有限元工程化的向项关键技术

本文是作者从事有限元应用开发工作的体会。从应用观点出发，作者认为：有限元数值分析及实验验证，有限元前后处理，一体化有限元软件接口，远程登录计算，是有限元方法在工程界得以普遍应用的四项关键技术；每项关键技术都在平行地发展并互相促进。     

有限元方法在变形曲线曲面造型中的应用

变形同线曲面造型方法是将ＣＡＧＤ中参数化几何描述方法与某些力学原理相结合，自动确定曲经曹面的各种控制参数，使满足给定的几何约束条件，克服忆部修改和整体光顺的矛盾，可用于构造具有复杂形状的物体，在曲线曲面插值，光顺和光滑拼接，以及Ｎ边域构造方面有优越性基于能量函数的变形模型是由能量函数，几何约束和外部载葆定义的变分问题，应用有限元技术求解可变形曲线曲面，本文对应用有限元方法时的一些关键技术，如有限元     

桥梁集成CAD系统中的有限元后处理子系统

ＢＩＣＡＤＳ是正在研制中的新一代桥梁集成ＣＡＤ系统，桥梁专用有限元后处理———ＦＥＭＰｏｓｔ是其中的重要子系统。ＦＥＭＰｏｓｔ的研制采用了当今先进的软件开发技术，实现了一致的图形界面和文档可视化等。本文简要介绍了ＦＥＭＰｏｓｔ子系统研制的关键技术和作为桥梁专用有限元后处理的突出功能。     

船舶面向对象有限元的应用研究

本文在论述了船舶结构有限元软件研究现状的基础上，综述了面向对象有限元方法的特征以及在船舶结构有限元分析软件研究中的应用。最后简要阐述了在VC6．0环境下，基于MFC类库应用面向对象方法如何编制船舶结构有限元程序Marifep。     

工程CAD系统中的有限元对象的实现

本文介绍作者研究开发的一种空间分析有限元系统，它采用面向对象的程序设计方法，编制了嵌入式有限元分析对象，它可以嵌入各种ＣＡＤ分析系统，可以用于各种弯，坡，斜桥，箱梁桥及异型桥梁结构的三维受力分析。     

枕寰枢复合体有限元模型的建模研究

在生物力学的研究中,枕寰复合体易损伤,针对结构的安全性和可靠性,建立合理有效的枕寰枢复合体有限元模型,提高结构的精度.通过CT断层扫描图片,应用医学影像处理技术、逆向造型等计算机辅助建模方法,建立了包括韧带及软骨的枕寰枢复合体有限元模型;对关键技术进行了研究,对模型进行了相应技术指标的评价和有效性验证.验证结果表明,可以在节约大量前处理时间的基础上,建立具有精细解剖结构的高精度八节点六面体有限元模型,为枕寰枢复合体有限元分析及其生物力学的研究工作奠定基础.     

Matlab中有限元脚本程序的编程

介绍在MATLAB中进行有限元计算时脚本编程的方法。脚本编程方法比使用图形界面作图方法求解更加灵活，对复杂的边界条件处理更加容易控制，它扩展了MATLAB在有限元计算方面的应用范围。     

流体结构耦联有限元分析的新进展

一、前言当前，科学研究和工程界对有限元领域的新技术发展和应用都表现出了极大兴趣，促进了有限元技术的不断发展和进步。本文主要介绍应用ADINA 程序解决的几个复杂的流体-结构耦联的工程难题。ADINA程序在生物医学领域中的应用越来越广泛，ADINA求解生物工程问题的能力也是     

高压电器开发研讨与评审阶段的SolidWorks应用

本文叙述了在高压电器开发研讨与评审阶段，如何有效快速地提高产品性能，降低开发成本，缩短产品开发周期。作者通过Solid Works三维CAD的应用，迅速进行实体建模、有限元分析和装配体分析，同时应用eDrawings的审阅与共享3D模型功能，极大提高了新品开发效率。     

DA0动态绑定机制在非线性有限元分析程序中的应用

运用有限元方法分析大型结构时，由于数据量巨大，其前后处理工作量相当可观，将数据库技术用于有限元数据的管理，能够大大提高后处理的效率。利用Microsoft Visual C 的MFC DA0(数据库访问对象)所提供的动态绑定机制，可以大大提高有限元数据管理的灵活性。作者在开发非线性有限元分析系统的过程中，采用Microsoft Access 2000关系型数据库为数据载体，文章详细阐述了MFC DA0动态绑定机制在有限元数据管理中的实现方法。     

Combinations of collocation and finite-element methods for Poisson''s equation

In this paper, we provide a framework of combinations of collocation method (CM) with the finite-element method (FEM). The key idea is to link the Galerkin method to the least squares method which is then approximated by integration approximation, and led to the CM. The new important uniformly V⁰_h-elliptic inequality is proved. Interestingly, the integration approximation plays a role only in satisfying the uniformly V⁰_h-elliptic inequality. For the combinations of the finite-element and collocation methods (FEM-CM), the optimal convergence rates can be achieved. The advantage of the CM is to formulate easily linear algebraic equations, where the associated matrices are positive definite but nonsymmetric. We may also solve the algebraic equations of FEM and the collocation equations directly by the least squares method, thus, to greatly improve numerical stability. Numerical experiments are also carried for Poisson's problem to support the analysis. Note that the analysis in this paper is distinct from the existing literature, and it covers a large class of the CM using various admissible functions, such as the radial basis functions, the Sinc functions, etc.     

Evaluation of the damage in the vault and portico of the pre-Romanesque chapel of San Salvador de Valdediós using frictional contacts and the finite-element method

Monuments are by definition unique buildings which cannot be reduced to any standard structural scheme. In this study, we have used quasi-static loads, which is common practice in many finite-element (FEM) analyses of masonry structures. Thus it is difficult to evaluate their reliability, because in addition to the many uncertainties that exist in all ‘old’ buildings, no statistics on the behaviour of similar buildings are available. In this paper we describe a study of the structure of the chapel of San Salvador de Valdediós and proposals for its restoration. The non-linear analysis is based on the application of FEM to each of the stone blocks in this ancient structure. The blocks are assembled side by side using ‘contact elements’ in order to reproduce the mechanical behaviour of the mortar and the surface conditions of the blocks, some of which are seriously damaged. A clear understanding of the structural behaviour, based on sophisticated analysis tools, can reduce the extent of the remedial measures necessary for the restoration of the chapel vault and portico. In this case, severe damage to the chapel vault has affected the portico, resulting in the possibility of a structural collapse. Finally, based on the numerical results obtained for different load cases and hypotheses, we propose a solution for the repair of this part of the chapel using either traditional materials or compatible substitutes.     

读取AutoCAD图形交换文件的两个应用

本文介绍了从ＡｕｔｏＣＡＤ中提取图形数据的分析，并列举了这方面的两个应用：其一是把ＡｕｔｏＣＡＤ图形转换成Ｗｉｎｄｏｗｓ图形，其二是使用ＡｕｔｏＣＡＤ描述结构，进行有限元分析，并回送信息在ＡｕｔｏＣＡＤ下显示出分析结果。     

Numerical method for the solution of the regulator equation with application to nonlinear tracking

A numerical method to solve the so-called regulator equation is presented here. This equation consists of partial differential equations combined with algebraic ones and arises when solving the output-regulation problem. Solving the regulator equation is becoming difficult especially for the nonminimum phase systems where reducing variables against algebraic part leads to a potentially unsolvable differential part. The proposed numerical method is based on the successive approximation of the differential part of the regulator equation by the finite-element method while trying to minimize a functional expressing the error of its algebraical part. The method is analyzed to obtain theoretical estimates of its convergence and it is tested on an example of the “two-carts with an inverted pendulum” system. Simulations are included to illustrate the suggested approach.     

Ellipsis 3D: A particle-in-cell finite-element hybrid code for modelling mantle convection and lithospheric deformation

We have extended the two-dimensional geodynamics finite-element code “Ellipsis” to three-dimensions. Ellipsis uses a hybrid particle in a cell scheme, which combines a fixed mesh of computational points and a dense arrangement of mobile material points. The fixed Eulerian mesh allows very fast computation, performed in Ellipsis via a multigrid iteration method, while the Lagrangian particle reference frame allows the tracking of material interfaces and history-dependent properties such as strain history for strain-softening materials. The method is exceptionally useful in very large deformation analyses, where purely Lagrangian approaches would be severely hampered by the need for remeshing to minimize element distortion. The Gnu Public Licensed Ellipsis3D code lends itself to combined 2D/3D model prototyping, and has proven to be an excellent geodynamics teaching tool for modelling, covering mantle convection, lithospheric extension and plume–lithosphere interaction.     

The effect of DNA probe distribution on the reliability of label-free biosensors

As the design of label-free DNA biosensors matures, and their sizes reduced to enhance their sensitivity, not much has been researched about the variations in the received signal with the positioning of the probes on the sensitive surface. We approach this issue computationally in this paper. By adopting the finite-element model on a three-dimensional biological field-effect transistor (BioFET) slice, and running Monte-Carlo simulations on the positions of the DNA molecules, we extract the expected variations in the signal. Then, we show that signal-to-noise (SNR) ratio can be low enough to hinder the functionality of the device, placing a limitation on how low the sensitivity of a sensor of a certain size can be.     

An improved finite-element contact model for anatomical simulations

This work focuses on the simulation of mechanical contact between nonlinearly elastic objects, such as the components of the human body. In traditional methods, contact forces are often defined as discontinuous functions of deformations, which leads to poor convergence characteristics and high-frequency noises. We introduce a novel penalty method for finite-element simulation based on the concept of material depth, which is the distance between a particle inside an object and the objects boundary. By linearly interpolating precomputed material depths at node points, contact forces can be analytically integrated over contact surfaces without raising the computational cost. The continuity achieved by this formulation reduces oscillation and artificial acceleration, resulting in a more reliable simulation algorithm.     

Point placement algorithms for Delaunay triangulation of polygonal domains

In some applications of triangulation, such as finite-element mesh generation, the aim is to triangulate a given domain, not just a set of points. One approach to meeting this requirement, while maintaining the desirable properties of Delaunay triangulation, has been to enforce the empty circumcircle property of Delaunay triangulation, subject to the additional constraint that the edges of a polygon be covered by edges of the triangulation. In finite-element mesh generation it is usually necessary to include additional points besides the vertices of the domain boundary. This motivates us to ask whether it is possible to trinagulate a domain by introducing additional points in such a manner that the Delaunay triangulation of the points includes the edges of the domain boundary. We present algorithms that given a multiply connected polygonal domain withN vertices, placeK additional points on the boundary inO(N logN + K) time such that the polygon is covered by the edges of the Delaunay triangulation of theN + K points. Furthermore,K is the minimum number of additional points such that a circle, passing through the endpoints of each boundary edge segment, exists that does not contain in its interior any other part of the domain boundary. We also show that by adding only one more point per edge, certain degeneracies that may otherwise arise can be avoided.     

Structural natural-frequency shape-sensitivity analysis: a fixed-basis-function finite-element approach

The domain-shape-sensitivity of structural natural frequencies is determined using a new finite-element approach called the fixed-basis-function finite-element approach. The approach adopts the point of view that the finite-element grid is fixed during the sensitivity analysis; therefore it is referred to as a Fixed Basis Function Shape Sensitivity finite-element analysis. This approach avoids the requirement of explicit or approximate differentiation of finite-element matrices and vectors and the difficulty or errors resulting from such calculations. Effectively, the sensitivity to boundary shape change is determined exactly; thus the accuracy of the solution sensitivity is dictated by the accuracy of the finite-element analysis. The sensitivity analysis is undertaken within the context of Rayleighs principle and is developed in quite general terms. It is shown that the evaluation of sensitivity matrices involves only modest calculations beyond those for the finite-element analysis of the reference problem; certain boundary integrals on the reference location of the moving boundary are required. In addition, boundary reaction forces and sensitivity boundary conditions must be evaluated. The present formulation separates solution sensitivity from finite-element grid sensitivity and provides a unique representation of boundary perturbations within the context of isoparametric finite-element formulations. The work is illustrated for beam as well as plate problems. Excellent agreement is obtained for shape-sensitivity calculations that compare exact solutions, fixed-basis finite-element results, and overall finite-difference approximations to the finite-element sensitivity results. It is illustrated that the finite-element eigenvalue problem and the fixed-basis finite-element eigenvalue-sensitivity results exhibit similar accuracy and convergence characteristics.