强化、软化和理想塑性特性,本文以刚塑性随动强化模型为例说明产生简单剪切振荡现象,是与模型在简单剪切变形下,其强化和软化特性发生交替变化的现象有关。为使弹塑性本构模型更符合实际,要求它们必须满足如下条件:即对任意弹塑性加载变形过程,本构模型所给出的应力应该是非振荡的,所描述的强化和软化特性,不存在从软化阶段至强化阶段的过渡。     

韧性材料中的一个新的动态孔洞增长模型

本文提出了一个可用来描述韧性材料动态断裂过程的新模型.基体是由具有过应力形式的弹-粘塑性本构关系的材料构成.文中给出了在常等效应变率下的含孔洞材料的动态加载面及其相应的近似解析表达式.当材料单元经受球对称载荷作用时,本文的模型将退化为Carroll-Holt-Johnson模型.当材料的应变率敏感参数趋于零时,本文模型将退化为Gurson模型.本文的研究还表明,在一般情况下正交性法则是不成立的.最后,将本文模型与近年来Pan,Saje,Needleman和Perzyna等人所提出的含孔洞材料的粘塑性本构模型进行了比较.     

高温合金GH4133B动态本构模型与失效模型研究

根据典型航空发动机机匣常用高温合金GH4133B在不同温度(298~1 073 K)、不同应变率(10~(-1)~5×10~3s~(-1))下的力学性能试验结果,结合机匣包容性分析用的J-C(Johnson-Cook)本构模型在实际应用中本身存在的不足,提出了一种更为准确地描述GH4133B合金力学行为的修正J-C本构模型(modified J-C model,MJC model),同时结合GH4133B在不同温度、不同应力三轴度的破坏行为,建立了基于J-C时效判据的一个经验型的失效模型.通过模型预测结果与试验结果对比,发现所建立的本构模型和失效模型能很好地预测GH4133B塑性流动应力及破坏行为.     

善用一个模型,巧解一类题

求线段的最值,同学们往往感到困难,对于一类求线段的最大值和最小值得问题可以利用以下模型求解.一、建立模型已知:线段AB=6,线段AC=4,固定线段AB,将线段AC绕点A旋转,探求线段BC的最大值和最小值.分析为了求到线段BC的最大值和最小值,先构造一个含有线段BC的三角形,而且另外两条边是有数值的线段,如图1(1).线段AC绕点A旋转,当C落到BA延长线上     

静止裂纹尖端的理想塑性应力场

在裂纹尖端的理想塑性应力分量都只是θ的函数的假设下,利用平衡方程和屈服条件,本文导出了裂纹尖端的理想塑性应力场的一般解析表达式.将这些一般解析表达式用于具体裂纹,我们就得到Ⅰ型,Ⅱ型,Ⅲ型及Ⅰ-Ⅱ复合型裂纹尖端的理想塑性应力场.     

Special finite elements including stress concentration effects of a hole

Special finite elements are developed for efficient evaluation of stress concentration around a hole in complex structures. The complex variable formulation is used to derive a special set of stress functions which embody the stress concentration effects of a hole. The stress functions in combination with an independent displacement field assumed along the element boundary are used to construct the special elements with the hybrid displacement finite element method. Several numerical examples are presented to show that the used of special finite elements to model critical regions around a hole, together with conventional finite elements to model other regions away from the hole, is not only very convenient but also highly accurate.     

拟牛顿流的一种三变量域模型的有限元方法的数值分析

0．引言目前，涉及高温条件下材料蠕变性质的粘弹性流动问题已引起人们广泛的研究兴趣，不少文章讨论了如何对其进行数值求解（见［1］－－［41），首先，人们研究了较简单的仅以速度，压力两个变量来表述此现象的模型问题（如［1，2］）等．鉴于应力变量在材料性质方面的特殊重要性，最近J．Baxanzer等人在［3］中首次对应力满足幂函数规律的蠕变流研究了包含应力、速度和压力三种变量的模型问题的有限元逼近，当粘性的牛顿部分为零时（详见下述）在假定速度与应力、速度与压力有限元空间之间同时满足两种＊＊B条件以后，证明了有限元解…     

含孔洞有限板与加固板的连接问题的分区广义变分原理解法

本文提出了一种新的有限元解法,采用复变函数作为有限单元模式,结合运用分区广义变分原理,解决了经贴焊加固板后的含孔洞有限板应力集中系数的计算问题,得到了级数形式的解析解.计算实践表明,本方法成功地分析了加固板与含孔洞有限板在焊接线上的位移连续和内力平衡问题.由于仅需划分三个单元,故与常规有限元方法比较,本方法可大大节约计算机内存,提高精度,降低计算时间.应力集中系数和焊接线处应力的数值计算结果列于诸表之中,可供工程技术人员设计参考.     

Simulation of Rate Dependent Plasticity of Polymers

Polycarbonate is an amorphous polymer which exhibits nonlinear deformation before failure. It shows a pronounced strength-differential effect between compression and tension. Strain rate influences the mechanical response of the polycarbonate. In particular, the yield stress is increased with increasing strain rate. The concept of stress mode dependent weighting function is used in the proposed model to simulate the asymmetric effects for different loading speeds. In this concept, an additive decomposition of the flow rule is assumed into a sum of weighted stress mode related quantities. The characterization of the stress modes is obtained in the octahedral plane of the deviatoric stress space in terms of the mode angle, such that stress mode dependent scalar weighting functions can be constructed. The resulting evolution equations are updated using a backward Euler scheme and the algorithmic tangent operator is derived for the finite element equilibrium iteration. The numerical implementation of the resulting set of constitutive equations is used in a finite element program for parameter identification. The proposed model is verified by showing a good agreement with the experimental data. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of finite element approximations of a phase field model for two-phase fluids

This paper studies a phase field model for the mixture of two immiscible and incompressible fluids. The model is described by a nonlinear parabolic system consisting of the nonstationary Stokes equations coupled with the Allen-Cahn equation through an extra phase induced stress term in the Stokes equations and a fluid induced transport term in the Allen-Cahn equation. Both semi-discrete and fully discrete finite element methods are developed for approximating the parabolic system. It is shown that the proposed numerical methods satisfy a discrete energy law which mimics the basic energy law for the phase field model. Error estimates are derived for the semi-discrete method, and the convergence to the phase field model and to its sharp interface limiting model are established for the fully discrete finite element method by making use of the discrete energy law. Numerical experiments are also presented to validate the theory and to show the effectiveness of the combined phase field and finite element approach.

     

An analytical solution for time-dependent stress field of lined circular tunnels using complex potential functions in a stepwise procedure

Time-dependent behavior of surrounding mass plays a significant role in designing underground constructions. Considering simple configuration of lined circular tunnels, a lot of solution have been proposed to this problem. However, many assume hydrostatic initial stress field, and other solutions are only applicable to simple rheological models and could not account for viscosity effect in long-term time periods. In this study, an analytical plane strain solution is proposed for lined circular tunnels under non-hydrostatic initial stress field, assuming rock mass as a viscoelastic material obeying Burgers model, while concrete lining is supposed to have linear elastic behavior. The solution which employs complex variable method combined with correspondence principle benefits from time discretization approach enabling the solution to take into account the viscosity effect in the both short-term and long-term periods of time, while predicting stress components accurately. The results obtained by the proposed solution were compared with those predicted by finite element COMSOL software which exhibited a close agreement. It was found that by increasing time both the proposed analytical solution and finite element numerical method tend to an oblique asymptote due to viscosity effect of Maxwell body in the Burgers model. Finally, a parametric analysis was performed with respect to Burgers model coefficients which showed different behavior for short and long periods of time.     

Formulation and evaluation of a finite element model for the linear analysis of stiffened composite cylindrical panels

A finite element model for linear static and free vibration analysis of composite cylindrical panels with composite stiffeners is presented. The proposed model is based on a cylindrical shell finite element, which uses a first-roder shear deformation theory. The stiffeners are curved beam elements based on Timoshenko and Saint-Venant assumptions for bending and torsion respectively. The two elements are developed in a cylindrical coordinate system and their stiffness matrices result from a hybrid-mixed formulation where the element assumed stress field is such that exact equilibrium equations are satisfied. The elements are free of membrane and shear locking with correct satisfaction of rigid body motions. Several examples dealing with stiffened isotropic and laminated plates and shells with eccentric as well as concentric stiffeners are analyzed showing the validity of the models.     

Partial hybrid finite elements for composite laminates

Three types of partial hybrid finite elements are presented in order to set up a global/local finite element model for analysis of composite laminates. In the global/local model, a composite laminate is divided into three different regions: global, local, and transition regions. These are modeled using three different elements. In the global region, a 4-node degenerated plate/shell element is used to model the overall response of the composite laminate. In the local region, a multilayer element is used to predict detailed stress distribution. In the transition region, a multilayer transition element is used to smoothly connect the two previous elements. The global/local finite element model satisfies the compatibility of displacement at the boundary between the global region and the local region. It also satisfies the continuity of transverse stresses at interlaminar surfaces and traction conditions on the top and bottom surfaces of composite laminates. The global/local finite element model has high accuracy and efficiency for stress analysis of composite laminates. A numerical example of analysis of a laminated strip with free edge is presented to illustrate the accuracy and efficiency of the model.     

Static contact analysis of spiral bevel gear based on modified VFIFE (vector form intrinsic finite element) method

Since the intrinsic limitations of FEM (Finite element method) and lumped-mass method, we derive the formula of 8-node hexahedral element based on VFIFE (vector form intrinsic finite element method) method and applied it in contact analysis of gears. This paper proposed a new method to determine pure nodal deformation, which could simplify the computation compared to the traditional VFIFE method. Combining the VFIFE method and matching contact algorithm, we analyzed spiral bevel gear meshing problems. Spiral bevel models with two different mesh densities are calculated analyzed by the VFIFE method and FEM. Performance indicators of gears are extracted and compared, including contact forces, contact and bending stresses, contact stress patterns and loaded transmission errors. The results show that the VFIFE method has a stable performance and reliable accuracy under coarse or refined mesh conditions, while the FEM inaccurately calculates the contact stress of the coarse mesh model. The examples demonstrate that the proposed method could precisely analyze gear meshing problems with a coarse mesh model, which provides a new solution for gear mechanics.     

Development of size-dependent consistent couple stress theory of Timoshenko beams

In this paper, a linear size-dependent Timoshenko beam model based on the consistent couple stress theory is developed to capture the size effects. The extended Hamilton's principle is utilized to obtain the governing differential equations and boundary conditions. The general form of boundary conditions and the concentrated loading are employed to determine the exact static/dynamic solution of the beam. Utilizing this solution for the beam's deformation and rotation, the exact shape functions of the consistent couple stress theory (C-CST) is extracted, which leads to the stiffness and mass matrices of a two-node C-CST finite element beam. Due to the complexity and high computational cost of using the exact solution's shape functions, in addition to the Ritz approximate solution, a two primary variable finite element model of C-CST is proposed, and the corresponding general deformation and rotation fields, shape functions, mass and stiffness matrices are calculated. The C-CST is validated by comparing the prediction of different beam models for a benchmark problem. For the fully and partially clamped cantilever, and free-free beams, the size dependency of the formulations is investigated. The static solutions of the classical and consistent couple stress Timoshenko beam models are compared, and a criterion for selecting the proper model is proposed. For a wide range of material properties, the relation between the beam length and length scale parameter is derived. It is shown that the validity domain of the consistent couple stress Timoshenko model barely depends on the beam's constituent material.