常航速船波势及船波阻力的边界元法

利用满足Laplace方程,线性化自由面条件及无穷远处条件的Havelock兴波源涵数,建立了关于常航速稳态船波势函数的边界积分方程.针对这个积分方程,建立了相应的数值计算方法,编制了一般三维问题的边界元法计算机程序,可用来计算全潜和半潜物体的稳态绕流场及船舶兴波阻力.     

Diffraction by a nonplanar screen

This paper is concerned with diffraction of short waves by a nonplanar screen (two-dimensional case, Dirichlet boundary condition). The high-frequency asymptotic approximation to the solution is obtained. First the wave field of the primary wave is found in a neighbourhood of the screen edge and then this field is continued along the boundary. Secondary waves arise here as the consequence of interaction between the edge and the primary wave. The secondary wave is diffracted by another edge of the screen, and a third order wave arises, and so on. This process gives the formulas for the wave field in a neighbourhood of the screen. Green's formula is used to continue the solution outside of this neighbourhood.     

The application of finite element analysis to the solution of Stokes wave diffraction problems

A new finite-element based method of calculating non-linear wave loads on offshore structures in extreme seas is presented in this paper. The diffraction wave field is modelled using Stokes wave theory developed to second order. Wave loads and free surface elevations are obtained for fixed surface-piercing structures by solving a boundary value problem for the second-order velocity potential. Special attention has been given to the radiation condition for the second-order diffraction field. Results are presented for three test examples, the vertical cylinders of Kim and Yue and of Chakrabarti, and an elliptic cylinder. These results demonstrate that early problems with the application of second-order theory arising from inadequate radiation conditions have been overcome.     

Normal wave diffraction on a plate submerged in a liquid: Level gauge model,factorization method modification,and waveguide quasiresonances

An exact solution is obtained for onemore new diffraction problem whose transcendental difficulty has been known since Sommerfeld and Kirchhoff. The model of waveguide level gauge, where the main problem is the bulk diffraction of normal waves in a layered structure consisting of an elastic plate between two semi-infinite liquid layers, is investigated. The boundary value problem is solved by using a modification of the Wiener–Hopf factorization method; the factorization is used twice to solve two systems of underdetermined functional equations, and this is a specific characteristics of the problem and amethodological novelty. The proposed modification is acceptable for the class of such problems. The diffracted spectra are analyzed; the waveguide quasiresonances are physically treated; the effect of pure Lamb wave propagation under the liquid is established; the narrow-band backward-wave modes are determined.     

各向异性对半圆形河谷散射影响的数值分析

半圆形河谷场地可构造为包含河谷的广义子结构和具有规则边界的开挖场地两部分,基于土-结构相互作用SSI原理,建立子结构控制方程。利用比例边界有限元SBFEM求解开挖场地动刚度,解析求解各向异性介质自由场qP波波动,将两者代入控制方程,可求得广义结构的动力响应。与文献中各向同性半空间中半圆形河谷在P波入射下的位移结果对比,验证了方法的精度和有效性。进一步分析了椭圆各向异性和非椭圆各向异性对半圆形河谷在qP波入射下位移分布的影响。数值算例显示,介质的各向异性改变了半圆形河谷散射位移的空间分布,增大了水平向位移的峰值;同时,介质的各向异性加剧了入射角对散射波场位移分布的影响。     

基于吸收边界条件的有限元方法和离散切比雪夫展开的二维缺陷识别

结合考虑了吸收边界条件的有限元正演方法,通过离散切比雪夫多项式在特定离散点的展开逼近待识别函数,实现了无限区域内二维缺陷的识别。正问题计算中引入的吸收边界条件虽然不能严格地模拟无限域对近场波动的影响,但能够以满足实际需要的精度模拟这一影响,且具有解耦特性,极大地简化了数值计算,在反演计算中,离散点取在切比雪夫多项式的零点处,使逼近时最大偏差最小,数值算例表明此方法的有效性。     

An asymptotic estimate of the edge effects in the high frequency Kirchhoff diffraction theory for 3-d problems

In the context of wave propagation through a three-dimensional acoustic medium, an analytical approach to estimate the boundary effects in the high-frequency (single) diffraction by thin rigid obstacles is developed. Starting from the classical Kirchhoff (approximate) representation, explicit formulas regarding three sample cases are obtained. The improvement with respect to previous approaches, usually based on refinements of the classical Ray Theory, is evaluated by comparison with the results from a direct numerical solution of the main integrals involved.     

两跨输电线非线性主共振响应分析

研究两跨输电线非线性共振响应问题,应用Hamilton变分原理推导了两跨输电线的振动微分方程以及对应的边界条件。利用Galerkin离散方法和多尺度法,得到了单模态主共振响应。研究结果表明:幅频响应曲线表现出软、硬弹簧性质,随着外激励幅值的增大,输电线系统响应由软弹簧性质向硬弹簧性质转换;系统阻尼减小或外激励幅值增大时,系统幅值个数也随之发生变化,表现出多值和跳跃现象。     

L2 Well-Posedness of Planar Div-Curl Systems

Criteria for the existence and uniqueness of solutions of div-curl boundary value problems on bounded planar regions with nice boundaries are developed. The boundary conditions to be treated include prescribed normal component of the field, tangential component of the field and disjoint combinations of these conditions. Under natural assumptions on the data, when either tangential or normal components are given on the whole boundary, weak (finite-energy) solutions exist if and only if a compatibility condition holds. If the region is simply connected this solution is unique. When the region is multiply connected, there is a finite-dimensional family of solutions. The dimension of the solution space is the Betti number of the region. The problem is well-posed with a unique solution when certain line integrals are further prescribed. L ² estimates of the solutions are given. If mixed tangential, and normal, components of the field are specified on different parts of the boundary, no compatibility condition is required for solvability. In general, though, there is considerable non-uniqueness of solutions. Well-posedness is recovered by specifying certain line integrals. L ² estimates of the solutions are given. The dimensionality of the solution space depends on the topology of the boundary data. These results depend on certain weighted orthogonal decompositions of L ² vector fields on the region which are related to classical Hodge-Weyl decomposition results.     

Thermographic flow visualization by means of non-negative matrix factorization

In order to investigate the areas of different flow regimes in the boundary layer of an airfoil, thermography is a powerful flow visualization tool. However, the distinguishability between boundary layer flow regimes such as laminar or turbulent is limited due to systematic and random inhomogeneity in the measured temperature field, hindering a clear separation of the flow regimes. In order to increase the distinguishability of different flow regimes, a time series of thermographic images is evaluated by means of a non-negative matrix factorization. As a result, the non-negative matrix factorization creates images that contain the dominant features of the measured images, while reducing systematic temperature gradients within the flow regimes by up to a factor of five. This way an increase of the distinguishability between every pair of consecutive flow regimes can be achieved on the surface of a non-heated cylinder in cross-flow condition. As a further application example of the non-negative matrix factorization, the distinguishability between the flow and the laminar-turbulent transition zone on a heated helicopter airfoil is also increased by a factor of five. Hence, non-negative matrix factorization is capable of enhancing thermographic flow visualization for increasing the distinguishability of different flow phenomena.     

Two-dimensional integral equation for a thin wind turbine blade rotating in the round tunnel

The paper presents a mathematical treatment of the aerodynamic problem about a thin wind turbine blade rotating in the round tunnel. The radius of the blade is almost the radius of the tunnel. This permits formulation of the boundary condition on the tip vortex line to the simple slip condition over the surface of the tunnel. By applying a standard technique from potential theory, the problem is reduced to a two-dimensional integral equation whose kernel is connected with a special Green's function satisfying the homogeneous Neumann boundary condition on the tunnel surface. This Green's function is constructed in an explicit analytical form.     

ANTI-PLANE ANALYSIS FOR ELLIPTICAL INCLUSION IN MAGNETOELECTROELASTIC MATERIALS

This paper considers the multi-field coupling in magneroelectroelastic composite materials consisting of the inclusion and the matrix are magnetoelectroelastic materials. The mechanical,electric and magnetic fields around an elliptical cylinder inclusion are formulated by complex potentials. Inside the inclusion,the strain,electric and magnetic fields are found to be uniform and vary with the shape of the ellipse. When the inclusion is reduced to a crack,along the interface,the strain,electric field strength and magnetic field strength equal the corresponding remote ones,which can be used as the boundary condition. Special cases,such as a rigid and permeable inclusion,a soft and impermeable inclusion,a line inclusion and a crack problem are discussed in detail.     

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.     

AN IMPLICIT SURFACE TENSION ALGORITHM FOR PICARD SOLVERS OF SURFACE–TENSION–DOMINATED FREE AND MOVING BOUNDARY PROBLEMS

One of the methods for solving a free or moving boundary problem is the use of Picard solvers which solve the geometry and the velocity field successively. When, however, the kinematic condition is used for updating the geometry in this technique, numerical stability problems occur for surface-tension-dominated flow. These problems are shown here to originate from the unstable integration of the local smoothing of the surface by surface tension. By an extension of the surface tension contribution to the flow field an implicit treatment of surface tension is obtained which overcomes these stability problems. The algorithm is applicable to both free and moving boundary problems, as will be shown by examples in this paper.     

Finite element analysis of lift build-up due to aerofoil indicial motion

In this paper the problem of impulsively started aerofoil or suden change of incidence of an aerofoil in incompressible potential flow is investigated. The essence of solution lies in the representation of a timely and spatially varying wake in a largely irrotational potential flow field. This is achieved by representing the wake through velocity potential difference, which seems to be the only way of imposing a velocity difference condition in the finite element context with velocity potentials as the basic unknowns. Superposition is employed to meet various boundary conditions, which is justified by the linearity of the problem. The finite element solutions are compared with those from singularity method.     

Mixed Boundary Value Problems for Stationary Magnetohydrodynamic Equations of a Viscous Heat-Conducting Fluid

We consider the boundary value problem for stationary magnetohydrodynamic equations of electrically and heat conducting fluid under inhomogeneous mixed boundary conditions for electromagnetic field and temperature and Dirichlet condition for the velocity. The problem describes the thermoelectromagnetic flow of a viscous fluid in 3D bounded domain with the boundary consisting of several parts with different thermo- and electrophysical properties. The global solvability of the boundary value problem is proved and the apriori estimates of the solution are derived. The sufficient conditions on the data are established which provide a local uniqueness of the solution.     

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind-Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.     

宁波大桥主墩墩址软弱带成因机制研究

通过对宁波大桥主墩墩址软弱带详细的地质勘测和综合方法研究，内中包括粘土泥质物Ｘ射线衍射分析，软弱带岩石化学成分和不同成因砂和砾石的成分和特征研究，特别是软弱带的显微构造和物质来源的研究，本文对这一软弱带的成因机制着重进行了探讨。研究发现，这一软弱带在结构上可划分为三部分或三层结构，下部为挤压破碎带、中部为风化产物、上部为地表水贯入充填堆积。它表明这一软弱带经历了三种不同的地质作用的演化过程或具有三种物质来源。这一研究结论对大桥的设计和施工有重要的影响和意义。     

Unsteady flow calculation in a radial flow centrifugal pump with spiral casing

The prediction of the two-dimensional unsteady flow established in a radial flow centrifugal pump is considered. Assuming the fluid incompressible and inviscid, the velocity field is represented by means of source and vorticity surface distributions as well as a set of point vortices. Using this representation, a grid-free (Lagrangian) numerical method is derived based on the coupling of the boundary element and vortex particle methods. In this context the source and vorticity surface distributions are determined through the non-entry boundary condition together with the unsteady Kutta condition. In order to satisfy Kelvin's theorem, vorticity is shed at the trailing edges of the impeller blades. Then the vortex particle method is used to approximate the convection of the free vorticity distribution. Results are given for a pump configuration experimentally tested by Centre Technique des Industries Mécaniques (CETIM). Comparisons between predictions and experimental data show the capability of the proposed method to reproduce the main features of the flow considered.