色散波的自适应开路边条件

本文从一类色散波的积分形式解出发,在陈和邹提出的自适应开路边条件的基础上,采用进一步引入局部瞬时等价波速,和将非线性色散关系式ω(k)在某个适当选定的k_0处作Taylor展开这两种不同方式,得到了几类不同的、可用于色散波,特别是色散水波的开路边条件。并利用两类有解析解的例子,计算了几种开路边条件的“聚散比”。计算结果表明,本文提出的方法是有效的。     

The high precision open boundary conditions designed for transient waves

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Two-dimensional linear elasticity by the boundary node method

This paper presents a further development of the Boundary Node Method (BNM) for 2-D linear elasticity. In this work, the Boundary Integral Equations (BIE) for linear elasticity have been coupled with Moving Least Square (MLS) interpolants; this procedure exploits the mesh-less attributes of the MLS and the dimensionality advantages of the BIE. As a result, the BNM requires only a nodal data structure on the bounding surface of a body. A cell structure is employed only on the boundary in order to carry out numerical integration. In addition, the MLS interpolants have been suitably truncated at corners in order to avoid some of the oscillations observed while solving potential problems by the BNM (Mukherjee and Mukherjee, 1997a) . Numerical results presented in this paper, including those for the solution of the Lamé and Kirsch problems, show good agreement with analytical solutions.     

Bending of a rectilinear regular polygonal plate with a circular hole by concentrated edge couples

Summary This paper presents a solution for the deflection, moments and shearing forces in a rectilinear regular polygonal plate, with even number of sides having a central circular hole, subjected to concentrated edge couples at two opposite points of the outer boundary. Complex variable technique has been employed to find the solution of the problem. The solution involves an infinite system of linear algebraic equations and a method of solving them is provided. The solution for a corresponding plane stress (strain) problem has been derived. Numerical results are presented in the form of tables and graphs.     

Spherical ceramic pebbles subjected to multiple non-concentrated surface loads

This paper presents an analytical solution for the stress distributions within spherical ceramic pebbles subjected to multiple surface loads along different directions. The method of solution employs a displacement approach together with the Fourier associated Legendre expansion for piecewise boundary loads. The solution corresponds to spherically isotropic elastic spheres. The classical solution for isotropic spheres subjected diametral point loads is recovered as a special case of our solution. For the isotropic pebbles under consideration, stresses within spheres are numerically evaluated. The results show that the number of loads does have significant influence on the maximum tensile stress inside the sphere. Moreover, the applicability of solutions using the series expansion method for stresses near surface load areas is also examined. The stresses evaluated with large enough number of terms agree quite well with those derived from FEM simulations, except around the edge of circle load area.     

A simplified frequency equation and its approximate solution of a beam with an incipient crack from a wave perspective

This paper presents a simplified frequency equation and its approximate solution to predict the modal frequencies of a beam with an incipient crack. The physical implication of the simplified frequency equation is fully described from a wave perspective for the cracked beam with arbitrary support conditions. The approximate solution of the proposed frequency equation is derived from a wave perspective as well. The asymptotic equivalence is demonstrated between the approximate solution and that obtained by the first order perturbation method as the mode number increases. The validity of the proposed approach is demonstrated through comparison to both numerical results from finite element analysis and experimental data.     

Approximate theories for wave propagation and vibrations in elastic rings and helical coils of small pitch

From the equations of linear elasticity, three levels of approximate theories are derived for in-plane deformation and motion of thin, circular rings. The accuracy of each theory is determined by comparison with harmonic wave solutions of the elasticity solution. Boundary conditions for uniqueness are established. The results may also be applied to helical coils of small pitch and to cylindrical shells when the equations are converted to plane strain.     

Buoyant plumes due to mass diffusion

This paper presents the results of a numerical study of laminar axisymmetric plumes that emanate from a point source of mass diffusion. Various flow configurations that arise in mass diffusion plumes are identified. In the ambient, the cases of constant concentration and stable density stratification are considered. The governing conservation equations of mass, momentum, and species diffusion are cast in finite-difference form using an explicit scheme. Boundary layer and Boussinesq approximations are incorporated. Upwind-differencing is employed for convective terms. Velocity and concentration fields are obtained for various values of Schmidt number, and concentration stratification levels in the ambient. The results are explained in terms of the basic physical mechanisms that govern these flows. The complex interactions between the buoyancy and the Schmidt number, and the stratification parameter are discussed.     

AN ANALYTICAL SOLUTION OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES SIMPLY SUPPORTED AT TWO OPPOSITE EDGES WITH ARBITRARY NUMBER OF ELASTIC LINE SUPPORTS IN ONE WAY

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三维Laplace方程边界元中线性单元的精确积分法

边界元中的边界积分计算影响计算精度和计算速度。非奇异积分一般采用数值积分，当配置点接近积分单元时，计算精度降低。未知函数线性插值得到的解是连续解，但计算难度增大。本文采用积分区域变换，将三维Laplace问题的二维积分化为一维积分，这样奇异积分和非奇异积分能采用精确积分的方法计算，使求解精度，计算速度都得到提高。     

Analytical approximate 3D solution for the longitudinally vibrating cylinder

Summary The paper presents a three-dimensional approximate solution of a longitudinally vibrating cylinder. It is based on the frequency equation for free waves travelling along an infinitely long cylinder which follows from the radial boundary condition on the lateral surface of the cylinder. An equivalent longitudinal traction is calculated by integration of the normal stresses over the end cross section. The full solution of the longitudinally vibrating rod adapted to given axial boundary conditions is derived. The solution is compared to numerical results, and good agreement is obtained.     

The squeezing flow of a model suspension fluid

The paper is concerned with the squeezing flow of a model suspension fluid. The numerical solution obtained by a time-dependent Boundary Element Method is compared to an asymptotic solution at large radius. It is found that the kinematics are Newtonian in character, and the fibres quickly align themselves radially. Consequently, the squeezing force is only weakly dependent on the initial orientations of the fibres and the device can be used for measuring the effective viscosity of the suspension. The effective viscosity found from the squeezing flow agrees surprisingly well with experimental data and numerical data derived from the falling sphere geometry at low volume fractions ( < 0.1).     

A new microstructure-dependent Saint–Venant torsion model based on a modified couple stress theory

In this paper a new modified couple stress model is developed for the Saint–Venant torsion problem of micro-bars of arbitrary cross-section. The proposed model is derived from a modified couple stress theory and has only one material length scale parameter. Using a variational procedure the governing differential equation and the associated boundary conditions are derived in terms of the warping function. This is a fourth order partial differential equation representing the analog of a Kirchhoff plate having the shape of the cross-section and subjected to a uniform tensile membrane force with mixed Neumann boundary conditions. Since the fundamental solution of the equation is known, the problem could be solved using the direct Boundary Element Method (BEM). In this investigation, however, the Analog Equation Method (AEM) solution is applied and the results are cross checked using the Method of Fundamental Solutions (MFS). Several micro-bars of various cross-sections are analyzed to illustrate the applicability of the developed model and to reveal the differences between the current model and an existing one which, however, contains two additional constants related to the microstructure. Moreover, useful conclusions are drawn from the micron-scale torsional response of micro-bars, giving thus a better insight in the gradient elasticity approach of the deformable bodies.     

Free vibrations of an anisotropic cylindrical fiberglass shell reinforced by annular ribs and containing fluid flow

This paper presents the results of determining the free vibration frequency of a structurally anisotropic, cylindrical fiberglass shell reinforced by annular ribs and containing flowing fluid. Boundary Navier conditions are imposed on the ends of the shell. Natural vibration frequencies are calculated as dependences of the frequency on the fiberglass winding angle and fluid flow velocity for different values of the wave formation parameters and the parameters characterizing the geometric dimensions of the shell.     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

Wave motion in a thick cylindrical rod undergoing longitudinal impact

The paper presents a new formulation and the comprehensive analytical solution to longitudinal impact of thick elastic rods. In contrast to previously published works, the solution is derived based on the exact three-dimensional theory without using the classic Skalak’s decomposition. This new direct approach makes the analytical solution more transparent and much easier to obtain. The resulting formulas for basic mechanical quantities are derived using the residue theorem and their evaluation is made in such a way that the accuracy of presented results is significantly higher than those previously published. Based on these results, the transient wave phenomena occurring in the rods are discussed in detail. Additionally, the solution in time domain is obtained also by semi-analytical approach making use of numerical inverse Laplace transform. It is shown that the selected FFT based algorithm is accurate and robust enough, such that the analysis of wave motion in spatial and time domain can be done effectively preserving the results precision. Presented solution can be used as a benchmark for verification of numerical and experimental methods applied to elastodynamics problems.     

Main results of the third international PIV Challenge

This paper presents the main results of the third international PIV Challenge which took place in Pasadena (USA) on the 19th and 20th of September 2005. This workshop was linked to the PIV05 International Symposium held at the same place the same week. The present contribution states the objectives of the challenge, describes the test cases and the algorithms used by the participants, and presents the main results together with some discussion and conclusions on the accuracy and robustness of various PIV and PTV algorithms. As the entire amount of results obtained cannot be detailed, this contribution is written as a guide for the use of the full database of images and results which is available at .     

Main results of the Second International PIV Challenge

This paper presents the main results of the Second International PIV Challenge which took place in Busan (Korea) on the 19th and 20th of September 2003. This workshop was linked to the PIV03 International Symposium, which was held at the same place the following week. The present contribution gives the objectives of the Challenge, describes the test cases and the algorithms used by the participants, and presents the main results together with some discussion and conclusions on the accuracy and robustness of various PIV and PTV algorithms. As all the results obtained cannot be detailed, this contribution should serve as a guide for the use of the full database of images and results which is available at .     

二阶非自伴两点边值问题Galerkin有限元后处理超收敛解答计算的EEP法

将一维Ritz有限元法超收敛计算的EEP(单元能量投影)法推广到二阶非自伴常微分方程两点边值问题Galerkin有限元法的超收敛计算。在对精确单元的研究中,发现与Ritz有限元法不同,只要检验函数采用伴随算子方程的解,无论试函数取何形式,在结点处都可得到精确的解函数值。对近似单元的研究表明,EEP法同样适用于Galerkin有限元法,不仅保留了简便易行、行之有效、效果显著的特点,同时也保留了EEP法的特有优点,如:任一点的导数和解函数的误差与结点值的误差具有相同的收敛阶。     

The Dual-Reciprocity Boundary Element Analysis for Hydraulically Fractured Shale Gas Reservoirs Considering Diffusion and Sorption Kinetics

This work presents a new application of boundary element method (BEM) to model fluid transport in unconventional shale gas reservoirs with discrete hydraulic fractures considering diffusion, sorption kinetics and sorbed-phase surface diffusion. The fluid transport model consists of two governing partial differential equations (PDEs) written in terms of effective diffusivities for free and sorbed gases, respectively. Boundary integral formulations are analytically derived using the fundamental solution of the Laplace equation for the governing PDEs and Green’s second identity. The domain integrals arising due to the time-dependent function and nonlinear terms are transformed into boundary integrals employing the dual-reciprocity method. This transformation retains the domain-integral-free, boundary-integral-only character of standard BEM approaches. In the proposed solution, the free- and sorbed-gas flow in the shale matrix is solved simultaneously after coupling the fracture flow equation of free gas. Well production performance under the effect of relaxation phenomenon due to delayed responses of sorbed gas under nonequilibrium sorption condition is rigorously captured by imposing the zero-flux condition at fracture–matrix interface for the sorbed-gas transport equation. The validity of proposed solution is verified using several case studies through comparison against a commercial finite-element numerical simulator.