Solutions of the interior and exterior boundary value problems in plane elasticity by using dislocation distribution layer

Based on a previous publication (Savruk, 1981), a dislocation distribution layer method for the solution of interior and exterior boundary value problem (BVP) is studied in more detail. Properties of an integral operator in the resulting integral equation are studied. It is proved theoretically that the tractions applied on the outer boundary should be in equilibrium. In addition, a dislocation distribution layer method for the solution of exterior BVP is also suggested. In the exterior BVP, the tractions applied on the boundary may not be in equilibrium. In the exterior BVP, one must consider the single-valued condition of displacements. The formulation in the exterior BVP is not same as in the interior BVP. In the process of discretization, a technique for balance of the numbers of resulting algebraic equations and unknowns is suggested. Numerical examples prove that the suggested method can give sufficient accurate results.     

应用分形有限元方法于外域声场计算

 应用二级分形有限元方法计算了外域声场. 用一人工边界把外域声场分为两 部分，人工边界以内使用常规有限元方法，人工边界以外的无限大区域使用分形有限元方法. 使用分形有限元方法的优点是：一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵 和质量矩阵具有非常简单的关系；另一方面引用自动满足无限远辐射条件的全域插值函数把 节点自由度变换为一组广义坐标，因而计算量可以大大减少. 数值算例表明：该方法对于计 算无限大外域声场是有效的.     

Finite elements for exterior problems using integral equations

We present some integral methods for exterior problems for the Laplace equation. Then we give finite element approximations for these equations and some errors estimates. Finally, we indicate how these integral equations can be coupled with a usual finite element method on a bounded domain to solve an exterior non-linear problem which is linear far away.     

钢框架边节点抗火性能的试验研究

对8个H型截面钢框架边节点进行了抗火性能的试验研究。全部火灾试验在自行研制的火灾试验炉内进行,试验过程表明炉子性能稳定,使用方便。试验采用足尺试验形式,钢柱长3000mm,钢梁长1350mm,钢柱两端铰接,梁柱节点分为栓焊连接、全焊连接和端板连接。考虑节点形式、是否带加劲肋和端板连接节点的端板厚度三个影响因素。通过试验,得出了节点的破坏形式和节点转角随温度变化的规律。试验结果表明:火灾下,节点破坏的形式和节点的连接方式、是否带加劲肋有关;加劲肋的存在提高了端板连接节点的极限温度。     

伸缩虚拟边界元法解二维Helmholtz外问题

以位势理论为基础，提出了求解Helmholtz外问题的伸缩虚拟边界元法．给出了该方法在全波数域内获得唯一解的严格数学证明，其核心是通过伸缩虚拟边界使对偶内问题的特征频率(本征值)避开与波数重合，从而保证了解的唯一性，同以往前人提出的几种解法途径相比，该法简单得多；通过诸多边界曲线形状和不同边界量的声辐射算例，从计算精度、稳定性以及克服解的非唯一性等方面，对该方法进行了检验．计算结果表明：对远场或近场辐射声压，该方法都具有非常高的效率和精度．     

融合稀疏八叉树与卷积神经网络的汽车风阻系数预测

针对汽车风阻系数预测研究中参数化方法难以准确表征汽车外造型的难题,提出融合稀疏八叉树与卷积神经网络的汽车风阻系数预测方法。将汽车外造型按照八叉树结构离散,使用平均法向量对离散的复杂曲面进行简化,利用卷积神经网络对八叉树形式的汽车外造型进行特征提取,进而对汽车风阻系数进行快速预测。通过改变卷积层数与全连接层数,研究了不同卷积神经网络结构对风阻系数预测精度的影响。与参数化方法相比,本文提出的外造型表示方法能更好地描述模型细节,构建的卷积神经网络结构对风阻系数预测的最小相对误差为1.453%,且计算速度是CFD仿真的1620倍,具有较高的精度及计算效率。     

Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix

In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method (EMM) is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 × 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.     

Extension of the local domain-free discretization method to large eddy simulation of turbulent flows

In this work, an immersed boundary method, called the local domain-free discretization (DFD) method, is extended to large eddy simulation (LES) of turbulent flows. The discrete form of partial differential equations at an interior node may involve some nodes outside the solution domain. The flow variables at these exterior dependent nodes are evaluated via linear extrapolation along the direction normal to the wall. To alleviate the requirement of mesh resolution in the near-wall region, a wall model based on the turbulence boundary layer equations is introduced. The wall shear stress yielded by the wall model and the no-penetration condition are enforced at the immersed boundary to evaluate the velocity components at an exterior dependent node. For turbulence closure, a dynamic subgrid scale (SGS) model is adopted and the Lagrangian averaging procedure is used to compute the model coefficient. The SGS eddy viscosity at an exterior dependent node is set to be equal to that at the outer layer. To maintain the mass conservation near the immersed boundary, a mass source/sink term is added into the continuity equation. Numerical experiments on relatively coarse meshes with stationary or moving solid boundaries have been conducted to verify the ability of the present LES-DFD method. The predicted results agree well with the published experimental or numerical data.     

声辐射问题的二级分形有限元方法

利用分形有限元和常规有限元相结合的方法对中低频段声辐射问题进行了分析，由于引用了分形比α和能够自动满足无限远辐射边界条件的全域插值函数，大大降低了未知量的个数，从而可以在较短的计算时间和较低的内存消耗的条件下高效地解决问题，计算实例表明这种方法对于求解无界域声场问题是有效的。     

Acoustic scattering and radiation problems, and the null-field method

The best known methods for solving the scattering and radiation problems of acoustics are integral-equation methods. However, it is also known that the simplest of these methods yield equations which are not uniquely solvable at certain discrete sets of frequencies (the irregular frequencies). In this paper, we shall analyse an alternative method (the null-field method, or T-matrix method). We prove that the infinite system of null-field equations always has precisely one solution, i.e. the unphysical irregular frequencies do not occur with this method. Moreover, we also prove that the solution of the original boundary-value problem can always be determined (at any point exterior to the scatterer) from the solution of the null-field equations. We prove these results in two dimensions, for two radiation problems (the exterior Neumann problem and the exterior Dirichlet problem) and two scattering problems (scattering by a sound-hard body and scattering by a sound-soft body); similar results can be proved in three dimensions. We also prove some subsidiary results, concerning the solvability of certain boundary integral equations and the completeness of certain sets of radiating wave-functions, and give a discussion of related numerical techniques.     

Eigenfrequency analysis of cable structures with inclined cables

The approximate eigenfrequencies for the in-plane vibrations of a cable struc- ture consisting of inclined cables,together with point masses at various points were com- puted.It was discovered that the classical transfer matrix method was inadequate for this task,and hence the larger exterior matrices were used to determine the eigenfrequency equation.Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.     

An interval perturbation method for exterior acoustic field prediction with uncertain-but-bounded parameters

This paper proposes two interval analysis methods, called the first-order interval parameter perturbation method (FIPPM) and the modified interval parameter perturbation method (MIPPM), for use in exterior acoustic field prediction when there are uncertainties in both the material properties and the external load. Interval variables are used to quantitatively describe the uncertain parameters in the face of limited information. The conventional first-order Taylor expansion and perturbation terms are employed in the FIPPM, while the MIPPM introduces modified Taylor series to approximate the non-linear interval matrix and vector. The high-order terms of the Neumann expansion are retained to calculate the interval matrix inverse. A numerical example is given by comparing the results with a Monte Carlo simulation to demonstrate the feasibility and effectiveness of the proposed methods at evaluating the sound pressure ranges in an exterior acoustic field.     

A new concept of modal participation factor for numerical instability in the dual BEM for exterior acoustics

This paper presents the occurring mechanism why irregular frequencies are imbedded in the exterior acoustics using the dual boundary element method (BEM). The modal participation factor which dominates the numerical instability is derived for continuous and discrete systems. In addition, the irregular (fictitious) frequencies embedded in the singular or hypersingular integral equations are discussed, respectively. It is found that the irregular values depend on the kernels in the integral representation for the solution. A two-dimensional dual BEM program for the exterior acoustics was developed. Numerical experiments are conducted to verify the concept of modal participation factor.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

pFFT快速边界元方法模拟三维声散射

研究了用pFFT快速边界元方法模拟声散射问题的关键技术。采用Burton—Miller方程消除了声学边界元方法中外问题解的不唯一现象。为此,文中研究了采用常量元时该方程中超奇异积分的计算方法。最后,通过对平面声波的刚性圆球声散射的数值模拟,验证了建立的声学pFFT快速边界元方法。     

A method of calculating a regime of strong viscous interaction on a delta wing

A method is proposed for calculating the three-dimensional boundary layer on a delta wing in a regime of strong viscous interaction with the exterior hypersonic flow. The results of numerical solution of a boundary-value problem are given.     

A boundary-field equation method for a nonlinear exterior elasticity problem in the plane

This paper presents a new method for solving a nonlinear exterior boundary value problem arising in two-dimensional elasto-plasticity. The procedure is based on the introduction of a sufficiently large circle that divides the exterior domain into a bounded region and an unbounded one. This allows us to consider the Dirichlet-Neumann mapping on the circle, which provides an explicit formula for the stress in terms of the displacement by using an appropriate infinite Fourier series. In this way we can reduce the original problem to an equivalent nonlinear boundary value problem on the bounded domain with a natural boundary condition on the circle. Hence, the resulting weak formulation includes boundary and field terms, which yields the so called boundary-field equation method. Next, we employ the finite Fourier series to obtain a sequence of approximating nonlinear problems from which the actual Galerkin schemes are derived. Finally, we apply some tools from monotone operators to prove existence, uniqueness and approximation results, including Cea type error estimates for the corresponding discrete solutions.     

PVDF涂层建筑膜材单元结构力学性能的试验研究

使用PVDF涂层建筑膜材制成的结构,在承受外载荷情况下,力学行为非常复杂。在本文中,重点研究其单元结构在承受外载荷情况下的力学性能。首先,对PVDF涂层建筑膜材进行拉伸试验,测定其在常温和低温环境下膜的拉伸力学性能参数。然后,以制成的三角框架结构膜单元为对象,在常温条件下,从有限元分析和实际加载试验两方面计算得出结构单元在均布载荷下的位移、应变和应力分布。最后,对其进行强度验证,得出采用膜单元构建大型建筑是安全的结论。试验方法和结果可以应用于膜建筑结构的设计。     

A method of online damage identification for structures based on ambient vibration

IntroductionStructuralhealthmonitoringofbridgesandarchitectureshasbeenhighlyinteresting .Whensomebridgesarebuilt,thehealthmonitoringsystemsareinstalled ,whicharemadeupofmanysensors,suchaswindloadingsensors,stresssensorsandaccelerationsensors.Thesesensorscollectagreatdealofinformation .Howtheinformationisusedtoestimatethedamageofbridgestructureandanalyzethedurabilityofbridgestructureisasignificantresearchproblem .Existenceofstructuraldamageswithinstructuresleadstothechangesuchasthevibrationres…     

平面任意形状等剪切模量异质夹杂问题的解析解

本文研究任意形状夹杂域在受到远端均匀荷载和均匀本征应变作用下的弹性场问题,其中基体和夹杂的材料不同但具有相同的剪切模量。利用等效理论将远端均匀荷载引起的扰动转化为等效均匀本征应变的作用,再利用K-M势函数表达扰动场问题的界面连续条件;借助于黎曼映射定理,用洛朗多项式将平面光滑闭合曲线外部区域映射到单位圆外部区域,借助柯西积分公式和Faber多项式求解了等剪切本征应变下夹杂和基体的K-M势函数的显式解析解,其中考虑了夹杂相对于基体的刚体位移。将得到的结果与相关文献的结果进行对比,表明了本论文的方法和结果是有效的和正确的。