惯性载荷作用下结构拓扑优化

针对惯性载荷作用下的结构拓扑优化设计问题,基于结构整体柔顺度的灵敏度计算公式的推导,阐述了此类问题目标函数的非单调特征;根据载荷与单元刚度的设计相关性,分析了多种材料插值模型对优化结果和迭代过程的影响. 在此基础上,提出可变参数的RAMP模型,对不等式体积约束和纯自重作用下的拓扑优化问题,通过稳定的优化迭代过程得到逼近理论最优解的优化结果. 理论分析和数值算例表明,设计相关惯性载荷导致结构柔顺度的灵敏度不再永远为负值,即柔顺度不再是单调减函数;惯性载荷作用下拓扑优化结果并不总是达到体积约束上限,即材料用量越多结构刚度未必越大;已有的ESO和MP类优化方法的优化结果存在明显的区别,而选择适当的材料插值模型能够很好的将两类优化方法的结果统一起来.      

基于拓扑优化的声学结构材料分布设计

本文针对结构的声学设计问题进行研究,通过优化两种不同的材料在结构设计域内的拓扑分 布来最小化谐振结构所产生的声场中指定参考面/参考域内的声压。在研究中假定结构为线弹性小变 形结构,材料阻尼为Rayleigh阻尼,声学介质为无粘、可压缩、小扰动流体。对结构响应采用有限 元格式进行计算,对声场采用基于Helmholtz积分的边界元格式进行计算,由于声场在无穷远自由边 界的无反射条件在边界积分中能自动得到满足,该格式特别适合于具有开放边界的声场计算。建立 了结构有限元-声场边界元格式的耦合系统拓扑优化模型,导出了耦合系统敏感度分析的一般格式及 伴随格式。数值算例验证了所提出的结构-声学耦合系统优化方法的有效性和可靠性,并揭示了基于 声学准则的拓扑优化结果的有关特性 关键词边界积分,结构声学耦合系统,拓扑优化,敏感度分析,伴随方法     

基于分区加速和总体共轭梯度法的耦合界面数据传递问题研究

对于耦合动力学问题的分析过程,在界面上需频繁进行数据交换。为此,基于紧支径向基函数和多项式基函数推导了界面数据传递的插值算法,给出了传递矩阵的具体形式。通过分析时间复杂度,找出该算法在大节点量时效率不高的原因在于径向基矩阵的构造和传递矩阵的计算。为加快径向基矩阵的构造速度,提出分区加速处理以提高相关节点的搜索效率;为避免传递矩阵求解过程中的求逆运算,将其转化为多右端项的大型稀疏对称线性方程组问题,引入多右端项的总体共轭梯度迭代方法求解,并讨论了初始估计矩阵的选取方法。数值算例结果表明,结合使用分区加速原理和总体共轭梯度迭代方法,可在不损失插值精度的前提下显著提高求解效率。     

基于层次分解方法的桁架结构形状优化

对于桁架结构形状优化,应用层次分解优化方法,将设计变量分成杆件截面积和节点位置两类变量。求解时分为两层,第一层在给定节点位置下对杆件截面进行优化,同时考虑了应力、局部稳定约束和位移约束的重量最轻;第二层假定截面层的有效位移约束作用不变,求解一个使桁架刚度增强的二次规划问题,获得既不违反约束,又使目标函数不上升的新的节点位置,再返回第一层。两层交替进行直至收敛。     

基于SIMP材料插值模型的周期性结构拓扑优化

利用SIMP材料插值模型研究了双方向周期性结构的拓扑优化。为了使结构获得具有双方向周期性的拓扑形式,将优化域分成若干个子域,并构建了一个虚拟子域;将各子域内各单元的相对密度的平均值和应变能的平均值作为虚拟子域内单元的相对密度和应变能,以结构的最小柔度为目标函数,单元相对密度为设计变量,构建了周期性拓扑优化问题的数学模型,并在数学模型中加入额外的约束条件;采用优化准则法推导出虚拟子域设计变量的迭代公式,利用体积约束计算出拉格朗日乘子;通过平面矩形悬臂梁结构算例获得了具有双方向的周期性拓扑形式,验证了利用SIMP材料插值模型实现双方向周期性拓扑优化的可行性和有效性。     

结构优化半解析灵敏度分析的改进算法

提出了结构半解析灵敏度分析的改进算法,该算法实现简便,对于设计变量摄动步长具有极佳的数值稳定特性。首先,从总体角度推导静力问题半解析法灵敏度分析新算法,提出了位移与应力灵敏度列式,并给出了算法实施途径;然后,将此思路推广于自振频率、屈曲临界荷载和瞬态响应等多种问题,提出了相应的计算步骤。以梁单元与壳单元等典型结构为例,开展了多个算例测试。测试表明,改进算法计算精度和效率均有提升,特别是设计变量步长有更大的数值稳定区域,为复杂工程结构形状优化的灵敏度分析提供了新途径。     

基于等效静态载荷法的区间参数结构可靠性拓扑优化

研究了用等效静态载荷法,解决动态响应约束下的区间参数结构可靠性拓扑优化问题。对等效静态载荷赋予了新的含义:由等效静态载荷产生的区间静态响应与由动态载荷产生的区间动态响应,其对应的中值与离差均相等。利用泰勒展开计算出区间参数结构动态响应所有可能值组成的集合,再根据集合映射获得包含结构所有不确定信息的等效静态载荷集合,继而建立静态可靠性拓扑优化数学模型。通过集合映射和区间自然扩展,获得静态位移响应区间。基于区间非概率可靠性指标的定义,给出区间非概率可靠性约束的伴随法灵敏度分析算法。采用移动渐近线法完成此优化问题的求解。数值算例验证了模型的正确性和算法的有效性。     

车桥耦合振动分析的两种常用插值方法比较

利用模态综合法分析车辆与桥梁之间的相互作用时,合理地构造桥梁的插值振型函数可以大幅提高计算精度.其中,分段三次Hermite插值函数和三次样条插值函数较为常用.为研究二者的异同,以简支梁桥为例分别采用这两种插值函数构造结构梁单元模型的一维插值振型函数和板单元模型的二维插值振型函数.基于以上两类插值振型函数,分析单自由度簧上质量匀速过桥时,桥梁的跨中位移、跨中梁底正应力和轮-桥接触力时程响应.结果表明:无论是一维问题还是二维问题,由三次样条插值法构造的插值振型函数与结构的实际振型较为吻合,计算结果具有较高的收敛性和精度.而要达到相同的精度,分段三次Hermite插值法则须加密单元网格,但其误差仅存在于独立网格内,不会累积放大.     

考虑界面力学性能的组件及结构的协同优化

包含多个内嵌功能组件及支撑结构的多组件结构因其轻量化、多功能等优良特性被广泛应用于航空航天等领域.已有的多组件结构拓扑优化研究大多基于理想界面假设,忽略了材料连接界面可能发生的破坏. 本文针对包含多个内嵌式功能性组件的结构,考虑连接界面的力学性能, 对组件的形状、布局及支撑材料的拓扑进行协同优化,以实现多组件结构的优良承载性能. 首先,基于超椭圆模型对内嵌组件的形状及布局进行显式的参数化描述,并构造其水平集函数表达; 进而,结合组件及支撑材料的水平集拓扑描述、内聚力模型及扩展有限元方法(extended finite element method, XFEM), 在固定网格下对随优化迭代不断演化的结构拓扑及连接界面的力学性能进行准确描述;进一步, 建立水平集法框架下考虑界面力学性能的多组件结构拓扑优化列式,基于伴随变量法推导解析的灵敏度并采用梯度优化算法求解优化问题.本文采用该优化框架分别对内嵌组件的悬臂梁和MBB梁进行协同优化, 在优化过程中,发现组件的初始布局对最终设计有很大的影响, 并且可能导致不良结构.为了避免此情况, 本文提出了两个阶段的优化策略,即首先对组件布局和形状进行优化, 再进行结构和内嵌组件的协同优化.数值结果显示, 在优化结果中功能性组件及界面通常分布于结构受压应力作用的区域,且连接界面最优形状呈现为曲率较小的光滑曲线,该设计避免界面发生拉伸及剪切破坏, 有效提高了结构的承载力,同时也表明了本文所提出考虑连接界面力学性能拓扑优化方法的有效性.      

基于多目标优化NSGA2改进算法的结构动力学模型确认

传统结构动力学模型确认方法通常采用单目标优化,存在精度不足和稳定性差等缺点,难以满足实际工程需求。基于此,提出一种采用神经网络作为代理模型,建立以马氏距离和鲁棒性为不确定性量化指标的多目标优化模型,并将NSGA2多目标进化算法用于求解。针对NSGA2存在无法有效识别伪非支配解、计算效率低和解集质量较差等设计缺陷,提出一种基于支配强度的NSGA2改进算法INSGA2-DS。INSGA2-DS将支配强度引入非支配排序,采用新型拥挤距离公式和自适应精英保留策略,以提高收敛效率和解集质量。GARTEUR飞机算例的仿真结果表明,INSGA2-DS求解复杂工程问题时具有更好的收敛性和分布性,而考虑鲁棒性的结构动力学模型确认方法可以获得同时满足多种目标要求的Pareto解集,提高了模型确认的精度和稳定性。     

Boundary conditions at the interface between fluid layer and fibrous medium

The flow through a channel partially filled with fibrous porous medium was analyzed to investigate the interfacial boundary conditions. The fibrous medium was modeled as a periodic array of circular cylinders, in a hexagonal arrangement, using the boundary element method. The area and volume average methods were applied to relate the pore scale to the representative elementary volume scale. The permeability of the modeled fibrous medium was calculated from the Darcy's law with the volume‐averaged Darcy velocity. The slip coefficient, interfacial velocity, effective viscosity and shear jump coefficients at the interface were obtained with the averaged velocities at various permeabilities or Darcy numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Passages to the limit in the dynamic problem for a crack at the interface between elastic media

The paper analyzes numerically the passages to the limit in the dynamic problem for a penny-shaped crack at the interface between dissimilar linear elastic, homogeneous, isotropic materials as either the frequency of harmonic load or the difference between the properties of the materials decreases. It is shown that as the frequency decreases, the solution of the dynamic problem tends to that of the static problem, and as the physical and mechanical properties of the materials become less different, the original problem goes into the dynamic problem for a crack in a homogeneous body __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 7, pp. 26–34, July 2008.     

Model representations of the interaction between the solar wind and the supersonic interstellar medium flow. prediction and interpretation of experimental data

The planning and conducting of physical experiments requires the development of theoretical models capable either of predicting possible experimental data or explaining those already obtained. The processes taking place in the physical world can be understood only in terms of the close interaction between theory and experiment. Developing any quantitative or qualitative model of a physical phenomenon requires a mathematical apparatus, on the basis of which such models can be constructed. The branch of theoretical science using the methods of magnetohydrodynamics and hydroaeromechanics for studying space physics problems is usually called cosmic gasdynamics; it is mostly used in developing models of physical phenomena occurring under space conditions. In order to emphasize the importance of cosmic gasdynamics in the development of astrophysics and space research, we will present several examples of models constructed by aerodynamicists. These models not only played an important role in qualitative predictions but are still being developed due to the need for the quantitative interpretation of the experimental data. The solar corona was long thought to be a formation in a state of gravitational equilibrium (Chapman model). However, it turned out that the pressure at infinity obtained on the basis of this equilibrium solution is considerably greater than the estimated pressure in the interstellar gas surrounding the solar corona. In [1] it was concluded that in this case the solar corona gas must expand and a solution describing this expansion was obtained by invoking the steady-state hydrodynamics equations in the spherically-symmetric approximation. The solution of these equations led to the theoretical prediction of the solar wind, a radial flow of fully ionized hydrogen plasma issuing from the solar corona at a low subsonic velocity but already hypersonic at the Earth’s orbit. Subsonic-to-supersonic transition is ensured by solar gravitation which in this case plays the role of a convergent-divergent nozzle. Within a year, the theoretical prediction of the solar wind [1] was confirmed by its experimental detection [2] onboard the Soviet spacecraft Luna-2. It turned out that at the Earth’s orbit the mean velocity of the solar wind V _E ≈ 450 km·s^?1, the mean proton temperature T _E ≈ 6 · 10⁴ K (the electron temperature is somewhat higher), and the mean concentration of protons (and electrons) n _E ≈ 10 cm^?3. The first hydrodynamic model of the supersonic solar-wind flow past the Earth’s magnetosphere [3] was only qualitative, since it considered a flow past a plane magnetic dipole in the approximation of a thin layer between the bow shock and an “obstacle” embedded in the flow. However, it was constructed before the actual discovery of the solar wind and provided further important impetus to the development of models of the supersonic solar wind flow past planets with a detached shock. One more example is furnished by the gasdynamicmodel of the solar wind flow past cometary atmospheres, first suggested in In this work, a model of the interaction between the supersonic solar wind and the supersonic flow of the local, i.e., surrounding the Sun, interstellar medium is considered; it was first suggested in [6] in a much simplified formulation. This model has been actively developed in connection with the flights of the spacecraft Voyager 1 and 2, Ulysses, Hubble Space Telescope, SOHO, and others, exploring the outer regions of the solar system.     

Analytical investigation of the fluid flow in the interface region between a porous medium and a clear fluid in channels partially filled with a porous medium

In this paper analytical solutions for the steady fully developed laminar fluid flow in the parallel-plate and cylindrical channels partially filled with a porous medium and partially with a clear fluid are presented. The Brinkman-extended Darcy equation is utilized to model the flow in a porous region. The solutions account for the boundary effects and for the stress jump boundary condition at the interface recently suggested by Ochoa-Tapia and Whitaker. The dependence of the velocity on the Darcy number and on the adjustable coefficient in the stress jump boundary condition is investigated. It is shown that accounting for a jump in the shear stress at the interface essentially influences velocity profiles.     

简支梁大挠度弹性后屈曲载荷与变形的优化算法

针对简支梁结构大挠度后屈曲载荷与变形的计算问题,本文提出了一种直接求解其后屈曲载荷和变形的优化算法。在简支梁处于大挠度屈曲平衡状态下,将梁结构划分为有限子段,以待求后屈曲载荷为设计变量,根据起点的边界条件和每个子段满足的弯矩变形公式,累积计算出其他各个节点的坐标,以得到的终点坐标满足的边界条件构建目标函数模型。在此基础上,通过MATLAB编制优化程序分析了两个典型算例,并将理论结果与相关软件的计算结果进行对比,从而证明了本文算法的正确性。本文算法求解过程简单、快速,具有一定的实用性,为变截面结构大挠度弹性屈曲稳定性问题的研究提供了参考。     

固体炸药爆轰与惰性介质相互作用的一种扩散界面模型

提出一种保持热力学一致性的扩散界面模型,用来数值模拟固体炸药爆轰与惰性介质的相互作用问题。基于混合网格内各组分物质间可以达到力学平衡状态而不能达到热学平衡状态的假设,由混合网格能量守恒以及压力相等条件,推导出每种组分物质的体积分数演化方程。由此获得的扩散界面模型包括组分物质的质量守恒方程、混合物质的动量及总能量守恒方程,同时包括组分物质的体积分数演化方程和混合物质的压力演化方程。该扩散界面模型的主要特点是考虑了化学反应以及热学非平衡的影响。提出的扩散界面模型在物质界面附近不会出现物理量的非物理振荡现象、适用于任意表达形式的物质状态方程以及任意数目的惰性介质。

     

On the transformation toughening of a crack along an interface between a shape memory alloy and an isotropic medium

In this study, a bilinear cohesive zone model is employed to describe the transformation toughening behavior of a slowly propagating crack along an interface between a shape memory alloy and a linear elastic or elasto-plastic isotropic material. Small scale transformation zones and plane strain conditions are assumed. The crack growth is numerically simulated within a finite element scheme and its transformation toughening is obtained by means of resistance curves. It is found that the choice of the cohesive strength t₀ and the stress intensity factor phase angle φ greatly influence the toughening behavior of the bimaterial. The presented methodology is generalized for the case of an interface crack between a fiber reinforced shape memory alloy composite and a linear elastic, isotropic material. The effect of the cohesive strength t₀, as well as the fiber volume fraction are examined.     

基于77GHz毫米波雷达接收天线的周期性条形阵列解耦结构优化方法

阵列天线是77 GHz毫米波雷达的核心硬件之一,其天线性能决定着雷达的探测能力。由于工作频率的升高以及毫米波雷达小型化、集成化的发展趋势,使得雷达阵列天线阵元间距过密,从而相互干扰出现强互耦效应,严重恶化雷达阵列天线的性能。为了解决上述问题,本文提出了一种基于77 GHz毫米波雷达接收天线的周期性条形阵列解耦结构优化方法。该方法通过优化周期性条形阵列解耦结构单元的条形厚度和间距,在保证阵列天线辐射性能的基础上,来抑制毫米波雷达接收天线阵元间的互耦并提高其阵元间的隔离度。仿真结果表明,相比于无解耦结构的阵列天线,提出的解耦结构能够有效地降低毫米波雷达接收天线间的耦合,尤其在中心频率77.75 GHz处互耦减少了13.29 dB。在施加周期性条形阵列解耦结构前后,阵列天线均在77.5 GHz～78.5 GHz指定频段内正常工作,且合成辐射方向图的最大增益几乎保持不变,从而保证了毫米波雷达阵列天线的辐射性能。典型的数值算例能够很好地验证所提方法的有效性。     

基于单元相交的混合网格精确守恒插值方法

基于网格切割思想,发展了二维/三维混合网格条件下的单元相交算法,可精确计算任意两个多边形/多面体的交集。在此基础上,实现了基于单元相交(CIB/DC)的精确守恒插值算法。二维和三维验证算例表明,该方法能够保证插值过程中计算域内物理量的严格守恒,且具有比常规二阶插值更高的精度。