Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

Construction of Wave-free Potentials and Multipoles in a Two-layer Fluid Having Free-surface Boundary Condition with Higher-order Derivatives

There is a large class of problems in the field of fluid structure interaction where higher-order boundary conditions arise for a second-order partial differential equation. Various methods are being used to tackle these kind of mixed boundary-value problems associated with the Laplace’s equation （or Helmholtz equation） arising in the study of waves propagating through solids or fluids. One of the widely used methods in wave structure interaction is the multipole expansion method. This expansion involves a general combination of a regular wave, a wave source, a wave dipole and a regular wave-free part. The wave-free part can be further expanded in terms of wave-free multipoles which are termed as wave-free potentials. These are singular solutions of Laplace’s equation or two-dimensional Helmholz equation. Construction of these wave-free potentials and multipoles are presented here in a systematic manner for a number of situations such as two-dimensional non-oblique and oblique waves, three dimensional waves in two-layer fluid with free surface condition with higher order partial derivative are considered. In particular, these are obtained taking into account of the effect of the presence of surface tension at the free surface and also in the presence of an ice-cover modelled as a thin elastic plate. Also for limiting case, it can be shown that the multipoles and wave-free potential functions go over to the single layer multipoles and wave-free potential.

Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions

This research aims to analyze the static bending and free vibration behaviors of bidirectional functionally graded porous(BFGP)curved microbeams with elastic boundary conditions resting on a Pasternak’s elastic foundation in a hygro-thermal environment.Isogeometric analysis based on non-uniform rational B-splines,first-order shear deformation theory,nonlocal elasticity theory combined with the modified strain gradient theories,modified Timoshenko beam theory are formulated to depict bending and shear deformations of BFGP curved microbeams.Especially,because using the modified Timoshenko beam theory,this study removes the requirement for a shear correction factor and describes shear stress by zero at the upper and lower cross-sectional sites of the BFGP curved microbeam.Different from traditional boundary conditions,where the beginning and end positions of a curved beam are connected by an elastic system of straight and torsion springs.This allows for greater flexibility in controlling the stiffness of the springs to obtain arbitrary boundaries.To assess the accuracy and convergence of the proposed approach,validation numerical examples were conducted in the various examples.

Service Life Design for Concrete Engineering in Marine Environments of Northern China Based on a Modified Theoretical Model of Chloride Diffusion and Large Datasets of Ocean Parameters

In this study,through experimental research and an investigation on large datasets of the durability parameters in ocean engineering,the values,ranges,and types of distribution of the durability parameters employed for the durability design in ocean engineering in northern China were confirmed.Based on a modified theoretical model of chloride diffusion and the reliability theory,the service lives of concrete structures exposed to the splash,tidal,and underwater zones were calculated.Mixed concrete proportions meeting the requirement of a service life of 100 or 120 years were designed,and a cover thickness requirement was proposed.In addition,the effects of the different time-varying relationships of the boundary condition(Cs)and diffusion coefficient(Df)on the service life were compared;the results showed that the time-varying relationships used in this study(i.e.,Cscontinuously increased and then remained stable,and Dfcontinuously decreased and then remained stable)were beneficial for the durability design of concrete structures in marine environment.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

任意边界条件下Timoshenko梁及其修正理论的自振特性分析

提出一种求解任意边界条件下经典Timoshenko梁以及修正Timoshenko梁自振频率和振型的新方法。利用改进的傅立叶级数消除传统傅立叶级数的边界不收敛问题,然后通过Rayleigh-Ritz法导出Timoshenko梁的拉格朗日泛函,根据Hamilton原理将原问题转化为求解矩阵广义特征值问题。通过与解析解对比,本文采用的方法具有较好的收敛性以及较高的计算精度;通过数值计算发现,经典Timoshenko梁的自振频率略高于修正的Timoshenko梁,随着振型阶数的提高,经典Timoshenko梁的计算结果逐渐偏离文献解和有限元结果,而修正的Timoshenko梁能够保持较好的一致性;对于不同边界条件下修正Timoshenko梁的计算结果均能与有限元的计算结果吻合得很好。最后运用MATLAB编程软件将程序设计为App,对于不同情形的梁只需要修改参数即可,可为实际工程提供高效便捷的计算方案和可靠理论依据。

黏弹性Pasternak地基上修正Timoshenko梁横向自振特性分析

基于修正Timoshenko梁理论,建立黏弹性Pasternak地基上修正Timoshenko梁的横向振动控制方程,运用回传射线矩阵法推导出黏弹性Pasternak地基上两端简支修正Timoshenko梁自振频率和衰减系数的解析解,结合二分法和黄金分割法计算了经典边界条件下黏弹性Pasternak地基上修正Timoshenko梁的自振特性,对比分析了考虑剪切变形引起的转动惯量、梁长及不同的边界条件对结构自振特性的影响。研究表明:黏弹性Pasternak地基上修正Timoshenko梁的各阶自振频率和衰减系数小于经典Timoshenko梁的各阶自振频率和衰减系数;梁越短,剪切变形引起的转动惯量对结构自振频率和衰减系数的影响越大,且对高阶的影响明显大于低阶;边界约束条件越强,振动能量衰减越明显。

基于修正翘曲位移模式的薄壁箱梁剪力滞效应分析

选取剪力滞效应引起的附加挠度作为描述剪力滞变形状态的广义位移,在合理构造剪力滞翘曲位移函数的多参数修正模式基础上,提出薄壁箱梁剪力滞效应的分离解析理论,避免了已有文献中将剪力滞变形状态与初等梁挠曲变形状态联合在一起分析时的复杂性。用基于最小势能原理的变分法建立关于附加挠度的控制微分方程及边界条件。通过对箱形截面引入两个整体修正系数,使剪力滞翘曲应力在箱梁横截面上不合成轴力和弯矩,以充分反映剪力滞翘曲应力的自平衡性质。对悬臂翼缘板引入边界约束修正系数,以便反映悬臂翼缘板与顶板的不同边界约束对剪力滞翘曲模式的影响。根据空间有限元计算的翼缘板应力结果,确定悬臂板边界约束修正系数的具体数值。简支箱梁及连续箱梁数值算例表明,按本方法计算的翼缘板应力与空间有限元计算结果吻合良好,从而验证了本分析方法的正确性。

电磁脉冲作用下近地电缆外皮感应电流的全波分析

本文采用时域有限差分法 ,分析电磁脉冲作用下 ,地面附近同轴电缆所感应的外皮电流。在计算外皮感应电流时 ,既考虑了传输线模式电流 ,也考虑了天线电流。该方法适合分析各种电缆的外皮感应电流。所得结果与有关资料作了对比 ,说明本文的计算结果是合理的。

金属塑性成形三维有限元模拟过程中修正触模节点位置的一种新方法

提出了动态边界条件处理中修正触模节点位置的一种新方法——初矢修正法 ,从而解决了金属塑性成形三维有限元模拟中由于离散的模具网格造成的“死锁”问题。采用三维刚粘塑性有限元法 ,考虑工模具间的摩擦 ,采用作者所提出的网格重划方法对畸变网格进行重新划分 ,对叶片的锻造过程进行了模拟分析。在模拟过程中的每一加载步 ,均采用本文提出的初矢修正法对触模节点位置进行修正。叶片锻造三维有限元模拟的顺利进行 ,验证了采用本文所提出的初矢修正法修正触模节点的位置 ,可以避免由于离散的模具网格造成的“死锁”。因此该方法不但可行 ,而且可靠。

锂离子电池简化电化学模型:浓度分布估计

为了降低锂电池电化学模型的计算复杂度,提出基于修正边界条件的简化电化学模型,用于估计锂电池内部的电解液浓度分布.采用Pade逼近技术分析简化电化学模型解析解,可得到降阶的分子-分母型传递函数模型.分别采用19.38A和193.80A的脉冲充放电工况进行仿真对比,结果显示所提出简化模型的最大相对误差分别约为0.867%和8.670%.时域和频域模拟仿真结果表明:相比于传统电化学模型,该简化模型对电池内部电解液相的浓度分布估计具有理想的精度,同时计算复杂度得到显著优化,具备实时应用的能力.

河流混合污染物浓度二维移流扩散方程的解析计算及其简化计算的条件Ⅱ:顺直河流考虑边界反射

在保守物质恒定连续点源条件下,从包含河流纵向扩散项的二维移流扩散方程解析解出发,考虑两岸边界反射作用,给出了河流污染物浓度的二维解析计算方法及污染物的无量纲浓度分布方程。定义了能综合反映纵向移流作用与纵向、横向扩散作用比值的修正贝克来数Pw。在Pw相等以及在相对浓度达到10-6的精度条件下,通过数值计算给出了边界反射次数与修正贝克来数的回归关系式。当Pw≥7.5,忽略纵向扩散项的条件下,岸边排放与中心排放浓度分布的一半具有自动相似性。给出了河流污染物相对浓度分布、排放岸和对岸特征浓度点的无量纲纵坐标以及全断面均匀混合的无量纲距离与修正贝克来数Pw之间的关系曲线。研究结果论证了以修正贝克来数作为移流扩散方程简化的判据,并据此给出考虑边界反射时移流扩散方程的简化条件,其是可行的。

改进的阻尼透射边界

在计算结构动力学中，为了计入结构—地基的相互作用，必须在计算模型中引入透射边界。最方便而又常用的透射边界是简单阻尼边界。在此基础上文章提出了改进的阻尼透射边界。在一般动力反应计算中。

用于有耗介质FDTD计算的改进的Mur吸收边界条件

从常规Mur吸收边界条件的推导出发 ,引入有耗介质的相应参数 ,使其可应用于截断边界电磁参数不连续和介质为有耗的情形。通过模拟公式计算 ,并与常规Mur吸收边界条件对比 。

四阶微分方程非线性两点边值问题解的存在性

运用微分不等式理论 ,结合上下解方法 ,借助变形函数 ,得到了四阶微分方程具一般非线性边界条件的两点边值问题的解的存在性定理 .

一种广义时域有限差分算法

本文讨论了一种广义FDTD算法,它是建立在修正的Maxwell方程式基础上的。引入尺寸的比例因子和尺寸扩展因子使空间网格沿三个轴向的大小既具有不相等,亦具有可变扩展的能力,使这种算法具有广泛应用的能力。本文给出三个例子说明本方法所得结果是令人满意的。

Full-Wave Analysis of Slotline Using Time-Domain Finite-Difference Method

The transmission and dispersive characteristics of slotline are calculated in this paper. The tail of Gaussion pulse is improved because a modified dispersive boundary condition (DBC) is adopted. It leads to a reduction in computer memory requirements and computational time. The computational domain is greatly reduced to enable performance in personal computer. At the same time because edges of a boundary and summits are treated well, the computational results is more accurate and more collector.

无网格法中一种处理本质边界的新方法

无网格伽辽金法中形函数一般不具有插值函数的特征,本质边界条件需特殊处理.在通过拉格朗日乘子识别法强加本质边界条件的基础上,为提高计算精度,再对修正泛函使用罚函数法来强加本质边界条件.该方法不仅没有增加未知量的数目,刚度矩阵仍然正定带状,而且计算精度较高,对罚因子依赖性降低,能较好的模拟位移边界条件.以弹性力学问题为例进行了数值试验,计算结果表明,该方法不仅简单合理,而且具有较高的计算精度和数值稳定性.

离散支承梁分段动力学建模方法

为了更准确分析轨道交通振动与噪声的成因及传播机理,需要构建车辆-轨道耦合模型,模拟在移动载荷作用下全系统的动力学响应,其中,轨道结构振动方程作为模型中的重要组成环节,其求解方法对于模型数值分析的计算精度有直接影响。常用求解方法—Rayleigh-Ritz法是将简支梁的各阶振型作为基函数,通过模态叠加法求得轨道在外部激励作用下的动力学响应。然而,当轨道计算长度不足、周期支承特性缺失时,基于有限长简支梁得到的振型函数不能充分表征轨枕的离散支承特性,因此,针对一般离散支承梁,提出一种分段建模方法,通过边界条件把轨枕的约束作为弹性恢复力纳入轨道模型中,而不是作为外力项,从而求解出更符合实际的修正振型函数以及固有频率。进一步,对比动力学建模与有限元仿真结果,验证了所提方法在其适用范围内的精确性和有效性。

Transverse shear and normal deformation effects on vibration behaviors of functionally graded micro-beams

A quasi-three dimensional model is proposed for the vibration analysis of functionally graded(FG)micro-beams with general boundary conditions based on the modified strain gradient theory.To consider the effects of transverse shear and nor-mal deformations,a general displacement field is achieved by relaxing the assumption of the constant transverse displacement through the thickness.The conventional beam theories including the classical beam theory,the first-order beam theory,and the higher-order beam theory are regarded as the special cases of this model.The material proper-ties changing gradually along the thickness direction are calculated by the Mori-Tanaka scheme.The energy-based formulation is derived by a variational method integrated with the penalty function method,where the Chebyshev orthogonal polynomials are used as the basis function of the displacement variables.The formulation is validated by some comparative examples,and then the parametric studies are conducted to investigate the effects of transverse shear and normal deformations on vibration behaviors.