一种基于振型正交化的元素型模型修正方法

在振型正交化的一阶增量摄动格式基础上,综合元素型方法的灵活特点与矩阵型方法的公式简洁的优点,提出了内部元素联系矩阵这一概念,保持了刚度矩阵和质量矩阵的物理特性和内部元素的关联性的同时,有效的降低了求解增量方程组的欠定性,而且仅用前几阶试验频率和振型就能有效的修改系统的动力特性。最后分别用前两阶和前三阶试验频率及振型修正一个楼板结构和一个平面框架结构,表明了本方法的有效性和鲁棒性     

基于共旋法与稳定函数的几何非线性平面梁单元

建立一个准确、高效的几何非线性梁单元对于描述杆系结构的非线性行为至关重要。该文基于共旋坐标法和稳定函数提出了一种几何非线性平面梁单元。该单元在形成中把变形和刚体位移分开,局部坐标系内采用稳定函数以考虑单元P-δ效应的影响,从局部坐标系到结构坐标系的转换则采用共旋坐标法以及微分以考虑几何非线性,给出了几何非线性平面梁单元在结构坐标系下的全量平衡方程和切线刚度矩阵;在此基础上根据带铰梁端弯矩为零的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式。通过多个典型算例验证了算法与程序的正确性、计算精度和效率。     

两节点曲线索单元精细分析的非线性有限元法

从UL列式的虚功增量方程出发,引入索的基本假定,推导出了两节点曲线索单元切线刚度矩阵的显式;同时根据索的特性还导出了精确计算索单元索端力的表达式,从而建立起了一套完整的对拉索进行精细分析的非线性有限元法。应用本文方法,可进行大跨度悬索桥、斜拉桥以及张拉结构等的非线性有限元分析计算。算例结果表明,本文方法是精确有效的。     

分区混合元法分析平面裂纹问题

基于分区混合能量原理的分区混合元法是一种高精度有限元方法,可用于分析含裂纹、孔洞、切口等缺陷的问题。本文推导了分区混合元法中应力元的刚度矩阵;分析了应力元的多余零能模式,并证明了整体分析中对多余零能模式的消弭;文中还对分区混合元法中应力元的应力项数与应力单元尺寸对分析结果的影响进行了系统的讨论。     

计及二阶效应的梁杆系统动力响应分析方法研究

基于动力刚度法和有限元理论提出了一种考虑二阶效应计算梁杆动力响应的新方法。通过求解轴向力作用下Bernoulli-Euler 梁横向和轴向挠度自由振动微分方程,利用位移边界条件反解出待定系数,得到了动态精确形函数;使用经典有限元方法推导了考虑截面自身旋转惯量的质量阵和考虑二阶效应的刚度阵,该质量阵和刚度阵各元素均为轴力和圆频率的超越函数;建立了杆系结构瞬态动力学分析的动力平衡方程,给出了稳定和高效的求解方案。对几个典型的算例进行了计算分析,并与通用软件ANSYS 的计算结果进行了比较。计算结果表明:该分析梁杆系统动力响应的新方法具有较高的计算精度和效率,特别是能够准确地计入轴力对于梁杆动力响应的影响。     

低张力缆索有限元模型及其应用

为准确计算缆索在低张力时的运动状态,该文考虑缆索低张力状态时的拉伸刚度、弯曲刚度和扭转刚度,建立了一种适用于低张力缆索的三维有限元模型。首先基于细长杆理论推导了缆索的动力学微分方程,接着以三次样条曲线为试函数,运用Galerkin加权残值法导出了单元刚度矩阵,最后对其进行组合建立了缆索的整体矩阵方程,并采用Matlab编写了求解程序。将其应用于实例中,所得结果与实验结果相一致。研究成果为拖曳缆、系泊缆、潜行器脐带缆等海洋缆索的运动分析与设计提供了理论依据。     

Overcoming element quality dependence of finite elements with adaptive extended stencil FEM (AES‐FEM)

The finite element methods (FEMs) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES‐FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial basis functions, which we construct using local weighted least‐squares approximations. The method preserves the theoretical framework of FEM and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES‐FEM can use higher‐degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES‐FEM and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poisson equation and a time‐independent convection–diffusion equation. The numerical results demonstrate that AES‐FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor‐quality meshes. Copyright © 2016 John Wiley & Sons, Ltd.     

Rigid body considerations for non-linear finite element analysis

The purpose of the paper is to demonstrate how the concept of rigid body motions can be employed to derive the external stiffness matrix for an initially stressed finite element. Such a matrix is as important as the elastic and geometric stiffness matrices. It can be used not only in an eigenvalue analysis for testing the zero energy modes of a finite element under initial loadings, but for calculating the element forces in a step-by-step non-linear analysis. The two-dimensional beam element presented in this paper serves as a vehicle to demonstrate the concept involved. The principle of virtual work in its updated Lagrangian form has been adopted as the method of formulation. Several examples are provided to illustrate the adequacy of the present approach.     

用不完全模态测量数据修正有限元分析模型

提出一种基于不完全模态测量数据同时修正有限元质量矩阵与刚度矩阵的有效数值方法。运用代数特征值反问题的理论与方法，得到了满足正交关系及特征方程的最逼近有限元质量矩阵及刚度矩阵的唯一的修正质量矩阵与刚度矩阵（最优修正矩阵）。该方法有一个简洁的表达式，修正过程简单而且容易实现。数值算例表明，修正模型与模态试验数据具有非常好的一致性。     

A new enriched finite element for fatigue crack growth

This paper presents a numerical method for fatigue crack growth in the framework of finite element method, i.e. a new enriched element is presented in which only the analytical solutions around crack tips are used to describe the displacements and stresses fields. A special variational principle is introduced to simplify the mathematical derivations for discrete equation, and the stiffness matrix of the new enriched element is given in a compact form. Moreover, the stiffness matrix is found to be independent on the element size. Numerical examples on fatigue crack growth are given to illustrate the validity of the present method.     

Finite element method for piezoelectric vibration

A finite element formulation which includes the piezoelectric or electroelastic effect is given. A strong analogy is exhibited between electric and elastic variables, and a ‘stiffness’ finite element method is deduced. The dynamical matrix equation of electroelasticity is formulated and found to be reducible in form to the well-known equation of structural dynamics, A tetrahedral finite element is presented, implementing the theorem for application to problems of three-dimensional electroelasticity.     

竖向受荷长短桩基础的侧端阻力分析方法

运用幂函数有限项级数的表达式表示群桩中单桩的桩侧摩阻力分布函数,并基于弹性理论中的变形协调关系、桩体物理方程和力的平衡关系,推导了长短桩群桩基础中联系桩顶荷载和桩顶位移之间的刚度矩阵。利用该矩阵可以分析长短桩桩基础中桩侧摩阻力和桩端阻力的分布情况。对于不同桩长的群桩基础的侧阻力、端阻力与Poulos方法、Chow混合方法和有限元分析结果进行了比较,证明该方法是可行的,精度也满足要求。     

空间钢框架结构的改进双重非线性分析

为了探讨三维结构的高等分析方法,给出基于UL法的严格三维单元虚功增量方程,详细推导了考虑剪切变形影响的三维梁柱单元的几何非线性切线刚度矩阵和基于三维单元简化塑性区模型的双重非线性刚度方程,并编制空间钢框架结构的双重非线性分析程序。使用包括几何与材料双重非线性的数值算例来验证方法和计算机程序的可行性、精确度与有效性。利用该程序,只需一个单元/构件即可准确预测空间钢框架结构的极限承载力与失稳模态,提高了结构的非线性分析效率。     

矩形薄板弯曲问题的U变换-有限元法

该文扩展了U变换-有限元法分析弹性矩形薄板的范围。通过构造一个与简支、固支或二种边界条件组合的矩形板的等效系统,使刚度矩阵成为循环矩阵,采用U变换,成功解耦了有限元矩阵方程,使得有限元计算只须在一个单元上进行。给出了承受板中集中载荷和对边均布弯矩两种载荷形式下的板中挠度解析表达式。所得到的级数解不仅计算效率高,还能给出误差估计的显式表达式,能够直接掌控计算精度。算例中考察了几种不同边界条件下的计算结果,与已有理论结果的对比说明,该方法提高了计算的精度和效率。     

基于比例边界有限元法动态刚度矩阵的坝库耦合分析方法

针对坝体在水平向激励下的瞬态耦合问题和基于比例边界有限元法,推导了等横截面半无限水库的动态刚度矩阵,其值用贝赛尔函数计算。基于该动态刚度矩阵,建立了有限元法与比例边界有限元法的耦合方程,分析了水平向激励下任意几何形状的半无限水库的瞬态响应。其中,半无限水库分解成用有限元离散的任意几何形状的近场域和用比例边界有限元法模拟的远场域即等横截面半无限水库。通过比较动态刚度矩阵和动态质量矩阵模拟等横截面半无限水库的计算效率,发现它们计算精度相同,但动态刚度矩阵效率更高。数值算例表明了所发展的动态刚度矩阵与其耦合方程的正确性。     

一种利用模态测量数据修正刚度矩阵的新方法

模型修正即为利用模态测量数据修正存在但不准确的有限元模型。本文在假定有限元模型的质量矩阵与刚度矩阵均为对称非负定矩阵,并且质量矩阵是精确的情况下,提出了一种修正刚度矩阵的新方法。该方法借助于矩阵的Kronecker积与拉直算子,把需修正的变量分离出来直接对其进行修正运算,得到了满足特征方程与正交性条件的最逼近有限元刚度矩阵的唯一修正矩阵。该方法不仅保证了修正矩阵带状稀疏的特点,而且修正过程简单易行。数值例子验证了该方法的有效性。     

基于隔离非线性的实体单元模型与计算效率分析

实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。     

Free mesh method: A new meshless finite element method

A new meshless finite element method, named as the Free Mesh Method, is proposed in this paper. Once nodes are arranged in the domain to be analyzed, some temporary triangular elements are set around a node, i.e. a current central node. The contributions from the element matrices of the above temporary elements are assemebled to the total stiffness matrix. The above processes are performed on all the nodes in the domain. Finally, the solution is obtained by solving the total stiffness equation system as the usual finite element method. To demonstrate the effectiveness of the method, a simple two-dimensional heat conduction problem is solved.     

Finite control volume method as applied to a slider bearing with side-leakage

The Reynolds' equation, which governs the pressure distribution in the oil film of a lubricated bearing, has been solved numerically using finite difference and finite element methods. The latter depends on finding the integral formulation of the Reynold's equation, which is minimized to determine the pressure distribution. The finite control volume method uses the basic flow equations, assumes a given interpolation function for the pressure and, by considering the net flow towards each nodal point, the geometry stiffness is obtained which is identical to the element stiffness matrix obtained by the classical finite element approach. The motivation of the finite control volume method (FCVM) lies in the fact that the calculus of variation, a stumbling block for solution of certain flow problems, is not considered.     

太阳电池阵板间铰链副刚度参数辨识

以真实铰链副连接的有机玻璃帆板模型试验模态参数为基础 ,采用特征方程反问题的直接方法辩识铰链副的刚度参数。首先通过模态叠加法由可测自由度上的不完全试验振型拟合估计包括界面位移和转角在内的不可测自由度上的振型。然后以单板子结构的动柔度矩阵特征方程为基础。通过界面振型求解界面内力 ,并由铰链副连接元刚度矩阵建立平衡方程求解铰链副的刚度参数。工程应用实例表明良好的辨识精度和工程使用价值