广义节点有限元法

应用流形方法思想,通过引入广义节点的概念,对传统有限元方法进行改进,建立了可具有任意高阶多项式托值函数的广义节点有限元方法,计算结果表明,广义节点有限元方法较之传统有限元方法有较高的精度。     

平面非协调动态有限元法

本文通过引入高阶非协调位移模式，从Ｈｅｌｉｎｇｅｒ－Ｒｅｉｓｓｎｅｒ泛函出发，给出了非协调动态有限元的一般列式，得到了相应的收敛准则。算例表明本文方法简单、有效     

时间域有限元法

叙述时间域有限元法在国内外的进展，其中包括协调的、不协调的时间有限元法和时空有限元法，对其中的典型研究成果给出了简要介绍，从而指出这一领域深入研究的必要性．最后简要展望了时间域有限元法的发展前景．     

光滑扩展有限元方法及其特点研究

将光滑有限元法S-FEM（Smoothed Finite Element Method）的子域光滑应变技术和边域光滑应变技术同时引入到扩展有限元XFEM（Extended Finite Element Method）中，提出一种新的光滑扩展有限元法S-XFEM（Smoothed Extended Finite Element Method）。在单元选取及扩充结点选取时采用ES-FEM的光滑域划分方式，在数值积分计算刚度矩阵时采用基于三角形子域的CS-FEM积分思路，并给出了高斯点的积分策略。设计了S-XFEM程序架构并利用Matlab语言编制了S-XFEM计算程序。通过几个经典算例研究对比了XFEM和S-XFEM的特点，验证了S-XFEM的精确性和适用性。结果表明，XFEM和S-XFEM均具有很高的计算精确性和收敛性，XFEM计算精度略高于S-XFEM，而S-XFEM在网格独立性上则明显优于XFEM。     

不同拉压弹性模量壳体有限元法

1.计算假定不同拉压弹性模量的弹性理论在壳体有限元计算中应用的假定: (1)单元的内力、应力及应变状态用单元形心处的内力、应力及应变状态来代替,其精度随网格加密而提高。(2)沿壳厚将单元分层,假定单元内同一层为同一类区域。(3)根据各层区域类型的不同引入不同的弹性模量E~+、E~-和泊松比v~+、v~-,以E_1、v_1表示薄壳物理方程中的E、v。薄壳上各点为二维应力状态,σ_α、σ_β为主应力,则E_1、v_1按如下方法确定:     

反应烧结Si3N4陶瓷断裂韧性的实验研究

本文对反应烧结氦化硅 Si_3N_4陶瓷的断裂韧性进行实验研究,用三种不同试件进行了测试,这三种试件是:山形切口双悬臂粱试件,山形切口三点弯曲梁试件和直穿透切口三点弯曲梁试件.用有限元方法分析了直穿透切口三点弯曲梁切口宽度对应力强度因子的影响,结合断裂载荷测定值估算了材料的断裂韧性值,指出直切口无预制裂纹试件的测定值必须用有限元法进行修正才能得到正确结果.     

箱梁静力分析的三维有限单元法

采用三维梁、板单元 ,解决了薄壁箱梁的静力计算问题。结合在偏心荷载作用下箱梁的具体算例 ,给出箱梁翼板和腹板的翘曲正应力和剪应力分布曲线 ,并讨论了用荷载等效分解法计算箱梁时存在的一些问题     

国外几种大型微机有限元分析系统(FEAS)简介

本文简述当前国际上流行几种大型通用微机用有限元程序的概况，以及它们的比较与应用等     

SPACE-TIME FINITE ELEMENT METHOD FOR SCHRDINGER EQUATION AND ITS CONSERVATION

Energy conservation of nonlinear Schrodinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.     

哈密尔顿系统的连续有限元法及守恒性

利用常微分方程的连续有限元法,证明了线性哈密尔顿系统的连续一、二、三次有限元法为辛算法;对非线性哈密尔顿系统,本文证明了连续一次有限元在3阶量意义下近似保辛,且保持能量守恒,并在数值计算上探讨了守恒性和近似程度,结果与理论相吻合.     

Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system

This paper discusses the k-degree averaging discontinuous finite element solution for the initial value problem of ordinary differential equations.When k is even,the averaging numerical flux (the average of left and right limits for the discontinuous finite element at nodes) has the optimal-order ultraconvergence 2k + 2.For nonlinear Hamiltonian systems (e.g.,Schro¨dinger equation and Kepler system) with momentum conservation,the discontinuous finite element methods preserve momentum at nodes.These properti...     

Continuous finite element methods for Hamiltonian systems

By applying the continuous finite element methods of ordinary differential equations,the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudo- symplectic scheme respectively for general Hamiltonian systems,and they both keep energy conservative.The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems.The numerical results are in agree- ment with theory.     

关于无振荡、无自由参数有限元格式的研究

利用双曲守恒律方程的Ｔａｙｌｏｒ弱解表达式，建立了有限元法修正方程，选择合适的展开式系数能得到一系列数值格式．通过稳定性分析研究了格式的稳定性、色散误差与有限元修正方程导数项系数之间的关系，该关系与差分法的ＮＮＤ格式一致．在选定格式下，通过ＣＦＬ数可控制有限元离散解的振荡而使格式不含自由参数．最后，用数值算例验证了这一关系，并在二、三维欧拉方程作了推广应用．     

五零能模式材料设计的非线性有限元计算方法

五零能模式材料是一种新型人工超材料,特征为其弹性模量矩阵的6个特征值中5个为零,可用等效体积模量来描述,表现出类似流体的性质,可被应用于声学隐声斗篷的设计中。然而,根据A.N.Norris[1]提出的理论,设计五零能模式材料时,与应用变换声学方法设计一般声学人工超材料不同,要求其满足一非线性偏微分方程约束。本文利用非线性有限元的完全拉格朗日方法,推导了这一偏微分方程的弱形式,并给出了相应的非线性有限元计算列式,以及迭代求解的具体算法。最后,给出了五零能摸式材料设计的二维和三维坐标变换数值算例。     

Numerical analysis of one-dimensional nonlinear large-strain consolidation by the finite element method

The nonlinear partial differential equation model of Gibson et al. which governs one-dimensional large-strain consolidation is solved numerically using a semi-discrete formulation involving a Galerkin weighted residual approach. The use of quadratic Lagrange basis functions usually complicates the task of solving the system of time-dependent ordinary differential equations that are obtained with the semi-discrete Galerkin procedure. However, an efficient algorithm has been discovered yielding the advantages of quadratic interpolation without undue computational burden.Although considerable effort has already been made to solve the PDE of large-strain consolidation by numerical methods, a satisfactory set of benchmarks is still needed to assess accuracy. To fill this need, three procedures are reported which allow numerical solutions of the large-strain model to be reliably evaluated. One involves the use of perturbation methodology to provide a solution when only self-weight effects are present. A second utilizes an analytical solution developed by Philip when self-weight effects are absent and the third involves the exact calculation of the discharge flux through the upper boundary of a deposit consolidating through self-weight effects alone. All three are restricted to early-time consolidation and are illustrated in the context of the finite element method.     

A class of variational difference schemes for a singular perturbation problem

In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed. A class of variational difference schemes is constructed by the finite element method. Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation. The schemes studied in refs. [1], [3], [4] and [5] belong to the class.     

Nonlinear Parameter Identification of a Mechanical Interface Based on Primary Wave Scattering

We study stress-wave propagation in an impulsively forced split Hopkinson bar system incorporating a threaded interface. We first consider only primary transmission and reflection and reduce the problem to a first-order, strongly nonlinear ordinary differential equation governing the displacement across the interface, called the primary-pulse model. The interface is modeled as an adjusted-Iwan element, which is characterized by matching experimental and numerical eigenfrequencies as well as primary pulse amplitudes. We find that the adjusted-Iwan element parameters are dependent on preload and impact velocity (input force). A high-order finite element model paired with the identified adjusted-Iwan element is used to simulate multiple transmissions and reflections across the interface. We find that the finite element simulation reproduces the experimental results in both the wavelet and Fourier domains, validating the identification method. Our findings demonstrate that the primary-pulse model can be used for experimental parameter identification of nonlinear interfaces in waveguides.     

Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides

In this paper, a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1-D connected waveguides. First the partial differential wave equation is converted to simultaneous ordinary differential equations (ODEs) using Daubechies wavelet approximation in time. These ODEs are then solved using finite element (FE) technique by deriving the exact interpolating function in the transformed domain. Spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional FE. The localized nature of the compactly supported Daubechies wavelet allows easy imposition of initial-boundary values. This circumvents several disadvantages of the conventional spectral element formulation using Fast Fourier Transforms (FFT) particularly in the study of transient dynamics. The proposed method is used to study longitudinal and flexural wave propagation in rods, beams and frame structures. Numerical experiments are performed to show the advantages over FFT-based spectral element methods. The efficiency of the spectral formulation for impact force identification is also demonstrated.