基于增量本构关系弹塑性分析的无网格伽辽金法

在无网格伽辽金法的基础上，采用增量形式的无网格伽辽金法的插值方法，并利用应力应变增量形式表征材料的弹塑性本构关系，在小变形假设的前提下，提出了基于增量本构关系的弹塑性分析的无网格伽辽金法；采用罚参数修正了能量变分方程式，方便地实现了无网格伽辽金法的本质边界条件．对二维平面问题及轴对称问题的计算结果表明：运用增量形式的无网格伽辽金法进行弹塑性问题的数值分析，具有较高的计算精度，且适应性强，从而为材料的弹塑性分析计算提供了一种实用方法。     

无网格-有限元直接耦合法

基于广义单元概念,发展了一种无网格-有限元耦合的新方法,即无网格-有限元直接耦合法。该方法将有限元、无网格中数值意义上的单元定义为广义单元,利用在每一个单元内假设的形函数来分片地表示全求解域上待求的未知场函数。与其它耦合方法相比较,该方法既不需要构造过渡区形函数,又不增加额外的计算量。数值算例表明该方法具有效率高、简便实用的特点。     

The interpolating element-free Galerkin method for elastic large deformation problems

This paper presents an interpolating element-free Galerkin(IEFG) method for solving the two-dimensional(2D) elastic large deformation problems. By using the improved interpolating moving least-squares method to form shape function, and using the Galerkin weak form of 2D elastic large deformation problems to obtain the discrete equations, we obtain the formulae of the IEFG method for 2D elastic large deformation problems. As the displacement boundary conditions can be applied directly, the IEFG method can acquire higher computational efficiency and accuracy than the traditional element-free Galerkin(EFG)method, which is based on the moving least-squares approximation and can not apply the displacement boundary conditions directly. To analyze the influences of node distribution, scale parameter of influence domain and the loading step on the numerical solutions of the IEFG method, three numerical examples are proposed. The IEFG method has almost the same high accuracy as the EFG method, and for some 2D elastic large deformation problems the IEFG method even has higher computational accuracy.     

含两个圆形孔洞岩盐路基稳定性的数值分析

用无网格伽辽金法（EFGM）按平面应变问题对含两个圆形孔洞的岩盐路基进行稳定性分析,给出了针对不同孔洞埋深的临界载荷.数值结果表明,EFGM对于解决含两个孔洞的应力集中问题是有效且灵活的.     

Application in metal rheological forming of element-free Galerkin method

The element-free method is a new numerical technique presented in recent years.It uses the moving least square(MLS) approximation as its shape function,and it is determined by the basic function and weight function.The weight function is the mainly determining factor,so it greatly affects the accuracy of the computational results.The element-free Galerkin method(EFGM) was applied for the solution to plastic large deformation.The simulation of metal rheological forming was successfully done by programming and its results were visualized by using the plotting and data analyses software Tecplot.Then plastic strain under different stages during rheological forming and the three principal stresses at the last deformation were obtained.The example shows the feasibility of EFGM used for metal rheological forming and provides a new method for numerical simulation of rheological forming of complex parts.     

小波插值Galerkin法解二维静电场中的边值问题

提出了一种偏微分方程的数值解法,即小波插值Ｇａｌｅｒｋｉｎ法,它是利用具有紧支撑 　的 Ｄａｕｂｅｃｈｉｅｓ小波函数的自相关函数得到解空间的一组具有插值特性的 Ｒｉｅｓｚ基．讨论了 系数矩阵的预处理技术和多介质问题的处理方法;在混合边界条件的处理中使用了外小波, 既简化了边界条件的处理,又提高了近似解的精度．并将小波插值 Ｇａｌｅｒｋｉｎ法应用在二维 静电场边值问题的数值计算中,得到了较好的结果,与此同时给出了有限元法的计算结果．     

对称叠层板稳定计算的一种新方法

无单元法是一种新的数值算法,它信息处理简单,其基本思想是在计算域上用一些离散的点由最小二乘法来拟合场函数,从而摆脱了单元的限制,因为它应用了滑动最小二乘法,所以与有限元不同,它的近似场函数不一定精确通过计算点。这会使计算略为复杂,但与这种方法带来的方便性相比,这点缺陷是微不足道的,因此这种方法愈来愈引起人们的关注．笔者将无单元法用于对称叠层板的屈曲问题,通过计算不同边界条件下各向同性板和对称叠层板的屈曲荷载参数,验证了该法的有效性,且精度较高,有着广泛的工程应用前景．     

周期子波在二维声辐射和声散射中的应用

提出了一种新的求解二维Helmholtz积分方程的方法。它通过将边界量用周期子波展开,将Helmhotz积分方程化为一组代数方程求解。即可求解Dirichlet、Neumann问题,也可求解合边值问题,方程的系数形成可用快速子波变换。用该方法形成的Helmholtz积分方程的系数矩阵是一稀疏矩阵,这样大大提高了计算效率,本算例表明：该方法收敛快,精度高,相同的精度下,本方法求解的未知量大大少于边界元所用未知量。     

基于ANSYS的三维近不可压缩问题的有限元分析

有限元方法是数值求解三维弹性问题的一类重要的离散化方法.在实际工程中,有相当多的材料(如橡胶、塑料等)呈现出近不可压缩(泊松比ν→0.5)的性质,利用常规有限元进行求解时会出现体积闭锁(Locking)现象,需要采用某些特殊的方法.本文基于ANSYS平台系统研究了六面体网格剖分下高阶单元法、减缩积分法及基于u/p格式的混合高阶元法对求解混合边界条件的三维近不可压缩问题的有效性和鲁棒性(robustness).数值结果表明:这三种协调有限元法均能有效地克服三维弹性材料的Locking现象,其中混合高阶元法最为精确,计算所得位移值均随网格尺寸变小而稳定地收敛于理论解.     

无单元法在弹性地基板计算中的应用

无单元法（ＥＦＭ）在板弯曲（Ｃ１）问题中的应用,至今尚未见报道。本文将无单元法用于自由边界弹性地基板挠度内力的计算中,推导了地基析的无单元法刚度四公式,编制了地基板无单元法计算程序,并给出了算例,计算结果表明,无单元法解决地基板问题的精度是令人满意的,因此,无单元法用于解决板的弯曲问题是合理可行的。     

弹性静力学问题ANSYS求解与边界元求解比较

用基于有限元方法的ANSYS软件和边界元法求解二维弹性静力学问题,推导出二维弹性静力学问题的有限元公式和边界元公式,并采用常单元编写边界元程序.针对两个具体的算例,分别用这两种方法进行求解,并把解得的结果与精确解进行比较和分析,得出一些有意义的结论.     

改进型无网格Galerkin法与有限元法的耦合及其应用研究

采用改进型无网格Galerkin法与有限元(IEFG-FE)耦合的方法来计算裂纹问题。改进型无网格伽辽金法是基于一种改进的移动最小二乘(ani mproved moving least-squares,I MLS)近似。I MLS近似比现有的MLS近似有更高的计算效率和精度,且不会导致系统方程产生病态。这种耦合的方法不仅解决了无网格Galerkin法力学边界条件施加的难点,避免系统方程产生病态,而且还克服了无网格Galerkin法耗时较多的缺点。本文运用线弹性断裂力学理论,采用加权正交基函数对有限板单边裂纹的应力强度因子和受拉单边斜裂纹矩形板进行了分析。数值计算结果表明:该方法是一种具有收敛快、精度高、简便有效的通用方法,在工程中具有广阔的应用前景。     

三维无网格法与有限元法工程应用对比分析探讨

无网格伽辽金法基于移动最小二乘法的基础上,建立全计算域的高阶连续可导的插值函数,并只利用节点信息来建立离散模型的平衡方程。非线性有限单元法是在离散单元的基础上,构造连续可导的插值函数,进而建立平衡方程。本文应用无网格伽辽金法和非线性有限单元法及其相关理论编制三维计算程序,通过对工程算例的分析表明:无网格伽辽金法的计算精度高于有限单元法,应用于工程实例分析是有效可行的,已经成为有限单元法的有力补充。     

钢筋混凝土板分析的边界无单元法

提出了求解钢筋混凝土板弯曲问题的边界无单元法,使求解边界积分方程容易。算例表明,方法简单,精度高。     

应用无网格伽辽金法模拟疲劳裂纹扩展问题

无网格伽辽金法(EFGM)是近年来兴起的无网格法的一种,与传统的有限元等数值计算方法相比,它只需要节点信息和计算域的几何边界.由于不需要网格重构,裂纹扩展只需要通过自由裂纹面的延伸来模拟,这大大简化了裂纹模拟的过程.本文综述了EFGM在疲劳裂纹扩展中的应用,对扩展基的使用、权函数的选择及裂纹扩展的模拟方法和动态应力强度因子的计算进行了论述     

Buckling analysis of super-long rock-socketed filling piles in soft soil area by element free Galerkin method

In order to discuss the buckling stability of super-long rock-socketed filling piles widely used in bridge engineering in soft soil area such as Dongting Lake, the second stability type was adopted instead of traditional first type, and a newly invented numerical analysis method, i.e. the element-free Galerkin method (EFGM), was introduced to consider the non-concordant deformation and nonlinearity of the pile-soil interface. Then, based on the nonlinear elastic-ideal plastic pile-soil interface model, a nonlinear iterative algorithm was given to analyze the pile-soil interaction, and a program for buckling analysis of piles by the EFGM (PBAP-EFGM) and arc length method was worked out as well. The application results in an engineering example show that, the shape of pile top load-settlement curve obtained by the program agrees well with the measured one, of which the difference may be caused mainly by those uncertain factors such as possible initial defects of pile shaft and the eccentric loading during the test process. However, the calculated critical load is very close with the measured ultimate load of the test pile, and the corresponding relative error is only 5.6%, far better than the calculated values by linear and nonlinear incremental buckling analysis (with a greater relative error of 37.0% and 15.4% respectively), which also verifies the rationality and feasibility of the present method.     

无网格法在温度场中的应用

介绍无网格法的基本原理,推导二维温度场问题的无网格法计算公式,采用罚函数法满足本征边界条件;讨论权函数的选取原则,给出了二维温度场计算过程中的常用的权函数。基于MATI,AB编制无网格法的分析计算软件,通过对若干算例的计算分析,说明了无网格法具有计算精度高、后处理方便等优点,是一种具有潜力的温度场数值计算的新方法。     

A novel hybrid FEM-BEM method for 3D eddy current field calculation using current density J

To solve a large eddy current field is one of the most difficult problems in the numerical computation of electromagnetic field. For this purpose, currently, the FEM and the BEM are widely used. The former is good at dealing with the close regions, nonlinearity and complicated mediums and the latter is fit to solve the problems of open regions and linearity. However, for complicated eddy current field problems in electrical engineering, either the FEM or the BEM is not successful. Therefo…     

冻结壁发育状况的地质雷达探测研究

根据冻结工程中冻土和未冻土之间介电常数和电阻率的差异，研究了地质雷达探测冻结壁发育状况．采用时域有限差分法模拟冻结不同阶段的冻结壁的发育状况，获取冻结壁在雷达剖面上的反映特征，据此指导工程实测．计算结果和探测实例均表明，地质雷达可用于冻结壁发育状况的探测，查明其中的缺陷，便于及时处置冻结工程中可能出现的问题，是确保冻结工程安全的有效手段。     

碳／芳纶纤维混凝土梁热性能分析的边界元法

用边界元法分析了碳／芳纶纤维增强混凝土双T形桥梁的温度场及热传导状况。在二维无限域内单位强度点热源作用的温度场为基本解,用虚拟热源法求解梁结构在温度荷载下的稳态温度场。由于边界元法的数值离散特性,应用二次非协调单元简便可行地解决了数值计算中的角域问题和边界点法向取值不确定问题。算例表明本文方法具有较高的精度。