幂律全塑性罚函数随机有限元

用罚函数有限元方法解决平面应变下的体积下可压缩问题,应用摄动有限元理论发展幂律全塑性随机有限元,并以弹性模是E,泊松比u和节点坐标等的基本随机变量,推导有限元列式,给出单板受拉,梁受弯的算例。     

我国塑性本构关系研究的近况

本文概述了近十年来我国塑性本构关系研究的主要情况,包括微应变与有限变形下的一般性理论研究、微观与宏观相结合的本构理论讨论,实验研究和数值模拟的研究.     

冲击载荷作用下结构动态响应分析的罚函数有限元法

基于罚函数法，根据接触－冲击问题的边界条件，运用双线性参数法推导出用有限元模拟三维接触－冲击问题的具体算法，并对杆和梁在冲击载荷下的动态响应进行了仿真分析，取得较好计算结果。     

土塑性力学的建立与发展

土塑性力学是现代塑性理论在土力学中应用的一门新兴学科.本文回顾了近30年来土塑性力学的形成和发展,并介绍了它的主要内容.      

软岩三维非线性统一弹粘塑性本构模型有限元分析

在作者已建立的软岩三维非线性统一弹粘塑性软化本构模型基础上,讨论了软岩三维非线性统一弹粘塑性本构模型有限元分析过程,即推导了软岩三维非线性统一弹粘塑性屈服面(破坏面)的流动矢量表达式,便于编程与通用的有限元程序接口,进行二次开发;利用张量求导的原则,导出了流动矢量对应力求导公式中关键矩阵的具体表达式,并结合平面应力、平面应变和轴对称问题的特点进行了简化,得出了适合于分析二维问题的关键矩阵的表达式;采用流动矢量奇异性的统一处理方法,有效地处理了各种角点奇异性问题;最后给出了有限元分析的流程图,便于编制有限元程序.     

45钢动态塑性本构参量与验证

运用静态实验机和SHPB装置,对45钢在常温～750C、应变率为10-4～103 s-1下的力学行为进行了研究,拟合得到了Johnson-Cook本构模型参量。开展了Taylor圆柱撞击的火炮实验,运用LS-DYNA进行了相应的数值模拟,通过二者的比较对本构模型参量进行了验证,表明所得模型参量可以较好地描述材料在高速变形下的大应变力学行为。     

混凝土黏塑性动力损伤本构关系

从静力弹塑性损伤本构关系的基本框架出发, 综合考虑塑性应变与损伤 演化的率敏感性, 建立了能够较为全面地描述混凝土在动力加载条件下非线性性能的混凝土 黏塑性动力损伤本构模型. 为了考虑塑性应变的率敏感性, 基于Perzyna理论推导了有效应 力空间黏塑性力学基本公式, 采用改进的Perzyna型动力演化方程, 将损伤静力演化方程推 广到动力加载情形. 基于并联弹簧模型, 从概率论的角度推导给出了一维损伤静力演化方程, 并基于能量等效应变的基本概念将其推广到多维损伤演化. 利用数值模拟, 计算得到了 混凝土在不同应变率下的应力应变全曲线, 同时得到了一维动力提高因子和二维动力强度包 络图, 数值结果与试验结果的对比表明了该模型的有效性.     

基于微结构动态演化机制的单晶镍基高温合金晶体塑性本构及其有限元模拟

因其优异的高温力学性能,镍基单晶高温合金在航空航天和能源等领域得到了广泛的应用.镍基单晶高温合金优异的高温性能来源于其特有的两相微结构.基于代表体胞模型及分块均匀化方法,以位错密度为主要内变量,发展了一个包含两相微结构和位错演化信息的单晶镍基高温合金塑性行为的本构模型.该本构模型充分考虑了镍基单晶合金中位错在基体相和沉淀增强相中的多种演化机制,例如,基体位错八面体滑移、立方滑移、位错攀移、交滑移、位错弓出、位错切过沉淀增强相以及位错Kear-Wilsdolf(K-W)锁形成与解锁等.在商用有限元软件ABAQUS的框架下,编制了UMAT用户材料子程序.利用该用户子程序,对单晶和多晶镍基高温合金在不同温度、不同加载方向下的单调塑性、循环塑性、蠕变等典型行为进行了计算模拟.结果表明:该晶体塑性本构模型能"统一地"刻画镍基高温合金在不同温度、不同方向下的多种变形行为,并与实验结果具有良好的一致性.     

一种化学-力学耦合连续介质理论与数值格式

对化学驱动的连续介质化学-力学耦合系统进行研究,从热力学定律和化学势角度出发,推导了等温过程的化学-力学耦合本构关系和控制方程,利用变分方法建立了化学-力学耦合系统的能量泛函,得到化学-力学耦合控制方程的等效积分形式和相应的有限元列式. 结合算例,对连续介质的化学-力学耦合行为进行了数值计算,数值结果反映了化学与力学系统的相互耦合作用,即浓度变化能引起介质的变形,同样力学作用也能引起浓度重分布. 从全新的角度建立了描述连续介质的化学-力学耦合行为的基本理论和数值方法,能够较好地反映一类连续介质的化学-力学耦合行为.      

有限散射信号下二维缺陷形状识别的罚函数方法

研究在有限照射角度和频带宽度下二维缺陷的形状识别问题。首先,通过引进介质参数扰动函数,建立介质参数扰动函数和弹性波散射场之间的非线性关系,并将所关心的缺陷的形状识别问题转化为关于扰动函数的反演;然后,利用变分技术和优化方法求解,为了弥补散射数据的不足,在总的目标函数中,采用附加度量函数作为罚函数;最后,对后场散射远场测量时有限照射角度和频带宽度下几种典型缺陷进行了模拟识别,表明了;表明了罚函数法的有效性。     

A high-order characteristics/finite element method for the incompressible Navier-Stokes equations

In this paper we consider a discretization of the incompressible Navier-Stokes equations involving a second-order time scheme based on the characteristics method and a spatial discretization of finite element type. Theoretical and numerical analyses are detailed and we obtain stability results abnd optimal eror estimates on the velocity and pressure under a time step restriction less stringent than the standard Courant-Freidrichs-Levy condition. Finally, some numerical results obtained wiht the code N3S are shown which justify the interest of this scheme and its advantages with respect to an analogous first-order time scheme. © 1997 John Wiley & Sons, Ltd.     

Gauge finite element method for incompressible flows

A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J‐G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher‐order) finite elements. This method can achieve high‐order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARANIETRIC HYBRID FINITE ELEMENT ANALYSIS

IntroductionSince T.H.H.Pain firstly puts forward hybrid element method[1]in1964, the researchand application of hybrid element have got great development. T.H.H.Painet al.havemade important pioneer works in the domain of the research on incompatible displacementstructure hybrid elementstress pattern[2,3]in recentdecades. Reference [4] had provided theoptimizing design concept of hybrid element further and established standardization methodof incompatible displacement structure hybrid eleme…     

对流_扩散问题的6节点三角形单元流线迎风有限元法和自适应网格重分技术

A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.     

流体饱和两相多孔介质拟静态问题的混合有限元方法

针对基于混合物理论的两相多孔介质模型,采用Galerkin加权残值有限元法,导出求解所静态问题的基于us-uF-P变量的混合有限元方程,由于系统方程的系数矩阵非定,进而针对该方程组提出了一种失代求解方法,并由分片试验得出节点压力插值函数的阶须低于固体相节点的位移插值函数的阶的结论,算例结果表明,采用基于u2-uF-p变量的混合法计算所得的固体相和流体相速度以及固体相的有效应力与罚方法一致,而压力值的粗度高于罚方法。     

Boundary-type finite element method for wave propagation analysis

The boundary-type finite element method has been investigated and applied to the Helmholz and mild-slope equations. Four types of interpolation function are examined based on trigonometric function series. Three-node triangular, four-node quadrilateral, six-node triangular and eight-node quadrilateral elements are tested; these are all non-conforming elements. Three types of numerical example show that the three-node triangular and four-node quadrilateral elements are useful for practical analysis.     

Three‐dimensional simulation of planar contraction viscoelastic flow by penalty finite element method

The planar contraction flow is a benchmark problem for the numerical investigation of viscoelastic flow. The mathematical model of three‐dimensional viscoelastic fluids flow is established and the numerical simulation of its planar contraction flow is conducted by using the penalty finite element method with a differential Phan‐Thien–Tanner constitutive model. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The distributions of velocity and stress obtained by simulation are compared with that of Quinzani's experimental results detected by laser–doppler velocimetry and flow‐induced birefringence technologies. It shows that the numerical results agree well with the experimental results. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids. Copyright © 2009 John Wiley & Sons, Ltd.     

New stabilized finite element method for time‐dependent incompressible flow problems

A new stabilized finite element method is considered for the time‐dependent Stokes problem, based on the lowest‐order P₁?P₀ and Q₁?P₀ elements that do not satisfy the discrete inf–sup condition. The new stabilized method is characterized by the features that it does not require approximation of the pressure derivatives, specification of mesh‐dependent parameters and edge‐based data structures, always leads to symmetric linear systems and hence can be applied to existing codes with a little additional effort. The stability of the method is derived under some regularity assumptions. Error estimates for the approximate velocity and pressure are obtained by applying the technique of the Galerkin finite element method. Some numerical results are also given, which show that the new stabilized method is highly efficient for the time‐dependent Stokes problem. Copyright © 2009 John Wiley & Sons, Ltd.     

A boundary-type finite element model for water surface wave problems

A new combinative method of boundary-type finite elements and boundary solutions is presented to study wave diffraction-refraction and harbour oscillation problems. The numerical model is based on the mild-slope equation. The key feature of this method is that the discretized matrix equation can be formulated only by the calculation of a line integral, since the interpolation equation which satisfies the governing equation in each element is used. The numerical solutions are compared with existing analytical, experimental, observed and other numerical results. The present method is shown to be an effective and accurate method for water surface wave problems.