A dual reciprocity boundary face method for 3D non-homogeneous elasticity problems

The boundary face method is coupled with the dual reciprocity method (DRM) to solve non-homogeneous elasticity problems. We will analyze thin structures based on 3D solid elastic theory rather than the shell theory as in the finite element method (FEM). To circumvent the ill-conditioning problem that occurs in the radial basis function (RBF) approximation in thin structures, a special variation scheme for determining the RBF parameters is proposed. In addition, a new exponential RBF is used which has significantly improved the stability of the RBF, and its particular solution to the elasticity problem is derived for the first time. Comparisons of our method with the traditional DRM, the boundary element method (BEM) and the FEM have been made. Numerical examples have demonstrated that our method outperforms the BEM and FEM with respect to stability, accuracy and efficiency, especially when the structure in question has features of small size, such as thin shells.     

基于多频率交流阻抗测量的肉类水分检测方法

为减小肉类生物组织在不同频率激励信号作用下等效阻抗稳定性的差异对水分测量精度的影响,提出一种基于多频率交流阻抗测量的肉类水分检测方法。依据Cole定律建立生物电阻抗数学模型,并利用模型数据仿真论证高频等效阻抗的稳定性。利用FIR数字滤波器以及软件滤波算法去除信号中的干扰信号,提高阻抗测量的精度。在此基础上采用最小二乘法原理通过对肉类生物组织Cole圆弧曲线的拟合和逼近,求解阻抗模型参数中的高频等效阻抗并以此表征肉类生物组织的水分含量。为验证该文肉类水分检测方法的优越性,对猪肉样本进行阻抗检测实验和水分测量实验。实验结果表明:采用该文方法可以对肉类生物体水分含量准确测量,最大测量误差1%。     

On the optimal implementation of the boundary element dual reciprocity method—multi-domain approach for 3D problems

In this paper, aspects regarding implementation of the boundary element dual reciprocity method—multi-domain approach (DRM-MD), in respect to 3D problems are reviewed. Results of numerical tests on a 3D advection–diffusion problem with non-uniform velocity field are presented. The sensitivity of the accuracy and stability of the codes to the continuity of the elements, scaling, internal DRM nodes and mesh refinement have been tested. The results show that scaling is essential and that mesh refinement and/or internal DRM nodes improve the accuracy when the non-homogeneous term of the governing equation becomes dominant. The computer code implemented with discontinuous elements offers higher accuracy, especially for advection dominant transport, but is much slower than the computer code with continuous elements. At the present stage, the discontinuous element code has the advantage of flexibility since it can solve non-homogeneous domains.     

Application of the multiple reciprocity BEM to nonlinear potential problems

In this paper types of nonlinear potential problems are discussed and some of these problems are solved by the boundary element method. In order to avoid domain discretization the multiple reciprocity method is used. Solution of the problem is expressed in terms of a series which involves the higher order fundamental solutions and Laplacians of source terms. Convergence criteria as well as numerical examples are included.     

Dual reciprocity boundary element method using compactly supported radial basis functions for 3D linear elasticity with body forces

A new computational model by integrating the boundary element method and the compactly supported radial basis functions (CSRBF) is developed for three-dimensional (3D) linear elasticity with the presence of body forces. The corresponding displacement and stress particular solution kernels across the supported radius in the CSRBF are obtained for inhomogeneous term interpolation. Subsequently, the classical dual reciprocity boundary element method, in which the domain integrals due to the presence of body forces are transferred into equivalent boundary integrals, is formulated by introducing locally supported displacement and stress particular solution kernels for solving the inhomogeneous 3D linear elastic system. Finally, several examples are presented to demonstrate the accuracy and efficiency of the present method.     

Modified reciprocity method for the calibration of small-volume chambers

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 43–45, January, 1988.     

A truly boundary-only meshfree method for inhomogeneous problems based on recursive composite multiple reciprocity technique

This study presents a novel technique called the recursive composite multiple reciprocity method (RC-MRM), to develop a truly boundary-only meshfree boundary particle method (BPM) for general inhomogeneous problems. It does not require any inner nodes to evaluate the particular solution, and thus it is a truly boundary-only numerical method. “Composite” in the RC-MRM implies that the RC-MRM employs a high-order composite differential operator rather than a high-order Laplacian operator in the standard MRM to annihilate inhomogeneous term of various types and enables the present BPM to handle a much wider variety of inhomogeneous problems, while the “recursive” algorithm in the RC-MRM significantly reduces CPU time and storage requirements of the original MRM. In addition, we also find high-order harmonic solutions of the Laplacian operator. Numerical illustrations reveals that the present BPM has rapid convergence, high accuracy and efficiency, and mathematical simplicity, through various two- and three-dimensional benchmark problems.     

谱峭度方法在柔性薄壁轴承故障特征频率提取中的应用

柔性薄壁轴承是一种特殊的轴承,工作时其内、外圈都受力变形为椭圆,这导致正常柔性薄壁轴承的振动信号存在周期性冲击,这种冲击背景使柔性薄壁轴承的故障特征提取更为困难。谱峭度方法是利用峭度对信号中的瞬态成分敏感这一特性,根据峭度值最大原则来准确提取共振带,克服了传统共振解调技术存在带通滤波器参数需要人工预先确定的缺陷。对自适应谱峭度,基于滤波器组的快速谱峭度以及基于短时傅里叶变换的快速谱峭度进行了对比分析,利用它们提取柔性薄壁轴承内、外圈故障特征频率,对这三种方法的特征提取效果进行了比较,结果表明自适应谱峭度方法更适合于提取柔性薄壁轴承的故障特征频率。     

Study on the true and spurious eigensolutions of two-dimensional cavities using the dual multiple reciprocity method

In this paper, true and spurious eigensolutions for a circular cavity using the dual multiple reciprocity method (MRM) are analytically derived and numerically verified by the developed program. The roots of spurious eigenequation are found analytically by using symbolic manipulation software. A more efficient method is proposed by choosing a fewer number of equations from the dual MRM instead of all of the equations in the dual MRM. Numerical experiments are performed by using dual MRM program for comparison purposes. A circular cavity of radius 1 m with Neumann boundary conditions is considered, and the results match very well between the theoretical prediction and the numerical experiments for the first four true eigenvalues and the first two spurious eigenvalues. Also, a noncircular case of square cavity is numerically implemented. The true eigensolutions can be easily solved by the dual MRM program in conjunction with the singular value decomposition technique. At the same time, the boundary modes and the multiplicities of the true eigenvalues can also be determined.     

Remedy for round-off error accumulation observed in a neutron diffusion calculation using the multiple reciprocity boundary element method

A round-off error accumulation is observed in a multiple reciprocity computation for a fission neutron source iteration problem when a certain convergence condition is not satisfied. The present paper presents a reformulation of the multiple reciprocity method to remove the numerical problem. The neutron diffusion equation (NDE) is arranged using Wielandt's spectral shift technique in such a way that the convergence condition is always satisfied through source iterations. The boundary integral equation in this case requires the fundamental solution to the standard Helmholtz equation, while the fundamental solution corresponding to the correspoding to the original NDE was one to the modified Helmholtz equation. Except for this, the new multiple reciprocity formulation is identical to the original one for the fission source iteration problems. Some test calculation results indicate that a rapid and stable convergence can be realized using the new method and no round-off error accumulation is observed any more.     

Experimental evaluation of 3D electrical impedance tomography with total variation prior

In electrical impedance tomography (EIT), two- or three-dimensional (2D or 3D) distribution of the electrical conductivity is reconstructed based on potential measurements from the surface of the object. In many industrial and medical applications of EIT, the conductivity distribution is discontinuous – due to, e.g. phase or tissue boundaries. Previous studies have shown that such features in the conductivity can be preserved by using total variation (TV) prior model in the EIT image reconstruction. Recently, both 2D and 3D TV models have been utilized in EIT simulation studies. This far, however, EIT reconstructions with TV models have been evaluated experimentally only in 2D cases or translationally invariant 3D cases. In this paper, an experimental study of EIT with a TV prior in a 3D geometry is presented. In addition, we propose the selection of the prior parameters in the TV model based on the prior information of materials in the target, and their conductivity ranges. The results demonstrate the robustness of the proposed parameter selection strategy, and verify that the use of the TV prior yields sharp reconstructions in 3D EIT.     

基于镜像法提取多层介质中3D电容参数的研究

提出了一种适用于任意多层电介质分层结构中的3D互连电容参数提取的新方法--反射镜像法.该方法无需对格林函数进行推导,而是根据自由电荷反射原理计算反射镜像的位置和镜像电荷系数从而获得各级镜像分布,继而计算任意多层电介质环境下的3D电容,包括底层或顶层介质接地情况下的3D电容.该方法可克服级数形式的格林函数因受限于电介质分层数目而难以适应大规模集成电路中复杂多变电介质环境下的3D电容参数提取问题.通过对导体面元建立层次式数据结构,这一方法可以利用层次式算法(hierarchical method)实现计算加速.实验证明,该方法能在保证可靠精度的情况下达到迅速收敛,与层次式加速算法结合后,计算效率可达到FastCap法的数倍.     

Amplitude-phase method of measuring acoustic system impedance in the low- and infralow frequency bands

Translated from Izmeritel'naya Tekhnika, No. 12, pp. 43–44, December, 1989.     

Matrix-type multiple reciprocity method applied to the modified Helmholtz neutron flux mode in nuclear criticality system

The matrix-type multiple reciprocity method has been reformulated to analyze the modified Helmholtz neutron flux mode in a domain which has a strong neutron absorption. The fundamental solutions for the modified Helmholtz mode can be given simply by replacing the imaginary quantity iB₁ in the conventional Helmholtz-type solutions by a real quantity k₁. Test calculations demonstrate the validity of the present reformulation and the usefulness when applied to the nuclear criticality analysis.     

Calibration of vibration pickups by the reciprocity method

Summary The above calibration method provides absolute values of vibration transducers' sensitivity at higher frequencies by means of simpler methods, but with the same accuracy as equipments which set the required values of vibrations by vibrating plates of a complex design.The disadvantages of this method consist of repeated mechanical reconnection of the tested transducers, which lowers the accuracy of calibration. The author of this article together with S. D. Margolin have developed a switching technique which replaces mechanical reconnection of vibration transducers by electrical switching, thus speeding up the calibration and raising the accuracy of measurements [7].     

A scheme to randomly generate surface dust points for the 3D complex variable boundary element method (CVBEM)

A scheme to randomly generate dust points on the surface of a three-dimensional (3D) object is proposed. This scheme will potentially eliminate the bias of a density of points which are approximately equally spaced on the surface, as well as eliminate possible weighting requirements for areas of higher density. This method has the potential to reduce computational effort, as fewer points might be required to define the surface area. The global trial function vector can be assigned to these dust points and then entered into the complex variable boundary element method (CVBEM) commercial code. This scheme can be applied to each piece of a system that is comprised of a connected multiple geometry. A noticeable benefit of this approach is that the same problem can be studied several times, using a new random distribution of surface points each time. The smallest error can then be determined and that run selected. The Mathematica code used to generate the scheme is attached as an appendix.     

Resonant frequency range utilized electro-mechanical impedance method for damage detection performance enhancement on composite structures

One of the problems when using EMI method on composite structures with large surface areas can lead to unsuccessful damage detection due to a vague change in the impedance signature. In addition, a threshold value is usually defined to differentiate a damaged case from an intact case. Therefore, the change in the impedance signature subjected to damage must be significant enough to overcome the effects from other factors which can also cause a change in the impedance signature. In this study, a concept of enhancing the damage detection ability of EMI method using a piezoceramic (PZT) material is reported. The proposed technique eliminates the trial-and-error approach when determining a suitable frequency range by using a resonant frequency range acquired in the lower frequency range below 80 kHz, covering a large sensing area. The main idea is to create peaks in the impedance signature in a peak free zone by sacrificing the sensing area in order to significantly increase the sensitivity of the damage detection ability. The major advantages of the proposed technique is the utilization of the lower frequency range for damage identification using EMI method, while eliminating the time consuming problem of the trial-and-error method.     

On postponement strategies for product families with multiple points of differentiation

Several researchers have studied the benefits of product and process design that calls for delaying the differentiation of products. Previous research has focused on products having only one point of differentiation. However, in reality most product families have several points of differentiation. In this paper, we develop two models to study products with more than one point of differentiation. In each model, we examine the benefits of delayed differentiation at each of these points, and derive the necessary conditions when one type of delayed differentiation is more beneficial than the other. Our analysis indicates that demand variabilities, correlations and the relative magnitudes of the lead times play an important role in determining which point of differentiation should be delayed.