薄膜横向振动的有限元分析

构造了一种3节点三角形膜单元,以适用于平面薄膜横向振动的有限元分析.在给出单元形函数的基础上,根据最小势能原理建立了薄膜自由振动方程,并推导了单元刚度矩阵和单元质量矩阵.研究结果表明,单元刚度矩阵和单元质量矩阵形式简单,且自由度少;通过两个典型算例,证明3节点三角形膜单元的计算结果非常接近理论解,同时可以达到很高的精度...     

悬索桥结构分析中的索-鞍座单元

为在悬索桥结构的有限元分析中真实、简洁、高效地模拟索鞍,本文建立了一类新的单元。新单元包括索段的一端固定在与其接触部分为单一半径圆弧的索鞍上,另一端分别位于索鞍两侧的两节点“左索-鞍座单元”和“右索-鞍座单元”,以及索段两端点分别位于索鞍两侧,中间一点固定于鞍座上的三节点“索-鞍座单元”,后者的鞍槽可为两不同半径圆弧的组合。根据要求的成桥状态几何参数确定结构的无应力状态时,可利用前二者进行悬索桥的单跨分析。新单元通过自动调整索与鞍座的脱离点而处于平衡状态,从而简化了计算。单元算法的推导基于有限元分析的基本原理和弹性悬链线的精确解,并利用了处于平衡状态时索与鞍座之间的内力关系。新单元可象常规单元一样直接用于成桥状态或施工过程中悬索桥结构的有限元分析。设计的算例验证了新单元的正确性,并举例说明了新单元在悬索桥结构分析中的应用。     

Rigid finite element and limit analysis

According to the lower bound theorem of limit analysis the Rigid Finite Element Method (RFEM) is applied to structural limit analysis and the linear programmings for limit analysis are deduced in this paper. Moreover, the Thermo-Parameter Method (TPM) and Parametric Variational principles (PVP) are used to reduce the computational effort while maintaining the accuracy of solutions. A better solution is also obtained in this paper. The project supported by National Natural Science Foundation of China     

Non-local finite element analysis of damped beams

Non-local viscoelastic beam models are used to analyse the dynamics of beams with different boundary conditions using the finite element method. Unlike local damping models the internal force of the non-local model is obtained as weighted average of state variables over a spatial domain via convolution integrals with spatial kernel functions that depend on a distance measure. In the finite element analysis, the interpolating shape functions of the element displacement field are identical to those of standard two-node beam elements. However, for non-local damping, nodes remote from the element do have an effect on the energy expressions, and hence on the damping matrix. The expressions of these direct and cross damping matrices may be obtained explicitly for some common spatial kernel functions and Euler–Bernoulli beam theory. Alternatively numerical integration may be applied to obtain solutions. Examples are given where the eigenvalues are compared to the exact solution for a pinned–pinned beam to demonstrate the convergence of the finite element method. The results for beams with other boundary conditions are used to demonstrate the versatility of the finite element technique.     

压电材料轴对称有限元分析

给出了横观各向同性压电材料轴对称问题有限元法列式,叙述了压电材料有限元法分析中的一些特殊处理步骤,包括无量纲化和特征值问题计算中对电势自由度的凝聚。对压电材料轴对称问题的一些经典静力问题进行有限元计算,同时对压电圆板的轴对称自由振动进行了计算,和解析结果作了比较,二者符合良好。     

基于集群的并行有限元分析研究

利用面向对象的方法实现了基于集群的并行有限元分析.首先介绍构建高性能计算集群的系统分析新方法,并针对建成集群系统的特点,对并行消息传递库MPI进行了并行语义分析,进而对其主要的实现函数进行面向对象的重构而建立起OO消息传递库,以此为基础分别利用两种不同的策略实现了面向对象的并行有限元分析(OOParaFEA: Object-Oriented Parallel FEA),一种是通过对传统的基于域分解方法的并行PCG算法进行改造而在集群平台实现,另一种是对已有的基于子结构方法的串行有限元分析程序加以扩展,加入系统方程组并行求解器而达到有限元分析并行化的目的.多个分析算例表明,基于集群进行面向对象的并行有限元分析可以有效提高计算效率,为进一步的网络化CAD/CAE研究奠定良好基础.     

High-order triangular finite element for shell analysis

A curved-shell finite element of triangular shape is described which is based on conventional shell theory expressed in terms of surface coordinates and displacements Each of the three surface displacement components is independently represented by a two-dimensional polynomial of constrained-quintic order giving the element a total of 54 degrees of freedom. Two particular geometric forms of the element are considered, viz. doubly-curved shallow and circular cylindrical. The high level of accuracy which can be achieved using few elements is demonstrated in a range of problems where comparison is made with previous finite element solutions.     

Nonlinear finite element analysis of no-tension masonry structures

A numerical approach for structural analysis of masonry walls in plane stress conditions is presented. The assumption of a perfectly no-tension material (NTM) constitutive model, whose relevant equations are in the form of classical rate-independent associated flow laws of elastoplastic material, allows one to adopt numerical procedures commonly used in computational plasticity. An accuracy analysis on the integration algorithm employed in the solution of constitutive relations has been carried out. The results obtained for some relevant case-studies and their comparison with data, available in the literature show the effectiveness of the proposed method.

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Sommario Si presenta un approccio numerico per l'analisi strutturale di pareti in muratura in stato piano di tensione. L'assunzione di un modello costitutivo per materiale perfettamente non resistente a trazione (NTM), le cui equazioni sono esprimibili nella classica forma incrementale delle leggi dello scorrimento plastico di tipo associato per materiali elastoplastici, consente di adottare procedure numeriche comunemente utilizzate in plasticità computazionale. Si conduce un'analisi di accuratezza dell'algoritmo utilizzato nell'integrazione delle equazioni costitutive del modello esaminato. I risultati ottenuti per alcuni casi analizzati ed il confronto effettuato con esempi riportati in letteratura mostrano l'efficienza dell'approccio proposto.

     

钢－混凝土组合梁非线性有限元分析

提出了部分剪力连接钢-混凝土组合梁非线性有限元分析的简化模型，该模型同时考虑了钢、混凝土材料的非线性本构关系和剪力连接件的滑移非线性对组合梁刚度和强度的影响，推导了考虑滑移的剪力连接件单元刚度矩阵。利用该模型计算了连续组合梁的极限荷载、挠度、应力以及滑移，与已有的理论计算结果和实验结果吻合，证明本方法分析钢-混凝土组合梁非线性的可靠性和实用性。     

Superconvergence analysis of lower order anisotropic finite element

The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes.The corresponding error estimation is obtained.Moreover,by using the interpo- lation postprocessing technique,a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived.Numerical results are also given to verify the theoretical analysis.     

A penalty-hybrid finite element analysis of stokes flow

A type of penalty-hybrid variational principle is suggested for the analysis of Stokesian flow. On such a basis, a finite element model is formulated featuring, among others, a priori satisfaction of the deviatoric stress and hydrostatic pressure on linear momentum balance equations. Also in the present scheme the hydrostatic pressure is successfully eliminated at the element level, leaving only nodal velocities as solution unknowns. A series of 4-node and 8-node quadrilateral elements are derived and examined. Numerical examples demonstrating their characteristic behaviors are also included.The project Supported by National Natural Science Foundation of China     

薄膜褶皱的非线性屈曲有限元分析

有限元模拟已经成为目前薄膜褶皱预测的重要工具。本文采用ANSYS SHELL63单元对薄膜受剪情况下的褶皱形变进行了非线性屈曲分析。通过本征屈曲分析得到的模态模拟了薄膜的初始缺陷。利用本文的非线性有限元模型分析得到了薄膜褶皱的波长和幅度,并与理论分析结果进行了比较,结果相近。     

Probabilistic finite element analysis of a non-gasketed flange

Stress analysis of a non-gasketed flange was computationally simulated by a finite-element method and probabilistically evaluated in view of several uncertainties in the performance parameters. Cumulative distribution functions and sensitivity factors were computed for overall heat transfer rate due to the structural and thermodynamic random variables. These results can be used to quickly identify the most critical design variables in order to optimize the design and make it cost effective. The analysis leads to the selection of the appropriate measurements to be used in structural and heat transfer analysis and to the identification of both the most critical measurements and parameters Published in Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 133–143, May 2008.     

Stochastic finite element analysis of non-linear plane trusses

—This study considers the responses of geometrically and materially non-linear plane trusses under random excitations. The stress-strain law in the inelastic range is based on an explicit differential equation model. After a total Lagrangian finite element discretization, the nodal displacements satisfy a system of stochastic non-linear ordinary differential equations with right-hand-sides given by random functions of time. The exact solution of the above stochastic differential equation is generally difficult to obtain. To seek an approximate solution with good accuracy and reasonable computational effort, the stochastic linearization method is used to find the first and second statistical moments (i.e. the mean vector and the one-time covariance matrix) of the nodal displacements. Results of simple structures under Gaussian white-noise excitation indicate that the proposed method has good accuracy (generally underestimates the r.m.s. stationary response by 5–14%) and requires only a small fraction of the computation time of the time-history Monte-Carlo method.     

Plastic limit analysis of incompatible finite element method

This paper describes an incompatible finite element model satisfying the consistencycondition of energy to solve the numerical precision problem of finite element solution inperfectly plastic analysis.In this paper the reason and criterion of the application of themodel to plastic limit analysis are discussed,and an algorithm of computing plastic limitload is given.     

基于宏观三角形分区平板壳单元的非线性有限元分析

针对剪切闭锁效应,本文研究了一种基于假设自然应变方法的宏观三角形分区平板壳单元。利用通用有限元软件ABAQUS所提供的用户自定义单元(UEL)和用户自定义材料(UMAT)子程序,本文将宏观三角形分区平板壳单元和基于损伤能释放率的混凝土弹塑性损伤本构模型成功嵌入了ABAQUS的主分析模块。经典试验McNeice双向混凝土板的数值模拟结果表明:宏观三角形分区平板壳单元对于描述板壳结构的非线性损伤行为是行之有效的。     

组合单元法在砂井地基有限元分析中的应用

针对砂井地基的平面应变有限元分析,本文首次将组合单元法引入到砂井地基的分析中,提出砂墙组合单元。该单元对常规等参元进行改进,在单元内部同时考虑砂井的涂抹作用和井阻作用,从而克服了常规有限元法在计算砂井地基时单元数和节点数过多的缺点。将砂墙组合单元加入USAP有限元计算软件,工程算例分析结果表明：与已有的各砂井地基的平面应变解答和荷兰的基础工程有限元分析软件PLAXIS相比,解答合理并有效地考虑砂井的涂抹作用和井阻作用;与常规有限元法相比,在保证计算精度的前提下,减少了可观的单元数和节点数,降低了计算的工作量。     

Response variables correlation in stochastic finite element analysis

Summary Stochastic finite element techniques are used for estimating the uncertain response of discretized structural systems which are defined by random quantitites or are subjected to random excitations. Such techniques are especially useful in view of the development of probabilistic models for the estimation of the residual lifetime of components undergoing damage-accumulation processes. A special procedure for calculating the probability distribution of the single response variable was discussed in Ref. [1].Attention is focused in this paper on the improvements to be included for estimating the correlation between the response variables of interest and their joint probability distribution.

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Sommario La dicitura elementi finiti stocastici contraddistingue quell'insieme di tecniche numeriche che consentono una stima dell'incertezza che affligge la risposta di sistemi strutturali discreti o discretizzabili, caratterizzati da parametri aleatori o/e soggetti ad eccitazioni aleatorie. L'impiego di queste tecniche si è mostrato particolarmente utile nella definizione delle variabili di ingresso di quei modelli probabilistici con cui si stima la vita residua di elementi strutturali soggetti ad accumulo di danno. Un procedimento efficiente per ricavare la legge di distribuzione di probabilità della singola variabile di risposta era stato messo a punto in [1].In questo lavoro si discutono gli sviluppi necessari per includere la stima della correlazione tra due variabili e la determinazione di distribuzioni di probabilità congiunta.

     

随机有限元方法在断裂分析中的应用

在幂律非线性随机有限元基础上,以单边裂纹板为例给出计算含量钢继裂参数,J（J积分）,δ（裂纹张开位移）,Δ（由裂纹引起的裂纹板上下底面相对位移）,θ（由裂纹引起的裂纹板上下底在相对转角）及其对基本随机变量变化率的方法和分析算例。