Shape optimization of two-dimensional thermal conducting solid using boundary integral equation formulation

A method for shape design sensitivity analysis of two-dimensional thermal conducting solid is presented using the material derivative concept and the adjoint variable method. A general thermal boundary condition with heat convection is considered in addition to prescribed temperature and heat flux. The method for deriving the sensitivity formula is based on standard direct boundary integral equation formulation. The sensitivity of a general functional depending on temperature and heat flux is considered. The method is then applied to obtain the sensitivity analysis is demonstrated by a hollow cylinder problem with exact solution. A weight minimization problem of a thermal diffuser is considered as a practical application. The sensitivity by the presented method is compared with that by finite differences and an optimal shape is found by use of an optimization routine.     

Shape design sensitivity analysis based on boundary integral equation method considering general shape variations

This work is based upon the general formula for the shape design sensitivity of the elliptical operator. The classical engineering problems of potential, elasticity, and plate bending will be addressed. The derived formulas are suitable for computational purposes in conjunction with the boundary element method. Specific individual problems serve as illustration and their results are compared with those obtained by a different approach which is based on a variational method over the domain.     

双材料平面斜裂纹问题超奇异积分方程方法

由双材料平面问题的弹性力学基本解，应用互等功定律和坐标变换，得到双材料平面任意斜裂纹问题位移场及应力分量表达式，经代入裂纹岸应力边界条件，获得以裂纹岸位移间断作为基本未知量的超奇异积分方程组；通过适当的积分变换，用有限部积分原理处理超奇异积分，建立该问题的相应数值算法。文中对任意位置的裂纹问题进行计算，并较为系统地分析界面对裂纹应力强度因子的影响，当裂纹垂直或平行于双材料界面时，计算结果与已有结果一致。     

Shape design sensitivity analysis based on boundary integral equation method considering general shape variations

A procedure for shape design sensitivity analysis is developed using a standard boundary integral equation (BIE) formulation for elliptic problems with static response. The performance functional to be considered involves both the domain and boundary integrals, and a complete consideration is given in describing the shape variation by including the tangential as well as the normal component of the velocity field. The material derivative concept and the adjoint variable method as applied to the BIE formulation are basic tools for the derivation. This has opened a new unfied approach using the BIE to the shape design sensitivity problems.     

Dynamic responses of a multilayered pyroelectric hollow cylinder of crystal class 2 mm for axisymmetric plane strain problems

The dynamic solution of a multilayered pyroelectric hollow cylinder of crystal class 2 mm in the state of axisymmetric plane strain is obtained. By the principle of superposition, the solution is divided into two parts: One is quasi-static and the other is dynamic. The quasi-static part is obtained in an explicit form by the state space method, and the dynamic part is derived by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique. By using the obtained quasi-static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials can be finally determined. The present method is suitable for a multilayered pyroelectric hollow cylinder of crystal class 2 mm consisting of arbitrary layers and subjected to arbitrary axisymmetric thermal loads. Numerical results are finally presented and discussed.     

双材平面中环形界面环向裂纹问题的超奇异积分方程方法

从研究环形界面双相材料平面任点处沿径向、环向作用单位力时的弹性力学基本解出发,利用Betti定律、几何关系和虎克定律得到双材料平面环向裂纹问题的位移场和应力场表达式,经代入裂纹岸应力边界条件,导出极坐标下以裂纹岸位移间断为基本未知量的超奇异积分方程组;通过适当的积分变换,用有限部积分原理处理方程组中所包含的两类奇异积分—Cauchy奇异积分和超奇异积分,解决极坐标下环形界面双材料平面环向裂纹问题用超奇异积分方程法的理论描述与数值算法。在嵌入物半径足够大时,计算结果与已发表文献对直线界面情况下平行于界面裂纹问题的计算结果一致。     

界面裂纹的弹性T项

采用Maskhelishvili复势理论,利用界面裂纹特征展开的伪正交特性,提出了求解有限板问题的边界积分法,并给出了界面裂纹的弹性T项计算公式,计算了在三种加载形式下（均匀拉伸,紧凑拉伸和三点弯曲）含界面边裂纹有限板的弹性T项,并分析材料特性对它的影响。     

基于边界积分方程法的圆弧齿轮强度分析

提出用边界积分方程法(boundary integral equation method,BIEM)进行圆弧齿轮强度分析的设汁方法。在研究中依据弹性理论的柯西型积分,建立适合于各种载荷作用轮齿不同位置的齿轮强度分析数学模型。在理论方程式建模中采用间接式边界积分方程法,以应力函数作为解析对象,直接求解齿轮应力、轮齿刚度变形等。文中方法具有理论公式推导简捷、软件设计容易、使用方便的优点。本研究还进行了软件设计和实例应用解析,并通过与其他方法的结果比较证实本方法正确有效和实用价值。     

双相材料平行于界面裂纹问题的超奇异积分方程法

由双相材料平面问题的弹性力学基本解和相应裂纹问题的应力场一般表达式，通过微分运算及极限分析得到平行于界面裂纹问题的超奇异积分方程组，并在有限部积分的意义下建立相应的数值算法，把该问题的计算转化为对一个线性方程组的求解，就典型问题无量纲应力强度因子的计算结果表明，该方法与体力法与边界元分析基本一致。     

改进的无网格局部边界积分方程方法

将局部边界积分方程与改进的移动最小二乘法相结合,提出改进的无网格局部边界积分方程方法。改进的移动最小二乘法引入带权的正交基函数,可以克服现有的移动最小二乘法在构造近似函数时须要进行大量的矩阵求逆、计算量大、法方程组容易出现病态方程组的缺点。将改进的无网格局部边界积分方程方法应用于弹性力学问题,并推导出相应的离散方程。通过数值算例验证了该方法的有效性。与原有的局部边界积分方程方法相比,该方法具有计算量小、数值稳定性好并且不会出现病态方程组的优点。     

Boundary conditions for axisymmetric piezoelectric cylinder

For axisymmetric piezoelectric cylinder, the reciprocal theorem and the axisymmetric general solution of piezoelasticity are applied in a novel way to obtain the appropriate stress and mixed boundary conditions accurate to all orders for the cylinder of general edge geometry and loadings. A decay analysis technique developed by Gregory and Wan is converted into necessary conditions on the end-data of axisymmetric piezoelectric circular cylinder, and the rapidly decaying solution is established. The prescribed end-data of the circle cylinder must satisfy these conditions in order that they could generate a decaying state within the cylinder. When stress and mixed conditions are imposed on the end of cylinder, these decaying state conditions for the case of axisymmetric deformation of piezoelectric cylinder are derived explicitly. They are then used for the correct formulation of boundary conditions for the theory solution (or the interior solution) of axisymmetric piezoelectric cylinder. The results of the present paper enable us to establish a set of correct boundary conditions, most of which are obtained for the first time.     

A flaw in a cylinder

The problem of magnetostatics for the following model of a defective body is considered: an inclusion in the form of an infinite cylinder with an arbitrary cross section, which is limited by a smooth contour, is inside an infinite magnetic cylinder with a circular profile. An integrodifferential equation with respect to the strength vector of the resulting magnetic field, which contains an integral only over the boundary of the flaw cross section, was derived for this type of body. An algorithm for calculating such a field for the case of an inclusion in the form of a circular cylinder, which is misaligned relative to the large cylinder, was developed. The results of this study can be used in practice when testing cylindrical items with extended flaws.     

二维声学数值计算的径向插值有限元法

针对声学有限元分析中四节点等参单元计算精度低,对网格质量敏感的问题,将无网格径向插值技术引入到标准有限元中,构造径向插值形函数,推导径向插值有限元法(Radial interpolation finite element method,RIFEM)的二维声学数值计算公式。二维声学RIFEM采用标准有限元法形函数构造系统离散方程的声学刚度矩阵和边界积分矢量,保证了声压梯度和边界条件在区域边界的积分精度;采用径向插值形函数构造系统离散方程的质量矩阵,提高了声压数值近似函数的插值精度。对管道二维声腔模型和某轿车二维声腔模型的数值分析结果表明,与标准有限元法和SFEM相比,RIFEM的计算精度更高,对波数、单元尺寸和网格扭曲程度的灵敏度更低。因此RIFEM可以很好地应用于二维声学数值分析,具有广阔的工程应用前景。     

Slipline fields for axisymmetric tube drawing

A numerical method for constructing axisymmetric slipline fields for a Tresca material is discussed. The method is applicable to problems of indirect type where the shape of the starting characteristics has to be found by solving a nonlinear integral equation. An attempt is made to construct the axisymmetric analogue of Hill's well-known bar-drawing solution. However the solutions are only approximate as it is found that the Haar-Karman hypothesis is found to be invalid for this class of solutions.     

Crack problems in plane and antiplane elasticity using a singular integral equation

A numerical integration formula for the investigation of the singular integral of loakimidis for classical crack problems in plane and antiplane elasticity is developed. The method is based on a modification of the Gauss-Chebyshev quadrature and the definition of finite part integral having an algebraic sigularity of (−3/2) at the limits of integration. Once developed the procedure is applied to the determination of finite part integrals which have analytical solutions and the results are compared. Finally the integration for mula is applied to an actual crack problem and the stress intonsity factors are computed and presented.     

Torsion of compound bars—A relaxation solution

This paper deals with a finite-difference solution of the torsion problem of nonhomogeneous and compound prismatic bars. General, governing equations for both problems are developed and the boundary conditions for an interface between parts composed of homogeneous but different materials are stated. The case of multiply connected regions is discussed and integral conditions, analogous to the conditions in multiply connected homogeneous bars, are developed.

Examples illustrating various types of problems are worked out and the accuracy of the method demonstrated by comparison with some known solutions.     

弹性半空间中平片裂纹问题的超奇异积分方程方法

使用边界积分方程方法,在有限部积分的意义下,将弹性半空间中垂于自边界面的平片裂纹归结为一组以裂纹面位移间数为示知函数的超奇异积仞氖限部积分蜞 建立了数值人出了用裂纹面位移间尖力强度因子的公式。通过对圆形、菜和矩形等贡型的平片裂纹问题的计算,分析了自由边界面对裂纹前沿应力强度因子的影响。     

A boundary element solution approach for the conjugate heat transfer problem in thermally developing region of a thick walled pipe

This paper presents a sole application of boundary element method to the conjugate heat transfer problem of thermally developing laminar flow in a thick walled pipe when the fluid velocities are fully developed. Due to the coupled mechanism of heat conduction in the solid region and heat convection in the fluid region, two separate solutions in the solid and fluid regions are sought to match the solid-fluid interface continuity condition. In this method, the dual reciprocity boundary element method (DRBEM) with the axial direction marching scheme is used to solve the heat convection problem and the conventional boundary element method (BEM) of axisymmetric model is applied to solve the heat conduction problem. An iterative and numerically stable BEM solution algorithm is presented, which uses the coupled interface conditions explicitly instead of uncoupled conditions. Both the local convective heat transfer coefficient at solid-fluid interface and the local mean fluid temperature are initially guessed and updated as the unknown interface thermal conditions in the iterative solution procedure. Two examples imposing uniform temperature and heat flux boundary conditions are tested in thermally developing region and compared with analytic solutions where available. The benchmark test results are shown to be in good agreement with the analytic solutions for both examples with different boundary conditions.     

内压作用下发动机反向封头屈曲参数化研究

内压作用下发动机反向封头的稳定性是设计中的考虑重点.采用轴对称有限元方法对不同设计参数的等厚度和变厚度两大类反向封头进行稳定性研究,模型考虑封头开口加强环及封头与圆柱段连接处的局部加强影响.参数化研究椭球比、壁厚对封头临界屈曲载荷的影响.研究结果表明,等厚度反向封头的外形和变厚度的壁厚对结构临界屈曲载荷的影响十分敏感,在最小厚度一定的情况下,椭球比为1.413的变厚度封头是最小质量设计.另外文中给出可供工程实际设计参考的图表及曲线.     

The identification and study of the critical state of a transverse crack in a zone with a lap based on artificial neural networks

A method for the identification of the geometry of a transverse crack in a layer with a lap with subsequent estimation of the critical state of its structure is proposed. The solution of the problem proceeds in two steps, which form the general method. The determination of a crack in a layer is performed with the use of artificial neural networks, which use the data of an ultrasonic study. To determine an internal crack, the problem of the pulse excitation of a wave field in a considered object was studied. Using a piezotransducer on a free coating surface, the results of an action are obtained. The input vectors for the artificial neural network are considered to be a regularly digitized echo signal. Based on the generated database of input vectors, the optimal training algorithm and the structure of the network were determined. After reconstruction of the geometry of a crack, the critical state is estimated with the use of integral equations, which were obtained from the solution of the corresponding linear problem of elasticity theory. In this problem, the coating medium is replaced by special boundary conditions on the upper surface of the layer. When using a generalized Fourier transform in the equilibrium equations in displacements, the problem is reduced to a singular first-order integral equation, whose solutions were derived by the small parameter and collocation methods. The stress-intensity coefficients were obtained and analyzed directly near the tops of the crack for various coating materials and geometric parameters of the crack.