多孔介质中两相可混溶驱动问题的特征-混合动态有限元方法(英文)

数学上,多孔介质中一种不可压流体对另一不可压流体的相溶驱动由两个耦合的非线性偏微分方程组成,其中一个是关于压力的椭圆方程,另一个是关于浓度的抛物方程。本文用特征有限元方法结合动态有限元空间来逼近浓度,而压力和达西速度则由混合元方法来同时逼近。通过采用负模估计,我们给出了收敛性分析与误差估计。     

声表面波换能器激励的有限元仿真

采用有限元法分析了声表面波换能器电极上的激励问题。从声场波动方程、麦克斯韦方程以及压电本构方程出发,利用哈密顿原理,推导了在压电介质中声表面波有限元方程,然后采用Newmark法对有限元方程进行时域变换。分析了换能器电极上的静态电荷分布和动态电荷分布。对压电介质中声表面波振动振幅进行计算并分析了质点振动振幅随深度的变化情况。     

水力压裂的支撑剂输送分析

为了研究水力压裂中支撑剂输送过程,本文建立了支撑剂二维输送方程,以及含砂液的二维运动方程。这两个方程考虑了支撑剂沉降,并且采用了含砂液的流态指数和稠度系数与支撑剂体积浓度的函数关系。这两个方程与水力压裂三维裂缝模型中描述裂缝宽度与裂缝面上压力关系的积分方程是耦合的。裂缝延伸判据采用应力强度因子法则。应用有限元方法,模拟了水力压裂中的支撑剂输送过程。计算结果反映了支撑剂输送过程中的输送和沉降。     

极坐标系中弹性力学平面问题的Hamilton正则方程及状态空间有限元法

本文给出了极坐标系下弹性力学平面问题的Hamilton正则方程,并提出一种求解该方程的状态空间有限元法。文中通过对Hellinger-Reissner混和变分原理的修正,导出了Hamilton正则方程及其对应能量泛函,然后采用分离变量法对其场变量进行分离变量,这样就可在θ方向采用通常的有限元插值,而沿半径r方向采用状态空间法给出解析解答,从而实现了有限元法与控论制中状态空间的结合。通过计算表明,本文方法精度高。     

简支梁在无限大不可压缩流体和声学流体中的固有振动问题

本文用边界积分方程描述无限大声学流体,从而得到了控制圆截面简支梁在该流体中固有振动的积分-微分方程。在此方程基础上,分别用摄动法和有限元与摄动展开相结合的方法,计算了简支梁在无限大声学流体中的固有频率。当声速趋于无穷大时,得到了无限大不可压缩流体中简支梁的固有频率。本文的方法可推广到较为复杂的结构声辐射系统的固有频率的计算上。     

三维RIM充模模拟

采用混合数值方法对三维ＲＩＭ充模过程进行了数值模拟,即在模腔宽度上采用有限元法,而在厚度方向上采用有限差分方法,对三维问题进行求解。采用这种方法,避开了直接求取三维有限元所带来的困难,同时采用了任意拉格朗日－欧拉法处理流动前缘。文中对数值结果进行了讨论。     

一种考虑弹性多支承拉索索力求解的有限单元法

采用受拉杆件平衡控制方程的解析表达式作为形函数,构造了一种可以考虑初始内力的拉索单元。基于能量变分原理,采用该新单元导出了具有多个弹性支承拉索系统的有限元振动频率方程,确定了拉索的索力与频率的对应关系。并采用M ATLAB软件编制了索力计算的有限元程序,该程序适用于中间具有多点弹性支撑的拉索系统索力的精确计算。验证性试验和现场测试结果表明,按本文方法索力计算结果与实测结果吻合良好,精度高,能够满足实际工程需要。     

纸板厚度方向的力学模型建立

目的理论推导纸板在受到z向压缩和弯曲时的本构模型。方法对纸板进行z向压缩时,用Ramberg-Osgood方程描述加载过程的应力-应变关系。根据纸板的内部结构特点,用多孔弹性材料模型描述卸载过程的应力-应变关系。基于对纸板弯曲时变形过程的分析,利用复合材料层板模型和纤维网络模型描述弯曲时纸板层应力-应变关系。结果该模型能描述纸板在厚度方向上的力学特性,为建立完整的纸板本构建模提供参考,同时为有限元模拟纸板厚度方向变形提供依据。     

弹塑性接触有限元混合法及其在齿轮传动中的应用

弹塑性接触问题属于一种表面非线性和材料非线性耦合的双非线性问题。本文采用有限元混合法及Newton-Raphson迭代求解。通过有限元离散,建立相互接触物体的接触边界连续方程,求出接触边界上的力学参量,再耦合推导出弹塑性接触有限元列式,编制了相应的Fortran程序,并在通过实例考核以后分析了重点工程重载齿轮的弹塑性行为。数值计算结果表明,本文所提供的方法和程序是通用而有效的。计算结果令人满意。     

非线性双曲型方程有限元解的最优阶L~∞误差估计

关于线性椭圆型及双曲型方程有限元方法的L~∞模估计,已有工作[1—5]。本文给出了非线性双曲型方程有限元解的最优L~∞模误差估计。     

地震作用下水-轴对称柱体相互作用的子结构分析方法

针对水-轴对称柱体动力相互作用问题,提出了一种地震作用下水-结构相互作用的时域子结构分析方法。基于三维不可压缩水体的波动方程和边界条件,利用分离变量法将其转换为环向解析、竖向和径向数值的二维模型;基于比例边界有限元推导了截断边界处无限域水体的动力刚度方程,并将水体内域有限元方程和人工边界处的动水压力进行耦合,从而得到结构表面的动水压力方程;将轴对称柱体结构的有限元方程与动水压力方程耦合,从而得到水-轴对称柱体结构系统的时域有限元方程;数值算例验证该文提出的水-轴对称动力相互作用的子结构方法,结果表明:该文方法具有很高的精度和计算效率。通过对水中轴对称结构地震响应和自振频率的分析表明:地震动水压力对结构自振频率和动力响应的影响随水深的增加而增大。     

有限元法在粉末成形中的应用

对粉末成形的本构方程和有限元列式进行了系统全面的推导，并详细分析和讨论了有限元法分析粉体成形时的关键技术及目前粉末成形数值模拟存在的问题。     

An immersed finite element method with integral equation correction

We propose a robust immersed finite element method in which an integral equation formulation is used to enforce essential boundary conditions. The solution of a boundary value problem is expressed as the superposition of a finite element solution and an integral equation solution. For computing the finite element solution, the physical domain is embedded into a slightly larger Cartesian (box‐shaped) domain and is discretized using a block‐structured mesh. The defect in the essential boundary conditions, which occurs along the physical domain boundaries, is subsequently corrected with an integral equation method. In order to facilitate the mapping between the finite element and integral equation solutions, the physical domain boundary is represented with a signed distance function on the block‐structured mesh. As a result, only a boundary mesh of the physical domain is necessary and no domain mesh needs to be generated, except for the non‐boundary‐conforming block‐structured mesh. The overall approach is first presented for the Poisson equation and then generalized to incompressible viscous flow equations. As an example of fluid–structure coupling, the settling of a heavy rigid particle in a closed tank is considered. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment

A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial differential equation loses hyperbolicity. The approach is limited to rate‐independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extended finite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks. Copyright © 2003 John Wiley & Sons, Ltd.     

Determination of SIF for patched crack in aluminum plates by the combined finite element and genetic algorithm approach

In this paper, the finite element method is used to analyze the behaviour of repaired cracks in 2024‐T3 aluminum with bonded patches made of unidirectional composite plates. The problem is considered in Mode I condition. First the K_I stress intensity factor (SIF) is calculated by the finite element method using displacement correlation technique. Different plate and patch thicknesses and crack lengths are considered in the analyses. Then an equation is determined by using genetic algorithms for the calculation of stress intensity factor without any further finite element analysis. The equation gives reasonably accurate results.     

考虑局部拉索振动的斜拉桥抖振响应分析

桥梁结构的抖振响应受抖振力和结构动态特性的影响。在有限元分析中,建立结构动态特性矩阵时将斜拉索处理成直杆单元而忽略拉索局部振动的影响。在考虑拉索锚固点随结构运动的情况下,推导出斜拉索局部振动引起的拉索动张力公式。分析认为,虽然斜拉索的局部振动对结构整体抖振响应的影响不甚显著,但结构整体运动对斜拉索的局部振动有显著影响。     

A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.     

Axisymmetric nonlinear analysis of shallow spherical shells by a combined boundary element and finite difference method

This paper is concerned with the development of the mixed boundary element method and finite element method for the analysis of spherical annular shells under axisymmetric loads. The boundary element techniques are used to solve the equilibrium equation of shells and the central difference operator is adopted to deal with the compatibility equations. Iterative techniques are used throughout the analysis procedure. A number of numerical examples are given in the paper to illustrate the validity of the present approach.     

双层介质声传播问题的标准解及有限元解

文章通过双层介质中的声传播问题,研究了有限元方法在水下声场计算中的应用。基于传统的Galerkin方法推导出水下声场的有限元方程,采用四节点四边形单元离散求解物理域,可选择辐射边界条件、DtN (Dirichletto Neumann)非局部算子、完美匹配层来处理出射声场,得到有限元解。为了验证该有限元模型,需要高精度的参考解。水平不变均匀介质中的声传播问题存在解析解,但双层介质问题不存在解析解。因此,对于双层介质声传播问题,使用波数积分法推导出标准解。分别考虑了有限深度和无限深度双层介质两种情况,并进行了数值模拟。数值结果表明,文章所提的有限元模型与参考解非常吻合。此外,还发现当某号简正波的本征值非常接近割线时,简正波模型KRAKEN难以准确计算该号简正波的本征值,从而声场计算结果存在明显误差;但是有限元方法不需要计算本征值,所以当KRAKEN模型出现此类问题时,有限元方法仍能给出准确的声场计算结果,表明有限元方法在普适性方面优于简正波方法。