基于结构元的H模糊自适应边界元

针对实际工程系统初始设计阶段经常出现材料的物理特性、结构的几何尺寸以及承受的外来作用等不确定性的问题,研究具有模糊不确定性的边界条件,提出基于模糊结构元（Fuzzy Structure Element,FSE）理论的模糊边界元法.该方法能简便、高效地处理边界条件具有模糊不确定性的系统.数值方法本身具有误差且系统自身具有模糊不确定性,故进一步研究模糊边界元法的H自适应算法,给出实用的误差估计公式;对角点处进行H自适应分析,得到较高精度的解.数值算例验证该方法的有效性和优越性.     

An H-adaptive refinement BEM procedure using modified sample point error analysis in two-dimensional elastic problems

This paper's aim is to modify the sample point error analysis method proposed by Kawaguchi and Kamiya, and to develop an h-adaptive quadratic boundary element mesh refinement procedure to be used in the two-dimensional elastic problem. Two sample points are taken in each element. The extended error indicators are determined at each of the sample points, and the mesh refinement is enforced if the total error of an element is greater than the average. Examples show that, with the same requirement for accuracy, fewer iteration cycles are needed if compared with the previous version of the sample point error analysis. A crack problem is considered by the proposed method and the stress intensity factor at the crack tip is also calculated by the displacement extrapolating method. The results show the versatility of the modified sample point method in the theory of elasticity.     

An a posteriori error estimate and a comparison theorem for the nonconforming <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript> element

A posteriori error estimates for the nonconforming P ₁ element are easily determined by the hypercircle method via Marini’s observation on the relation to the mixed method of Raviart–Thomas. Another tool is Ainsworth’s application of the hypercircle method to mixed methods. The relation on the finite element solutions is also extended to an a priori relation of the errors, and the errors of four different finite element methods can be compared.      

Solution of mixed boundary value problems with local error bound by the finite element method

A method of analysis using finite element techniques is presented for second order, mixed boundary value problems in the plane. The technique focuses computational effort on specific points in the domain and provides absolute solution error bounds at those points by applying the hypercircle method. Solution error of less than 0.0003% and solution error bounds of ± 0.012% are obtained in sample problems. The solution accuracy is notably superior to what is obtained in the traditional finite element method with equivalent discretization. Two problems are presented to illustrate both the strengths and weaknesses of the method.     

Worst case bounds on the point-wise discretization error in boundary element method for the elasticity problem

In this work, point-wise discretization error is bounded via interval approach for the elasticity problem using interval boundary element formulation. The formulation allows for computation of the worst case bounds on the boundary values for the elasticity problem. From these bounds the worst case bounds on the true solution at any point in the domain of the system can be computed. Examples are presented to demonstrate the effectiveness of the treatment of local discretization error in elasticity problem via interval methods.     

基于边界面法的完整实体应力分析理论与应用

提出基于边界面法（Boundary Face Method,BFM）的完整实体应力分析方法.在该分析中,避免对结构作几何上的简化,结构的所有局部细节都按实际形状尺寸作为三维实体处理.以边界积分方程为理论基础的BFM是完整实体应力分析的自然选择.在该方法中,边界积分和场变量插值都在实体边界曲面的参数空间里实现.高斯积分点的几何数据,如坐标、雅可比和外法向量都直接由曲面算得,而不是通过单元插值近似获得,从而避免几何误差.该方法的实现直接基于边界表征的CAD模型,可做到与CAD软件的无缝连接.线弹性问题的应用实例表明,该方法可以简单有效地模拟具有细小特征的复杂结构,并且计算结果的应力精度比边界元法（Boundary Element Method,BEM）和有限元法（Finite Element Method,FEM）高.     

基于改进的PHT-样条自适应等几何配点法

将传统等几何配点法扩展至任意高阶单元并且满足自适应局部细分功能,提出一种基于改进的PHT样条单元的自适应等几何配点法.改进的PHT样条单元依然具有传统PHT样条单元局部细分功能,但因为传统PHT样条函数在层级网格划分后需要对部分基函数的定义域进行截断处理,所以在层级细分过于频繁区域,部分函数可能因为严重变形而影响计算稳...     

凹角区域外问题基于椭圆弧人工边界的自然边界元与有限元耦合法

木文以具有凹角长条型内边界的调和方程外问题为例,研究一种以椭圆弧为人工边界的自然边界元与有限元耦合法,给出了耦合变分问题的适定性及近似解的误差估计．理论分析及数值结果表明,用该方法求解带凹角长条型内边界的外问题是十分有效的．     

Early‐ and late‐lumping observer designs for long hydraulic pipelines: Application to pumped‐storage power plants

Pumped‐storage power plants typically feature very long hydraulic pipelines, which can be modeled by a set of partial differential equations. The estimation of the pressure and volumetric flow along the pipes is an important task for the operation of such a plant. Therefore, this work compares different early‐ and late‐lumping–based observer designs for this system. Two late‐lumping observers, ie, a Lyapunov‐based design and an observer using the backstepping design method, are examined. The Lyapunov‐based approach uses a simple boundary correction to stabilize the estimation error dynamics. In contrast, the backstepping‐based approach allows utilizing additional in‐domain correction to obtain a faster rate of convergence. For the implementation of these distributed‐parameter observers, the spectral element method as a flexible and computationally efficient discretization method is introduced. It is shown that, compared with that of the Lyapunov‐based design, the discretization of the backstepping‐based design requires additional spatial grid points for the accurate approximation of its feedback gains. For the early‐lumping approach, the spectral element method is used to approximate the model equations by a system of differential equations. Based on this approximation, an extended Kalman filter is designed. All observer designs are validated and compared for a representative test case.     

Interweaving Kohonen Maps of Different Dimensions to Handle Measure Zero Constraints on Topological Mappings

The usual Kohonen algorithm uses samples of points in a domain to develop a topological correspondence between a grid of neurons and a continuous domain. Topological means that near points are mapped to near points. However, for many applications there are additional constraints, which are given by sets of measure zero, which are not preserved by this method, because of insufficient sampling. In particular, boundary points do not typically map to boundary points because in general the likelihood of a sample point from a two-dimensional domain falling on the boundary is typically zero for continuous data, and extremely small for numerical data. A specific application, (assigning meshes for the finite element method), was recently solved by interweaving a two-dimensional Kohonen mapping on the entire grid with a one-dimensional Kohonen mapping on the boundary. While the precise method of interweaving was heuristic, the underlying rationale seems widely applicable. This general method is problem independent and suggests a direct generalization to higher dimensions as well.     

H-R自适应边界元的模糊误差估计方法

为克服在利用传统自适应边界元法求解弹性问题时需对不同问题设计不同误差估计公式的缺点,以专家经验为基础,利用模糊逻辑理论,提出一种新的误差分析方法.基于H-R自适应边界元法,用FORTRAN编写求解2个经典平面弹性静力学问题的程序.分析表明该误差分析方法能较好地估计边界元解的误差.     

Finite element mesh generation

The capabilities of a geometric modeller are extended towards finite element analysis by a mesh generator which extracts all its geometric and topological information from the model. A coarse mesh is created and subsequently refined to a suitable finite element mesh, which accomodates material properties, loadcase and analysis requirements. The mesh may be optimized by adaptive refinement, ie according to estimates of the discretization errors.A survey of research and development in geometric modelling and finite element analysis is presented, then an implementation of a mesh generator for 3D curvilinear and solid objects is described in detail.     

空间相机镜头结构分析

用结构设计软件SolidWorks建立某空间相机镜头的精确几何模型,在几何模型的基础上进行力学模型简化,并使用Patran建立相机镜头的有限元模型,然后使用MSC Nastran对该相机镜头进行静力分析、模态分析和随机振动分析,分析结果与试验结果误差小于5%.     

Identification of nonlinear elastic solids by a finite element method

The problem of utilizing experimental data to characterize the stress constitutive function for a nonlinear elastic solid is formulated as an inverse boundary value problem. The use of finite element discretization is extended by introducing a technique of material parameterization that utilizes finite elements defined over the domain of the stress constitutive function. The discretized identification problem is then reduced to a system of nonlinear algebraic equations that couples the data set and the discretized boundary value problem. The effect of errors in measured data is minimized by employing a weighted least squares error norm to generate the equations from which the unknown material parameters are obtained. An illustrative numerical experimental is included.     

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。     

基于综合法的火炮方向机齿轮传动误差分析

方向机对火炮射击精度影响很大,齿轮传动误差是方向机传动误差的主要来源。恰当的分析方法能提高方向机齿轮传动设计精度与效率。本文将齿轮传动误差分为静态误差与动态误差。结合理论分析,用概率分析法计算出静态误差;用有限元分析法计算出动态误差,最后得到总的传动误差。基于分析结果采样拟合出不同载荷下的误差曲线。将这种分析方法应用到火炮方向机齿轮传动误差分析中,得到了该火炮方向机齿轮传动在变载荷下的误差曲线。该分析方法为火炮方向机齿轮传动设计提供参考。为火炮其他部件的设计提供一种思路。     

An adaptive method for the determination of the order of element for acquiring the desired accuracy in 3D elastostatic FEM analysis

An adaptive method for the determination of the order of element (or element order) was developed for the finite element analysis of 3D elastostatic problems. Here the order of element means the order of polynomial function, which interpolates the displacement distribution in the element. This method was based on acquiring the desired accuracy for each finite element. From the numerical experiments, the relationship ξ=k(1/p)^β was deduced, where ξ is the error of the result of the finite element analysis relative to the exact value, p is the order of element, and k and β are constants. Applying this relationship to the two results of computations with different orders of element, the order of element for the third computation was deduced. A computer program using this adaptive determination method for the order of element was developed and applied to several 3D elastostatic problems of various shapes. The usefulness of the method was illustrated by these application results.     

催化剂反应中一类非线性边值问题的有限元配点法

§1.引 言 Galerkin方法是求解微分方程边值问题应用最广的一类有限元方法.文[1]利用配置点Galerkin方法研究了边值问题Ly=(a(x)y')+c(x)y=f(x),x∈I=(0,1)y(0)=y(1)=0的近似解.本文利用配置点Galerkin方法研究如下催化剂反应中质量转换问题:Ly=xy"(x)+(s-1)y'(x)+xq(x)y=xf(x,y),x∈I, (1)y'(0)=0, -y'(1)=A(y(1)-1) (2)     

Performance of the BEM solution in 3D acoustic wave scattering

A fixed cylindrical circular cavity and a cylindrical circular column of fluid of infinite length submerged in a homogeneous fluid medium, and subjected to a pressure point source, for which closed form solutions are known, are used to assess the performance of constant, linear and quadratic boundary elements in the analysis of acoustic scattering.This aim is accomplished by evaluating the error committed by the boundary element method (BEM) for a wide range of frequencies and wave numbers. First, the position of dominant BEM errors in the frequency versus spatial wave number domains are identified and related to the natural modes of vibration of the cylindrical circular inclusion. Then, the errors that occur by using constant, linear and quadratic elements are compared when the inclusion is modelled with the same number of nodes (i.e. maintaining computational cost). Finally, the importance of the position of the nodal points inside discontinuous boundary elements is analysed.     

某地铁车体静强度分析及试验验证

为优化某地铁中间车结构,缩短设计周期,建立车体有限元分析模型;依据EN 12663 2010标准,计算车体有限元模型在主要工况下的应力分布,并将仿真结果与试验数据进行对比分析.大多数点的仿真结果与试验数据很接近,误差大多数在10%以内,表明计算建模可靠;同时发现个别误差较大点所在位置,分析误差产生的原因.