Delaunay三角剖分在构造应力场数值模拟中的应用

运用有限元分析进行数值模拟的方法来研究构造应力场,首先需要对所有地质模型进行有限元三角型单元剖分。传统的手工剖分效率和精度都不高,利用计算机自动剖分可以达到较高的精度和效率,从而为高效地进行构造应力场数值模拟打下基础。本文提出了一种先无约束剖分再加入约束边的Delaunay三角网剖分算法,先对整个区域进行均匀的三角剖分,再以地质体界线为约束条件修改剖分,继而生成按地质体为剖分对象的三角网,并对其编程实现,实验证明该算法应用效果良好,并且避免了由于容差过小而导致的剖分三角形过于狭长的问题,程序实现简单,具有较强的鲁棒性。     

平面应力问题新型广义有限元法

结合广义有限元和理性有限元的优势,针对平面应力问题提出一种新型广义四边形单元.该单元考虑泊松效应,以节点位移自由度约束弹性力学平面应力方程的半解析解,构造单元位移模式的附加项,较准确地反映真实位移场,提高单元的计算精度.推导新型广义单元及其等参单元的形函数公式,设计分片试验和数值算例验证单元的精度.数值算例结果表明：在规则网格和非规则网格下新单元的计算精度均优于传统有限元和广义有限元.新单元具有精度高且易于程序实现的特点,可推广应用到实际工程的结构分析中.     

基于任意六面体单元数据场的可视化研究

任意８节点六面体单元是有限元分析中常见、且有效的体单元。为了有效地实现对任意六面体剖分结构的结果可视化,提出了基于体单元节点相关性的等值面构造算法,可简捷地确定出等值面的位置,进而得出任意剖面上的等值线,该等值面构造算法突破了以往算法中受规则立方体单元的限制,而且简单可行、实用可靠。     

单断层地质体真三维建模算法

针对断层地质体三维实体建模中存在的问题,提出了一种能够恰当表达断层地质体的真三维模型-VGTP模型.引进了虚拟地层延伸面的概念,减少了VGTP体元构成的复杂性,建立了一种基于VGTP模型的单断层地质体建模算法;针对一个VGTP体元中包含多种不同质地层体的情况,逐一计算包裹每种地层的多面体;通过一种多面体的四面体剖分算法-切角法,把地层多面体剖分成四面体.该算法屏蔽了建模过程的复杂性,整个建模过程较少用户干预,提高了建模过程的自动化水平,为矿山断层地质体三维建模提供了一种新的思路.     

地质结构重叠域的限定Delaunay三角剖分研究

在石油储量分析的三维地质建模中出现了重叠域，需要采用特殊处理使之能应用通常的三角网格剖分算法，通过引入桥边和相交环线的概念，提出了区域子分和联动剖分算法，为重叠域的限定Delaunay三角剖分给出了一种工程处理方法，并给出了该方法对三维地质建模中逆断层剖分的实例．该方法在机械零件的复杂裂纹区应力分析、异质结构中含非流形界面的有限元分析等领域也有参考价值．     

一种基于小波变换的三维体数据压缩算法

该文结合三维小波变换与八叉树算法,提出了一种新的三维体数据压缩算法。该算法利用小波的多分辩率分析能力对体数据进行压缩,同时结合了八叉树特点对体数据进行编码、存储与重构。实际应用表明该算法能较好地对体数据进行压缩,并且能快速地进行重构和随机地访问体单元数据。     

大坝地震反应数据场快速体绘制算法

为了弥补传统体绘制静止画面时，不能明确判断场值集中部位的不足，提出了一种快速体绘制算法，针对大坝地震反应有限元计算数据场，根据每个单元法线与视线夹角最小的表面来选择剖切方向，将单元剖切成多个四边形面后进行颜色融合和叠加，大大提高了体绘制速度，实现了动态观察体绘制图，从而清楚地分析场值集中部位。     

抛物问题中面向协调元的模型态误差估计方法

针对含有复杂几何属性的模型会给有限元网格剖分造成困难并产生大量冗余单元的问题,为了有效地提高有限元求解效率,在确保分析解可靠的前提下合理简化模型,提出一种估算模型简化前后分析解空间差异程度的方法.首先比较了模型简化前后的网格剖分结果及场函数之间的差异,在此基础上,依据面向仿射等价协调元和等参协调元2种单元的经典插值精度定理估计出模型简化前后分析解空间的差异程度,为判断模型简化策略是否合理提供客观依据.理论分析及实验结果表明,该方法能够客观地反映出模型简化前后分析解空间的实际差异.     

基于多角度光学投影表面重建的三维自发荧光光源定位算法

在自发荧光断层成像（Bioluminescent tomography imaging,BLT）中,双模态融合（光学模态与结构模态）可充分利用结构模态提供的高精度3D几何结构,重建三维表面荧光光通量分布,进而实现小动物内部荧光光源定位.然而,与纯光学模态相比,双模态融合存在采集系统复杂、成本高、数据处理繁琐及存在电离辐射（如CT）等问题.因此,研究基于纯光学3D几何结构的自发荧光光源定位方法对BLT具有重要意义. 本文在搭建纯光学自发荧光断层系统（All-optical bioluminescence tomography system,AOBTS）的基础上,提出一种基于多角度光学投影表面重建的三维自发荧光光源定位方法. 本方法由基于多角度光学投影的3D表面重建、多角度荧光无缝融合、荧光光通量的量化校正以及自发荧光内部光源重建4部分组成. 通过真实小鼠内部植入荧光光源实验表明,与传统纯光学方法相比,本文提出方法不仅改进了3D表面重建方法,而且增加了多角度荧光无缝融合,可实现真实小鼠的三维自发荧光光源定位,初步实验证明具有小动物预临床实验潜力.     

一种用于分布参数系统移动边界的自适应剖分数值方法

本文提出通过对具有移动边界分布参数系统中的移动边界的一步预报,自适应生成剖分 网格,然后通过系统的焓方程应用有限元方法求解,得到具有移动边界的分布参数系统的数值 解.结果表明,这种方法较好地解决了用有限元方法求解该类系统的数值解时遇到的移动边 界附近数值解精度与网格剖分过细所导致的计算量过大的矛盾.为具有移动边界的分布参数 系统的建模和仿真提供了一种有效的数值计算方法,同时也为研究系统的控制、估计、辨识等 问题的数值方法打下了基础.     

Two-stage source reconstruction algorithm for bioluminescence tomography using hybrid FEM

A two-stage source reconstruction algorithm for bioluminescence tomography (BLT) is developed using hybrid finite element method (FEM). The proposed algorithm takes full advantages of linear and quadratic FEMs, which can be used to localize and quantify bioluminescent source accurately. In the first stage, a large permissible region is roughly determined and then iteratively evolved to reduce matrix dimension using efficient linear FEM. In the final stage, high-convergence quadratic FEM is applied to improve reconstruction result. Both numerical simulation and physical experiment are performed to evaluate the proposed algorithm. The relevant results demonstrate that quantitative reconstruction can be well achieved in terms of computation efficiency, source position, power density, and total power when compared with previous studies.     

A spline wavelet finite element formulation of thin plate bending

The wavelet scaling functions of spline wavelets are used to construct the displacement interpolation functions of triangular and rectangular thin plate elements. The displacement shape functions are then expressed by spline wavelet functions. A spline wavelet finite element formulation of thin plate bending is developed by using the virtual work principle. Two numerical examples have shown that the bending deflections and moments of thin plates agree well with those obtained by the differential equations and conventional elements. It is demonstrated that the current spline wavelet finite element method (FEM) can achieve a high numerical accuracy and converges fast. The proposed spline wavelet finite element formulation has a wide range of applicability since it is developed in the same way like conventional displacement-based FEM.     

Intelligent finite element method: An evolutionary approach to constitutive modeling

In this paper, a new approach is presented, for constitutive modeling of materials in finite element analysis, with potential applications in different engineering disciplines. The proposed approach provides a unified framework for modeling of complex materials, using evolutionary polynomial regression-based constitutive model (EPRCM), integrated in finite element analysis. Evolutionary polynomial regression (EPR) is a computing technique that generates a transparent and structured representation of the system being studied. The main advantage of EPRCM over conventional constitutive models is that it provides the optimum structure for the material constitutive model representation, as well as its parameters, directly from raw experimental (or field) data. The proposed algorithm provides a transparent relationship for the constitutive material model that can readily be incorporated in a finite element model (FEM). The incorporation of EPRCM into FEM will be presented and the application of the resulting methodology for material modeling in finite element analysis will be illustrated through two examples.     

A Large scale finite element analysis using domain decomposition method on a parallel computer

A parallel finite element analysis based on a domain decomposition technique (DDT) is considered. In the present DDT, an analysis domain is divided into a number of smaller subdomains without overlap. Finite element analyses of the subdomains are performed under the constraint of both displacement continuity and force equivalence among them. The constraint is satisfied through iterative calculations based on either the Uzawa algorithm or the Conjugate Gradient (CG) method. Owing to the iterative algorithm, a large scale finite element analysis can be divided into a number of smaller ones which can be carried out in parallel.

The DDT is implemented on a parallel computer network composed of a number of 32-bit microprocessors, transputers. The developed parallel calculation system named the ‘FEM server type system’ involves peculiar features such as network independence and dynamic workload balance.

The characteristics of the domain decomposition method such as computational speed and memory requirement are first examined in detail through the finite element calculations of homogeneous or inhomogeneous cracked plate subjected to a tensile load on a single CPU computer.

The ‘speedup’ and ‘performance’ features of the FEM server type system are discussed on a parallel computer system composed of up to 16 transputers, with changing network types and domain decompositions. It is clearly demonstrated that the present parallel computing system requires a much smaller amount of computational memory than the conventional finite element method and also that, due to the feature of dynamic workload balancing, high performance (over 90%) is achieved even in a large scale finite element calculation with irregular domain decomposition.     

基于剖面的三维有限元可视化方法研究

提出了一种三维不规则数据场的任意形状截面快速剖切算法。该算法利用有限元网格共边的特点实现相交的单元体快速查找并有效减少求交计算次数。讨论了任意剖切面上的彩色云图生成方法。研究了在多剖切面的基础上,实了不规则数据场的体绘制。实践证明,该方法快速有效,效果良好。     

基于Kriging模型的航空发动机管道系统有限元模型修正

为获得精确可靠的航空发动机外部管道结构动力学模型,采用将Kriging模型与多目标遗传算法(MOGA)相结合的模型修正方法进行有限元模型修正.首先进行管道模型的模态试验和有限元建模,分别获得模态参数的试验值和有限元分析值；然后在合理的参数选取和试验设计(DOE)的基础上,拟合得到Kriging模型；最后基于Kriging模型采用多目标遗传算法进行有限元模型修正,并对比了不同修正方法的精度和修正效果.结果表明：采用Kriging模型进行有限元模型修正可以有效提升修正效果,获得更为准确的有限元模型；对于航空发动机管道系统,基于Kriging模型的模型修正方法相较于基于灵敏度分析的模型修正方法具有更高的修正效率和修正精度.     

基于投影法的四面体网格切割算法

四面体网格切割算法是有限元仿真中的重要组成部分，切割的结果决定了刚度矩阵的更新速度和精度。本文在研究Cotin算法和Bielser算法的基础上，采用了预投影的方法，将部分顶点投影到切割平面上，使原先的四面体分割转化为相邻四面体分离，以达到简化分割的目的。与Cotin算法和Bielser算法相比，由该算法得到的网格切割边界更加合理，剖分比更低，提高了刚度矩阵更新的速度和精度。     

Wavelet transformation based multi-time scaling method for crystal plasticity FE simulations under cyclic loading

Microstructure based mechanistic calculations, coupled with physically motivated crack initiation criterion, can provide effective means to predict fatigue cracking in polycrystalline materials. However the accommodation of large number of cycles to failure, as observed in the experiments, could be computationally exhaustive to simulate using conventional single time scale finite element analysis. To meet this challenging requirement, a novel wavelet transformation based multi-time scaling algorithm is proposed for accelerated crystal plasticity finite element simulations in this paper. An advantage over other conventional methods that fail because of assumptions of periodicity etc., is that no assumption of scale separation is needed with this method. The wavelet decomposition naturally retains the high frequency response through the wavelet basis functions and transforms the low frequency material response into a “cycle scale” problem with monotonic evolution. The method significantly enhances the computational efficiency in comparison with conventional single time scale integration methods. Adaptivity conditions are also developed for this algorithm to improve accuracy and efficiency. Numerical examples for validating the multi-scaling algorithm are executed for a one dimensional viscoplastic problem and a 3D crystal plasticity model of polycrystalline Ti alloy under the cyclic loading conditions.     

并行计算水下大尺度弹性壳体的低频声散射

有限元与边界元耦合模型是研究水下弹性壳体目标低频声散射常用的数值方法。应用该模型计算大尺度弹性目标的声散射时需要大量的计算时间与存储空间,采用并行数值的方式可以解决这一问题。首先并行计算生成有限元矩阵和边界元矩阵,然后应用并行化的广义极小残差(GMRES)迭代算法求解大型非对称线性方程组。详细叙述了并行GMRES(m)迭代算法的执行过程,并以球壳的声散射计算为例分析了迭代步数对算法收敛情况的影响。最后计算了Benchmark目标模型的低频散射声场,分析了其收发分置散射目标强度以及表面声场的分布。     

Research on delamination monitoring for composite structures based on HHGA–WNN

Due to the deficiencies of the training algorithms for available wavelet neural network used for structural health monitoring, a new hybrid hierarchy genetic algorithm was introduced by combining hierarchy genetic algorithm and least-square method to improve the learning procedure of wavelet neural network. The hybrid algorithm was able to determine the structure and parameters of the wavelet neural network simultaneously. In this algorithm, adaptive crossover and mutation probability were used to accelerate the genetic speed and avoid the occurrence of prematurity. The modal frequencies of a glass/epoxy laminates beam with varying assumed delamination sizes and locations were computed using finite element method and fed into the wavelet neural network to predict the delamination location and its extent. The simulation demonstrates that the wavelet neural network based on hybrid hierarchy genetic algorithm is robust, promising and converges very fast.