结构边界约束修改后的重分析方法

在结构设计优化中经常将结构边界约束作为设计优化对象,结构边界约束的修改通常导致系统的求解规模发生改变,使得快速准确分析修改后结构的响应成为一个挑战。本文发展了逐次矩阵逆(SMI)方法,提出了一种适合各种结构边界约束(包括初始结构中的约束)修改的快速重分析算法。该方法利用边界约束修改后对应刚度矩阵的对称性,有效缩减了计算量。数值算例表明,本文方法能够快速给出精确的重分析结果。     

AEROELASTIC OPTIMIZATION DESIGN OF COMPOSITE WING WITH CONSIDERATION OF STRUCTURAL INSTABILITY

从工程数学求解和有限元分析角度对复合材料结构的稳定性分析方法进行研究,基于这两个方面分别建立了同时考虑壁板稳定性约束和气动弹性约 束的气动弹性优化技术,并以大展弦比复合材料机翼为对象,进行气动弹性综合优化设计。研究表明,机翼气动弹性优化中若不考虑稳定性约束条件,虽然可以获得较小结构重量,但往往不满足稳定性要求;相比从有限元角度考虑结构失稳特征的气动弹性综合优化设计方法,通过工程数学方法对机翼结构进行分区失稳分析优化可以更加精准地控制变量,在满足各项性能指标,特别是稳定性约束的同时,进一步减轻了结构重量,提高了结构失稳因子。     

Voronoi Cell Finite Element Method for Fluid-Filled Materials

A modified Voronoi cell finite element method is proposed to allow for fluid pressure within porous materials. Traction on the hole boundary can equal the force generated by the pressure, and multiplying the Lagrange multiplier by the constraints, we derive a new function. The stiffness matrix and load vector were derived from the modified element energy functional. Numerical examples with various boundary problems were evaluated using the proposed model and compared with a conventional displacement-based finite element model. The results show that the proposed method can measure the irregular local stress on porous materials that contain randomly distributed and sized holes with specifics pressures. The proposed method significantly reduces the number of elements and nodes of the calculated porous structure.     

Improvements to compressible Euler methods for low‐Mach number flows

In the present study improvements to numerical algorithms for the solution of the compressible Euler equations at low Mach numbers are investigated. To solve flow problems for a wide range of Mach numbers, from the incompressible limit to supersonic speeds, preconditioning techniques are frequently employed. On the other hand, one can achieve the same aim by using a suitably modified acoustic damping method. The solution algorithm presently under consideration is based on Roe's approximate Riemann solver [Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43 : 357–372] for non‐structured meshes. The numerical flux functions are modified by using Turkel's preconditioning technique proposed by Viozat [Implicit upwind schemes for low Mach number compressible flows. INRIA, Rapport de Recherche No. 3084, January 1997] for compressible Euler equations and by using a modified acoustic damping of the stabilization term proposed in the present study. These methods allow the compressible Euler equations at low‐Mach number flows to be solved, and they are consistent in time. The efficiency and accuracy of the proposed modifications have been assessed by comparison with experimental data and other numerical results in the literature. Copyright © 2000 John Wiley & Sons, Ltd.     

连续体结构拓扑优化应力约束凝聚化的ICM方法

为克服应力约束下拓扑优化问题约束数目多、应力敏度计算量大的困难,提出 了应力约束化凝聚化的ICM方法. 在利用Mises强度理论将应力约束转换成应变能约束后, 提出了应力约束凝聚化的两条途径：其一为应力全局化的方法,其二为应力约束集成化的方 法. 由此建立了多工况下以重量为目标、以凝聚化应变能为约束的连续体结构优化模型,并 利用对偶理论对优化模型进行了求解. 4个数值算例表明：该方法具有较高的计算效率,得 到的拓扑结构比较合理,不仅适用于二维连续体结构,也适用于三维连续体结构.     

基于双向渐进结构优化法的“破损-安全”结构轻量化设计

“破损-安全”(fail-safe)设计通过冗余载荷路径设计提升结构的损伤容限(残余承载能力),是保障飞行器结构安全性的重要设计环节；然而，冗余结构形式不可避免地导致重量增加、效率降低，严重制约飞行器结构性能的进一步提升.论文基于双向渐进结构优化法(Bi-directional Evolutionary Structural Optimization),提出了一种“破损-安全”结构轻量化设计方法.具体地，设计方法采用“0/1”离散拓扑变量，以结构重量(材料用量)最小化作为优化目标，同时对局部破损结构的承载形变进行约束(低于安全阈值).针对渐进结构优化法难处理多设计约束的瓶颈，采用p范数法对局部破损结构的最大承载形变进行凝聚，并通过拉格朗日乘子将其耦合至优化目标函数，实现结构轻量化与“破损-安全”的同步设计.进一步地，并依据最大残余承载形变对局部区域破损之于“破损-安全”的影响程度进行判定，通过免除低影响局部破损区域的残余承载形变分析与约束，大幅度地提升了优化设计效率.通过系列基准测试算例，验证了论文“破损-安全”设计方法的有效性及高效性.     

A comparison between a collocation and weak implementation of the rigid‐body motion constraint on a particle surface

In this work, we implemented and compared two different methods to impose the rigid‐body motion constraint on a solid particle moving inside a fluid. We consider a fictitious domain method to easily manage the particle motion. As the solid as well as the fluid inertia are neglected, the particle can be discretized through its boundary only. The rigid‐body motion is imposed via Lagrange multipliers on the boundary. In the first method, such constraints are imposed in discrete points on the boundary (collocation), whereas in the second the constraint is imposed in a weak way on elements dividing the particle surface. Two test problems, that is, a spherical and an ellipsoidal particle in a sheared Newtonian fluid, are chosen to compare the methods. In both cases, the analysis is carried out in 2D as well as in 3D. The results show that for the collocation method an optimal number of collocation points exist leading to the smallest error. However, small variations in the optimal value can generate large deviations. In the weak implementation, the error is only mildly affected by the number of elements used to discretize the particle boundary and by the Lagrange multiplier's interpolation space. A further analysis is carried out to study the effect of an approximated integration of weak constraints. A comparison between the two methods showed that the same accuracy can be achieved by using less constraints if the weak discretization is used. Finally, the rigid‐body motion imposed via weak constraints leads to better conditioned linear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

空间几何构造分析的有限单元法

提出空间杆系几何构造分析的有限单元法，构造了两种单元(链杆单元和准梁单元)的几何约束矩阵，集成为整体矩阵并引入承条件后，通过对其阶数与秩的比较分析确定体系的几何可变性及静定性．本法原理简单，便于计算机实施，结果完备：对于几何不变体系，可指出多余约束的数目；对于几何可变体系，可给出体系的自由度数及相应的运动模态，并确定自由度的常变瞬变性质．     

Bogolyubov generating functional method in statistical physics and “collective”-variables transform within grand canonical ensemble

We show that the Bogolyubov generating functional method is a very efficient tool for studying distribution functions of both equilibrium and nonequilibrium states of classical many-particle dynamical systems. In some cases, the Bogolyubov generating functionals can be represented by means of infinite Ursell-Mayer diagram expansions, whose convergence holds under some additional constraints on the statistical system under consideration. The classical Bogolyubov idea to use the Wigner density operator transformation for studying nonequilibrium distribution functions is developed and a new analytic nonstationary solution to the classical Bogolyubov evolution functional equation is constructed. Published in Neliniini Kolyvannya, Vol. 10, No. 1, pp. 37–50, January–March, 2007.     

结构优化半解析灵敏度及误差修正改进算法

提出结构半解析灵敏度分析及其针对刚体位移的误差修正方法的改进算法, 构建灵敏度分析与误差修正项可分离形式. 该方法实现简便, 数值精度不受摄动步长与单元数目的影响. 首先从总体角度推得静力问题的误差修正半解析灵敏度分析方法, 提出了位移误差修正灵敏度列式, 并给出算法实施途径; 然后将此思路推广于自振频率、屈曲临界载荷问题, 提出了相应的计算步骤. 随后, 给出梁单元与壳单元误差修正项的具体推导方法, 并分别使用两种单元构建有限元模型进行算例测试. 结果表明, 该方法适用于多种分析类型, 数值精度不受单元数目与摄动步长的影响. 由于灵敏度分析与误差修正项可以分开计算, 该方法支持将误差修正项直接叠加于灵敏度求解结果进行误差修正, 使已有灵敏度分析程序得到充分利用. 尤其对于复杂工程结构的优化设计, 特别是形状优化设计以及尺寸、形状混合优化设计, 相比于原误差修正方法, 实现更为简便, 效率有所提升, 能为半解析灵敏度分析方法及其程序实现提供新的思路.      

多变量单元结构共振解耦动力优化设计方法

针对截面多变量单元结构的动力优化问题,建立了带频率约束的结构动力优化设计模型,对隐式非线性频率约束函数进行Taylor近似展开,给出了截面多变量单元频率梯度函数显式表达式,基于Kuhn-Tucker条件构建迭代算法,其中拉格朗日乘子通过建立联合方程组求解,形成了含多变量单元共振解耦优化设计方法。以矩形截面单元结构为算例的结果表明,所给单元多变量算法具有良好的准确性;截面变量对频率的贡献存在主次之分,区分指标可采用梯度值;次要变量的修正因子迭代中可采用定值,且其下限应尽可能降低,利于节约成本。本文工作对多变量复杂截面结构动力优化设计可提供理论指导,提高结构动力优化方法的适用性。     

FATIGUE LIFE PREDICTION OF SUS 630 （H900） STEEL UNDER HIGH CYCLE LOADING

The fatigue life prediction of high strength steel SUS 630 （H900） under high cycle loading is conducted with consideration of a characteristic fatigue length of material. Based on the WShler curve of smooth materials, a modified method for fatigue life prediction is approached. The characteristic fatigue length of material under cyclic loading is associated with the polycrystalline material. Rather than the stress at a point, the average stress within the characteristic fatigue length is implemented for the fatigue life prediction. The method can be applied to both the smooth and the defected material. The fatigue life prediction is also verified experimentally by specimens with various small circular holes. Through the comparison, it is found that the method can be adopted to predict the fatigue lives with different size effects.     

Finite-time synchronization control for uncertain Markov jump neural networks with input constraints

This paper is concerned with the problem of finite-time synchronization control for uncertain Markov jump neural networks in the presence of constraints on the control input amplitude. The parameter uncertainties under consideration are assumed to belong to a fixed convex polytope. By using a parameter-dependent Lyapunov functional and a simple matrix decoupling method, a sufficient condition is proposed to ensure that the considered networks are stochastically synchronized over a finite-time interval. The desired mode-independent controller parameters can be computed via solving a convex optimization problem. Finally, two chaos neural networks are employed to demonstrate the effectiveness of our proposed approach.     

Minimum fuel trajectory transfer in a general gravity field using a finite number of engine firings to cause velocity discontinuities

A method is presented to compute the firing logic for a rocket to transfer from one arbitrary trajectory to another such trajectory in a fixed maximum number of firings of the engine in a manner to minimize the amount of fuel consumed while satisfying various orbital constraints.

The iterative procedure presented may be used to solve other constrained non-linear parameter minimization problems. The method involves iteratively minimizing the first differential of the “cost” function subject to improving the first differentials of the constraints by using linear programming. Both equality and inequality constraints are amenable to solution by this method.     

钝头机体用嵌入式大气数据传感系统的解算精度研究1）

针对一种钝头机体用嵌入式大气数据传感(flush air data sensing,FADS) 系统的实施方案及求解精度展开研究. 基于15° 钝头体外形,在马赫数Ma = 2.04, 3.02, 5.01,攻角α 介于-5°和25°之间,不考虑侧滑角的情况下,采用势流理论及修正的牛顿流理论建立了该FADS 系统的气动模型. 首先利用经典的三点式算法建立了攻角的求解方案,并采用最小二乘曲线拟合的方法对误差进行了修正;随后建立相应的迭代衰减算法解算静压及动压,最后根据压力比与马赫数的关系求解马赫数. 对解算的数据与实际飞行参数进行了比较,结果表明,建立的钝头机体用FADS 系统的模型及算法精度较好,攻角绝对误差小于0.1°,静压相对误差小于5%,马赫数绝对误差小于0.01.     

An extended stress-based method for orientation angle optimization of laminated composite structures

Orientation optimization plays an important role in the lay-up design of composite structures.Earlier orientation optimization methods face the main problem of huge number of design variables.Recently,a patch concept is proposed to reduce the number of design variables.However,the traditional stress-based method can not deal with patch orientation optimization of composite structures.In this paper,we propose an extended stress-based method to deal with such problems.The considered problems are to minimize the mean compliance under multiple load cases or to maximize the eigenvalues of a composite structure.Four numerical examples are solved to demonstrate the efficiency of the new method.It is shown that the new method has the ability to deal with constraints on orientation angle,such as symmetric,antisymmetric and discrete orientation angle constraints.The iteration is less time-consuming because no sensitivity analysis is needed and a quick convergence rate can be achieved.     

分布式运动约束下悬臂输液管的参数共振研究

输液管道结构在航空、航天、机械、海洋、水利和核电等工程领域都有广泛应用,其稳定性、振动与安全评估备受关注.针对具有分布式运动约束悬臂输液管的非线性动力学模型,分别采用立方非线性弹簧和修正三线性弹簧来模拟运动约束的作用力,研究了管道在脉动内流激励下的参数共振行为.首先,从输液管系统的非线性控制方程出发,利用Galerkin方法进行离散化;然后,由Floquet理论得出线性系统在失稳前两个不同平均流速下脉动幅值和脉动频率变化时的共振参数区域;最后,考虑系统的几何非线性项和分布式非线性运动约束力的影响,求解了管道的非线性动力学响应,讨论了非线性项及运动约束力对管道参数共振行为的影响.研究结果表明,系统非线性共振响应的参数区域与线性系统的共振参数区域是一致的,分布式运动约束力对发生参数共振时管道的位移响应有显著影响;立方非线性弹簧和修正三线性弹簧模型所预测的分岔路径存有较大差异,但都可诱发管道在一定的参数激励下出现混沌运动.      

非光滑优化的双层规划模型及内点算法

对于包含接触约束的非光滑结构优化问题,其非光滑性体现在状态函数并不是处处可微的,针对含有应力约束及接触约束的非光滑结构优化问题,建立了一种双层规划模型,避免了求解时非光滑性所带来的问题,同时提出了一种迭代算法,用对偶内点二次规划进行分析,线性规划进行优化,算例表明这种方法十分有效。     

Improvement of a pressure gradient method and its application to an unsteady flow problem

The pressure gradient method using velocity components and components of a pressure gradient as dependent variables has been modified to solve incompressible Newtonian fluid flow problems numerically. Applying this modified method to unsteady-state development of flow in a circular cavity shows that, at least for the case of a low Reynolds number flow, relative errors produced by the proposed method are smaller for most time intervals than those produced by the primitive velocity-pressure variable method and by the standard pressure gradient method. Also it is found that the modified and standard pressure gradient methods can be applied to the unsteady circular cavity flow at a moderate Reynolds number of at least up to 200.