对称边界条件下轨道炮有限元/边界元仿真

基于deal.ii编写了电磁轨道炮有限元仿真程序,建立了拉格朗日运动坐标下电磁轨道炮的有限元仿真模型;通过使用有限元边界元耦合方法可以对电磁轨道炮的边界条件进行计算,而无需对轨道炮周边的空气划分网格,是一种处理电磁场边界问题的有效方法;但是,由于边界元方法,使用的是满秩矩阵,在三维情况下计算量大,利用轨道炮的对称性,使用对称边界条件,减少了参与计算的网格数目,从而减少计算量。

非对称边界的亚波长金光栅反射相位调制

以非对称性边界条件的亚波长金光栅多层结构为模型,借助散射矩阵理论,给出反射相位与光栅边界媒质折射率之间的形式化表达。在上述表达式的基础上,以前期设计的嵌入亚波长金光栅的硅基液晶(G-LCoS)结构为例,使用时域有限差分法开展仿真实验,通过不断优化亚波长金光栅的非对称边界条件,使得G-LCoS在可见光波段下实现多波长的近2π相位调制量。所给出的形式化表达式以及优化过程可为具有动态非对称边界条件的器件,特别是微纳尺度复调制器件的设计提供参考,并且能在一定程度上解释其物理机制。

基于NIAH的螺旋骨架复合柔性低温管道等效力学性能分析

FLNG(floating liquefied natural gas)是一种集LNG(液化天然气)的液化、存储、装卸为一体的新型海上浮式生产系统。螺旋骨架复合柔性低温管道是其中关键的核心配套装备,然而其结构形式复杂,各结构层之间存在着大量的接触、摩擦等非线性问题,使理论建模与数值分析求解较困难;针对螺旋骨架复合柔性低温管道的一维周期性特征,基于渐近均匀化理论新方法(novel implementation of asymptotic homogenization,NIAH),建立螺旋骨架复合柔性低温管道的微单胞模型并施加周期性边界条件,求解得到宏观结构的等效刚度参数。通过与精细有限元模型计算结果对比,发现其等效误差小于3.60%,计算成本缩减约32倍,验证了基于NIAH等效刚度计算的准确性与高效性;针对管道螺旋缠绕结构特征,提出双对称边界条件施加方法,其结果比传统的单对称边界条件减少了78.00%的误差;总结了不同周期性边界条件适用的结构特点,为螺旋骨架复合柔性低温管道的结构设计与分析提供可靠、快速的等效计算方法。

二并列方柱绕流的大涡模拟

在相关文献的基础上发展了二阶全展开ETG有限元计算格式,并与湍流的大涡模拟技术(LES)相结合,对雷诺数为10000条件下的二并列方柱绕流的流场进行了数值模拟,重点在于较好地捕捉低频大尺度旋涡及其随时间的演变。对于若干指定点,给出了压应力的时域过程并进行了频谱分析。结果表明,在边界条件完全对称的前提下,对称点压应力的频谱并不相同,但差别主要集中在频率略高、含能甚少的频段。

六角形节块中子输运计算程序快速求解策略初步研究

计算时间与计算精度是衡量中子输运方法应用的重要指标,针对如何在保证计算精度的前提下减少计算时间开销问题,本研究提出一种基于六角形节块中子输运计算程序的快速求解方法。采用60°周期性对称边界条件求解1/6堆芯,并对1/6堆芯进行并行计算。考虑到不同能群和节块所对应的响应矩阵间存在天然的脱耦性,以及响应矩阵方程求解时非重叠空间区域间可并行性,开发了基于MPI(Message Passing Interface)的响应矩阵构造及矩阵方程求解的并行程序。在并行情况下,针对TAKEDA4基准题开展了校核计算。结果表明:60°周期性对称边界条件和并行计算功能,能够在保证相同计算精度的前提下大大提升计算效率,验证了快速求解策略的正确性。相比于全堆芯串行计算,在9个计算核心数目下,1/6堆芯总计算时间开销在P1、P3、P5下分别可约降低了1/26、1/25、1/22,初步实现六角形节块的快速求解。

A truncated implicit high-order finite-difference scheme combined with boundary conditions

In this paper, first we calculate finite-difference coefficients of implicit finite- difference methods （IFDM） for the first and second-order derivatives on normal grids and first- order derivatives on staggered grids and find that small coefficients of high-order IFDMs exist. Dispersion analysis demonstrates that omitting these small coefficients can retain approximately the same order accuracy but greatly reduce computational costs. Then, we introduce a mirrorimage symmetric boundary condition to improve IFDMs accuracy and stability and adopt the hybrid absorbing boundary condition （ABC） to reduce unwanted reflections from the model boundary. Last, we give elastic wave modeling examples for homogeneous and heterogeneous models to demonstrate the advantages of the proposed scheme.

Peristaltic flow in an asymmetric channel with convective boundary conditions and Joule heating

The peristaltic transport of viscous fluid in an asymmetric channel is concentrated. The channel walls exhibit convective boundary conditions. Both cases of hydrodynamic and magnetohydrodynamic(MHD) fluids are considered. Mathematical analysis has been presented in a wave frame of reference. The resulting problems are non-dimensionalized. Long wavelength and low Reynolds number approximations are employed. Joule heating effect on the thermal equation is retained. Analytic solutions for stream function and temperature are constructed. Numerical integration is carried out for pressure rise per wavelength. Effects of influential flow parameters have been pointed out through graphs.

Analytical Solutions to the Fundamental Frequency of Arbitrary Laminated Plates under Various Boundary Conditions

In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N〉8-10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.

Analytical solutions for a uniformly loaded circular plate with clamped edges

A bi-harmonic potential function was constructed in this study. Love solution was employed to obtain analytical solutions of uniformly loaded plates with two different types of clamped edges. The treatment of clamped boundary conditions was the same as that adopted by Timoshenko and Goodier (1970). The analytical solution for the first type of clamped boundary condition is identical with that obtained by Luo et al.(2004), and the solutions for both types were compared with the FEM results and the calculations of thin plate theory.

基于两尺度代表体元的含孔隙复合材料单层板弹性常数预测

为预测含孔隙复合材料单层板的弹性常数,以单向纤维增强复合材料单层板为研究对象,首先,基于细观力学方法,提出了一种基于两尺度代表体元的含孔隙复合材料单层板弹性常数预测方法;然后,基于纤维排列和孔隙特征,建立了纤维-基体尺度的代表体元模型和含孔隙复合材料单层板的代表体元模型,并采用有限元方法求解弹性常数;接着,采用周期对称边界条件,在纤维-基体尺度先进行第1步等效,得到不含孔隙复合材料单层板的弹性常数;最后,在含孔隙复合材料单层板的代表体元模型上进行第2步等效,完成了含孔隙复合材料单层板弹性常数的预测。结果显示:应用该方法得到的计算结果与试验数据吻合较好;结合纤维、基体弹性常数及孔隙形态的模型,该方法可以反映各因素对复合材料单层板弹性常数的影响。

The random walking method for the steady linear convection-diffusion equation with axisymmetric disc boundary

In this article,the random walking method is used to solve the steady linear convection-diffusion equation(CDE)with disc boundary condition.The integral solution corresponding to the random walking method is deduced and the relationship between the diffusion coefficient of CDE and the intensity of the random diffusion motion is obtained.The random number generator for arbitrary axisymmetric disc boundary is deduced through the polynomial fitting and inverse transform sampling method.The proposed method is tested through two numerical cases.The results show that the random walking method can solve the steady linear CDE effectively.The influence of the parameters on the results is also studied.It is found that the error of the solution can be decreased by increasing the particle releasing rate and the total walking time.