The method of mixed boundary condition for a kion of linear and nonlinear composite structure

This paper deals with the axisymmetrical deformation of shallow shells in large deflection which are in conjunction with linear elastic structures at the boundary: A method of mixed boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a single structure and the integral equations are given. The perturbation method is used to obtain the solutions and an example of composite structure consisting of a shallow spherical and a cylindrical shell is presented.Communicated by Yeh Kai-yuan     

混合边界各向异性矩形板的静力分析

采用一般解析解和配点法相结合的方法,求解混合边界各向异性矩形板的弯曲问题.先由弯曲挠度的微分方程求出各种类型的齐次解和特解,然后组成一般解析解,再将板的每个边等分 为很多微小的段,仅对每一微段的中点建立应满足的边界条件,由全部边界条件方程式即可求得全部积分常数.以每边一半边界为平夹、另一半边界为简支或自由的方板为例进行了计算,并与四边均为简支的方板进行了对比,表明理论简单,结果实用.     

A wavelet finite-difference method for numerical simulation of wave propagation in fluid-saturated porous media

In this paper, we consider numerical simulation of wave propagation in fluidsaturated porous media. A wavelet finite-difference method is proposed to solve the 2-D elastic wave equation. The algorithm combines flexibility and computational efficiency of wavelet multi-resolution method with easy implementation of the finite-difference method. The orthogonal wavelet basis provides a natural framework, which adapt spatial grids to local wavefield properties. Numerical results show usefulness of the approach as an accurate and stable tool for simulation of wave propagation in fluid-saturated porous media.     

A boundary element method for calculating the SH waves scattering from arbitrarily shaped holes in an anisotropic medium

The scattering problem of elastic wave by arbitrarily shaped cavities in an infinite anisotropic medium is investigated by the boundary integral equation (BIE) method. The formulations of BIE are derived with the help of generalized Green's formula. The discretization of BIE is based upon constant elements. After confirmation of the accuracy of the present method, some numerical examples are given for various cavities in a full space, in which an isotropic body with a circular cylinder hole is used for comparison and good agreement is observed. It has been proved that the method developed in this paper is effective.     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

A projection scheme for Navier-Stokes with variable viscosity and natural boundary condition

Combiningthe Navier-Stokes systems with Neumann (or natural) boundary condition to characterize a fluid flow is frequent. The popular projection (or pressure correction) methods inspired by Chorin and Temam are not well adapted to such boundary condition, which translate in loss of accuracy. If some alternative projection methods have been proposed to reduce the accuracy loss due to the Neumann condition in case of Newtonian fluids, little has been proposed for generalized Newtonian fluids. In this work, we propose two methods derived from the incremental pressure correction projection that can be used for fluids with inhomogeneous or variable viscosity with natural boundary condition. Both time and space accuracy of the methods will be illustrated using a manufactured solution.     

On the Interior Transmission Problem in Nondissipative, Inhomogeneous, Anisotropic Elasticity

In this paper, the interior transmission problem for the non absorbing, anisotropic and inhomogeneous elasticity is investigated. The direct scattering problem for the penetrable inhomogeneous, anisotropic and nondissipative scatterer is first studied and the existence and uniqueness of its solution are established. In the sequel, the interior transmission problem in its classical and weak form is presented and suitable variational formulations of it are settled. Finally, it is proved that the interior transmission eigenvalues constitute a discrete set. This revised version was published online in June 2006 with corrections to the Cover Date.     

Anisotropic Cartesian grid method for steady inviscid shocked flow computation

The anisotropic Cartesian grid method, initially developed by Z.N. Wu (ICNMFD 15, 1996; CFD Review 1998, pp. 93–113) several years ago for efficiently capturing the anisotropic nature of a viscous boundary layer, is applied here to steady shocked flow computation. A finite‐difference method is proposed for treating the slip wall conditions. Copyright © 2003 John Wiley & Sons, Ltd.     

PSEUDOSPECTRAL－FINITE DIFFERENCE METHOD FOR THREE－DIMENSIONAL VORTICITY EQUATION WITH UNILATERALLY PERIODIC BOUNDARY CONDITION

ＰＳＥＵＤＯＳＰＥＣＴＲＡＬ－ＦＩＮＩＴＥＤＩＦＦＥＲＥＮＣＥＭＥＴＨＯＤＦＯＲＴＨＲＥＥ－ＤＩＭＥＮＳＩＯＮＡＬＶＯＲＴＩＣＩＴＹＥＱＵＡＴＩＯＮＷＩＴＨＵＮＩＬＡＴＥＲＡＬＬＹＰＥＲＩＯＤＩＣＢＯＵＮＤＡＲＹＣＯＮＤＩＴＩＯＮＸｉｏｎｇＹｕｅ－ｓ...     

Generalized stroh formalism for anisotropic elasticity for general boundary conditions

The Stroh formalism is most elegant when the boundary conditions are simple, namely, they are prescribed in terms of traction or displacement. For mixed boundary conditions such as there for a slippery boundary, the concise matrix expressions of the Stroh formalism are destroyed. We present a generalized Stroh formalism which is applicable to a class of general boundary conditions. The general boundary conditions include the simple and slippery boundary conditions as special cases. For Green's functions for the half space, the general solution is applicable to the case when the surface of the half-space is a fixed, a free, a slippery, or other more general boundary. For the Griffith crack in the infinite space, the crack can be a slit-like crack with free surfaces, a rigid line inclusion (which is sometimes called an anticrack), or a rigid line with slippery surface or with other general surface conditions. It is worth mention that the modifications required on the Stroh formalism are minor. The generalized formalism and the final solutions look very similar to those of unmodified version. Yet the results are applicable to a rather wide range of boundary conditions.     

Finite element method for shallow water equation including open boundary condition

A method to deal with an open boundary condition in the analysis of water surface waves, the tide, etc. by means of the finite element method is proposed in this paper. The present method has two important features relating to the treatment of the open boundary condition. The first feature is to consider the non-reflective virtual boundary condition which has been developed in the numerical wave analysis method. The incident wave conditions without spurious reflected waves can be imposed at the open boundary. The second feature is to identify the amplitude of the components of incident waves in terms of observed water elevations in the field of standing waves. This can be done as a parameter identification based on an optimization problem by applying the conjugate gradient method. The applicability of this method to wave propagation problems is verified by several numerical computations.     

An analytical method for a mixed boundary value problem of circular plates under arbitrary lateral loads

In this paper by using the concept of mixed boundary functions,an analytical method is proposed for a mixed boundary value problem of circular plates.The trial functions are constructed by using the series of particular solutions of the biharmonic equations in the polar coordinate system.Three examples are presented to show the stability and high convergence rate of the method.     

A mixed FE-BE method for coupled vibration of gravity dam-reservoir system with variable water depth

To solve the coupled vibration of a gravity dam-reservoir system with variable water depth by using a hybrid element method, the fluid region with variable water depth needs to be discretized by FE meshes. However, such a method asks for a great computational cost owing to the excessive unknowns, especially when the fluid region with variable water depth is relatively large. To overcome the shortcoming, a refined boundary element method is proposed to analyze the fluid field, in which only the discretization for the boundary of the variable depth region is required. But as a basis of this approach, it is necessary to construct a new Green's function corresponding to an infinite strip region. The problem is solved as the first step in this paper by employing Fridman's operator function theory, and then a mixed FE-BE formulation for analyzing the free vibration of the gravity damreservoir system is derived by means of the coupling conditions on the dam-reservoir interface. Finally, a numerical example is provided to illustrate a great improvement of the method developed herein over the hybrid element method. The project supported by the National Key Research Plan of China.     

Partitioned subiterative coupling schemes for aeroelasticity using combined interface boundary condition method

The combined interface boundary condition (CIBC) method has been recently proposed for fluid–structure interaction. The CIBC method employs a Gauss–Seidel-like procedure to transform traditional interface conditions into velocity and traction corrections whose effect is controlled by a dimensional parameter. However, the original CIBC method has to invoke the uncorrected traction when forming the traction correction. This process limits its application to fluid–rigid body interaction. To repair this drawback, a new formulation of the CIBC method has been developed by using a new coupling parameter. The reconstruction is simple and the structural traction is removed completely. Two partitioned subiterative coupling versions of the CIBC method are developed. The first scheme is an implicit strategy while the second one is a semi-implicit strategy. Iterative loops are actualised by the fixed-point algorithm with Aitken accelerator. The obtained results agree with the well-documented data, and some famous flow phenomena have been successfully detected.     

复合材料周期结构数学均匀化方法的一种新型单胞边界条件

数学均匀化方法是计算周期复合材料结构的有效方法之一,单胞边界条件施加的合理性直接决定了影响函数控制方程的计算效率和精度,进而影响均匀化弹性参数和摄动位移的计算精度.本文首先将单胞影响函数作为虚拟位移处理,给出了单胞在结构中真实的边界条件,结果表明,四边固支适合作为二维结构单胞边界条件;其次,针对二维结构提出了超单胞周期边界条件,有效提高了影响函数的计算精度,并使用与虚拟位移相对应的虚拟势能泛函验证超单胞周期边界条件的有效性;最后,利用数值分析验证多尺度渐进展开方法的计算精度,强调了二阶摄动的必要性.     

Adomian-modified decomposition method for large-amplitude vibration analysis of stepped beams with elastic boundary conditions

The main objective of this paper is to apply an Adomian modified decomposition method for solving large amplitude vibration analysis of stepped beams with various general and elastic boundary conditions. Damaged or imperfect supports of beams can be modeled by using elastic boundary conditions composing of translational and rotational springs. For the beams subjected to dynamic severe loading, it is important to include the nonlinear term of axial stretching force developed by the large vibration amplitude in the governing equation for more accurate design. By using the method, the convergence studies for linear and nonlinear vibration analyses of stepped beams are shown for determining an appropriate number of terms in the solutions. The accuracy of the present results is validated numerically by comparing with some available results in the literature. New results of nonlinear frequency ratios of stepped beams with different boundary conditions are presented and discussed in detail. Aspects of step ratio, step location, boundary conditions, vibration amplitudes, etc., which have significant impact on linear and nonlinear frequencies of such beams are taken under investigation.     

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

This paper describes the formulations of the method of fundamental solutions (MFS), which is a famous meshless numerical method representing a sought solution by a series of fundamental solutions to solve slow mixed convections in containers with discontinuous boundary data. In the derivations, the fundamental solutions were obtained by using the Hörmander operator decomposition technique. All the velocities, temperatures, pressures, stresses and thermal fluxes corresponding to the fundamental solutions were addressed explicitly in tensor forms. Although the MFS is highly accurate for smooth boundary data, its convergence becomes poor when it is applied to problems with discontinuous boundary data. To compensate for this drawback, we enriched the MFS by adding the local discontinuous solutions to the series of fundamental solutions. This enriched MFS was applied to solve the benchmark problems of a lid‐driven cavity and natural convection in rectangular containers. In addition, the numerical solutions were compared with the analytical solutions. Then, the meshless numerical method was further utilized to solve mixed convections in a triangular cavity and a cavity with a cosine‐shaped bottom. These numerical results demonstrated the applicability of the enriched MFS to two‐dimensional mixed convections in containers with discontinuous boundary data. Copyright © 2010 John Wiley & Sons, Ltd.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

A second-order radiation boundary condition for the shallow water wave equations on two-dimensional unstructured finite element grids

A second-order radiation boundary condition (RBC) is derived for 2D shallow water problems posed in ‘wave equation’ form and is implemented within the Galerkin finite element framework. The RBC is derived by matching the dispersion relation for the interior wave equation with an approximate solution to the exterior problem for outgoing waves. The matching is correct to second order, accounting for curvature of the wave front and the geometry. Implementation is achieved by using the RBC as an evolution equation for the normal gradient on the boundary, coupled through the natural boundary integral of the Galerkin interior problem. The formulation is easily implemented on non-straight, unstructured meshes of simple elements. Test cases show fidelity to solutions obtained on extended meshes and improvement relative to simpler first-order RBCs.