基于投影法求解不可压缩流的高精度紧致格式

本文建立了一种基于投影法的求解不可压缩Navier-Stokes(N-S)方程的高精度紧致差分格式。该方法时间上采用Kim和Moin二阶投影法离散,空间上采用高精度紧致格式离散,并提出了一种新的离散压力边界的紧致格式,同时对计算结果进行分析以验证该投影法的精度和格式稳定性。文中Taylor涡列数值计算结果表明,Kim和Moin投影法能使得压力场和速度场均达到时间二阶精度,且高精度紧致格式投影法也具有空间高阶精度。驱动方腔数值模拟结果显示,本文对N-S方程的离散格式具有很好的可靠性,适用于对复杂流体流动的小尺度问题的数值模拟和研究。     

一种改进的水平集方法在Navier-Stokes问题形状优化中的应用

本文将经典的形状灵敏度分析方法与一种改进的水平集方法相结合,给出了Navier-Stokes问题形状优化的一种新方法。该算法是在固定的Euler网格上进行计算且在优化过程中不需要对水平集函数进行重新初始化,从而可以有效地节省计算时间。数值算例说明该算法是稳定、高效的。     

应用四边形单元稳定化有限元方法求解定常不可压缩流动问题

本文回顾了李剑等针对Stokes和Navier-Stokes方程提出的一种新稳定化有限元方法,该方法采用局部高斯积分残差技术,适用于最低阶等阶(双)线性有限元对.对于等价双线性元对,给出了求解Stokes和Navier-Stokes方程的一些数值算例,验证了理论分析的正确性.     

基于遗传算法和梯度算法的衍架结构动力学形状优化

本文提出了一种基于遗传算法和梯度算法的衍架动力学形状优化方法，该方法综合了梯度算法的快速收敛与遗传算法的全局搜索能力。算例表明了本文方法的有效性和工程适应性。     

基于遗传算法和梯度算法的桁架结构动力学形状优化

本文提出了一种基于遗传算法和梯度算法的桁架动力学形状优化方法 ,该方法综合了梯度算法的快速收敛与遗传算法的全局搜索能力。算例表明了本文方法的有效性和工程适应性。     

基于形状优化的机械设计方法

现代机械产品的设计，不再仅仅局限于对于产品结构性能的满足上，还要满足节约材料的要求，从而控制零件制造成本。对于现代设计，形状优化时在设计过程中必须考虑的问题，各种方法的使用，使形状优化下的机械设计更加具有合理性和结构稳定性，特别是利用计算机的形状优化，更是在机械设计方面提高了设计的科学性。     

求解大规模优化的混合共轭梯度法

为了有效求解大规模无约束优化问题,在PRP方法和FR方法的基础上,给出了满足共轭条件的新的混合共轭梯度法.在强Wolfe线性搜索下,证明了此算法的全局收敛性.在特定条件下,新公式与HS公式一致,因此可看作是对HS方法的修正.对7个经典无约束优化问题的数值实验结果表明,所提出的新方法数值稳定.相比已有方法,随着问题规模的增大,所提方法在迭代次数,优化精度及梯度调用次数方面表现出明显优势.     

形状误差minimax问题的机器求解

本文研究最小条件意义下评定各项形状误差的统一计算法。在线性极差极小化理论的基础上,本文提出了“最佳作用点集合”的概念,将关于评定基准向量的连续最优化问题转化为关于作用点集合的组合最优化问题。进而,本文采用测量点的概率删点技术和评定基准向量的线性保号变换,使问题可采用成熟的Dantzig算法求解。从而,实现了形状误差评定中minimax问题的机器求解。     

用边界元法进行形状优化

本文用边界元法与序列无约束优化方法相结合,对平面应力下的弹性体进行了形状优化,在优化过程中,用虚拟目标法处理多目标问题。为避免烦锁的灵敏度分析,采用了“新单纯形方法”。文中作的例题,获得满意结果。     

基于并行混沌和复合形法的桁架结构形状优化

针对多工况下受应力、位移和局部稳定性约束的桁架形状优化问题,提出了基于并行混沌优化算法和复合形法的混合优化算法。该算法综合利用了并行混沌的全局搜索能力,复合形法的快速局部搜索能力和混沌细搜索。首先,利用并行混沌优化算法快速搜索到全局最优解附近,然后应用改进复合形法以并行混沌的优化解为初始复形进行搜索,提高了最优解的搜索速度,最后应用混沌细搜索策略提高最优解的精度。两个典型数值算例验证了该混合优化方法对桁架形状优化问题的有效性和稳定性。     

简支梁在无限大不可压缩流体和声学流体中的固有振动问题

本文用边界积分方程描述无限大声学流体,从而得到了控制圆截面简支梁在该流体中固有振动的积分-微分方程。在此方程基础上,分别用摄动法和有限元与摄动展开相结合的方法,计算了简支梁在无限大声学流体中的固有频率。当声速趋于无穷大时,得到了无限大不可压缩流体中简支梁的固有频率。本文的方法可推广到较为复杂的结构声辐射系统的固有频率的计算上。     

用形状优化法延长零件寿命

 本文论述如何能够将经典的强度分析方法与现代的计算力学方法相结合。这里并不只局限于利用有限元方法 (FEM)确定危险应力的数值 ,而且还利用形状优化法提供的可能性使最大应力得以降低 ,并由此实现零件的预期寿命。     

Surface Phenomena in the Hydrodynamics of an Incompressible Fluid

By taking as an example the outflow of an incompressible fluid through a hole with small geometric parameters under the conditions of supersmall pressures, we attempted to evaluate the effect of surface phenomena on its flow by the similarity method. The Navier–Stokes differential equation was supplemented by parameters allowing for the effect of surface forces. The modified Navier–Stokes equation was subjected to similarity conversion. This yielded a dimensionless group that includes the whole range of variable parameters affecting the fluid flow, namely, the generalized criterion Pv. The graphic dependence of the coefficient of the fluid flow rate on the generalized criterion Pv is presented on the basis of experimental data.     

Maxwell流体不可压缩流动稳定性的多尺度分析与数值模拟

本文对Maxwell流体小尺度不可压缩周期流,通过多尺度分析获得控制扰动流的大尺度均场方程和紧凑形式的四阶有效张量.对稳态平行流,通过对均场方程中均匀化算子的特征值进行理论分析,得到控制大尺度扰动流稳定性的临界粘性系数.然后对不同参数和初始条件,采用基于同位网格改进的SIMPLEC算法对均场方程和大尺度扰动流控制方程进行数值模拟,验证了多尺度理论预测的正确性,从而说明了本文所用多尺度分析方法和数值算法的有效性和可靠性.     

Integrating the Lambert W Function to a Tolerance Optimization Problem

This paper explores the integration of the Lambert W function to a tolerance optimization problem with the assessment of costs incurred by both the customer and a manufacturer. By trading off manufacturing and rejection costs, and a quality loss, this paper shows how the Lambert W function, widely used in physics, can be efficiently applied to the tolerance optimization problem, which may be the first attempt in the literature related to tolerance optimization and synthesis. Using the concept of the Lambert W function, a closed‐form solution is derived, which may serve as a means for quality practitioners to make a quick decision on their optimal tolerance without resorting to rigorous optimization procedures using numerical methods. A numerical example is illustrated and a sensitivity analysis is performed. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization Technique for Design of Automotive Air Filter Housings with Improved Fluid Dynamic Performance and Filtration

A filter housing design technique has been developed that computes the housing geometry required to provide a user-specified velocity distribution through the filter. Appropriate control of the flow field across the filter can improve filter efficiency. Two-dimensional computational designs have been performed specifying a uniform velocity distribution through the filter. This distribution corresponds to a uniform, constant pressure drop across the filter from the upstream to the downstream side. A computational optimization method is used to minimize the variation in the pressure drop along the filter by changing the geometry of the upper wall. Computational fluid dynamics (CFD) calculations of the viscous laminar flow upstream and downstream of the filter are performed using two-dimensional Navier-Stokes equations. As the upper wall profile is numerically changed, the CFD solution for the computations is repeated and the pressure drop variation is reevaluated until an optimum configuration is achieved. The optimization results have produced a pressure distribution that is very close to the specified uniform distribution. Experimental verifications were performed using a laser Doppler anemometer to measure the velocity distribution just upstream of the filter and a pressure transducer to measure pressure drops across the filter. The velocity distribution in this (optimized) housing is more uniform than other housing models having the same fundamental rectangular geometry.     

《大尺寸空间薄膜结构形状控制研究》

高形状精度要求与形状易变性之间的矛盾是限制大尺寸空间薄膜结构空间应用的主要技术瓶颈之一。本文主要从技术层面论述大尺寸空间薄膜结构形状保持和振动抑制的方法。首先,阐述薄膜结构形状误差源及形状控制必要性分析;然后,论述国内外空间薄膜结构形状控制的研究现状,包括控制方案、传感器及执行器;最后,提出大尺寸空间薄膜结构形状控制的关键技术。     

多结点等参单元形态函数的确定

本文对高阶单元形态函数的分析,是严格遵照形函的定义,引用复盖线和复盖面,其中包括圆弧和圆球复盖技巧。各种单元形态函数的确定,都有详细步骤,简便,直观,省时。较一般专著确定形函数的插值方法优越。     

Motion of a Viscous Incompressible Fluid in a Pipe in a Rotating Coordinate System

An analytical solution of the problem on steady motion of a viscous incompressible fluid in a circular pipe has been obtained with regard for the action of Coriolis forces. It is shown that the rotation of the coordinate system as a result of the destruction of the laminar regime of flow and the appearance of a partially nonuniform three-dimensional vortex flow on its basis lead to an increase in the hydrodynamic drag of the pipe.     

Chaotic Shape and Translational Dynamics of 2D Incompressible Bubbles under Forced Vibration in Microgravity

Nonlinear shape oscillations of 2D incompressible bubbles in an inviscid fluid, subject to a forced vibration in microgravity, have been studied numerically. Forced vibration induces an oscillatory translational motion as well as shape oscillations. It is shown that for large enough oscillation amplitudes, the coupling between the shape oscillation and the translational motion of a bubble results in a chaotic behaviour. For two-bubble systems, the bubbles may attract each other. The attraction force is stronger at higher Bond numbers. Higher Bond numbers also yield larger bubble deformation.