具有动应力和动位移约束的离散变量结构形状优化设计方法

讨论了动应力、动位移约束下离散变量状优化设计问题。首先用拟静力算法,将结构惯性力极值作为静载荷施加到结构上,求得结构的动位移和动内力,然后将考虑动应力约束和动作移约束的离散变量结构优化设计问题化为静应力和静位移约束的优化问题。在求解过程中,将单元内力作了一阶近似,并将多约束问题转化为单约束问题,然后利用两类变量统一考虑的离散变量结构形状优化设计的综合算法进行求解。     

有限长轴承非稳态油膜力自由-移动边界问题的有限条解法

讨论了不可压缩流体润滑的动载径向滑动轴承油膜压力分布的自由移动边界问题的有限条解法．将自由边界问题转化为全域(矩形域)的具有不等式约束的微分方程的边值问题，进一步化为具有不等式约束的泛函极值问题。借助有限条法在矩形域上离散这个泛函，得到了一个特殊的二次泛函的规化问题。通过变量平移变换，使其化为标准的二次规划问题。然后借助于牛顿非光滑算法，迭代求解非线性的互补方程。给出了有限长轴承真实的油膜应力分布。对于所求解方程的系数矩阵的高度稀疏性。给出了紧缩存储算法。节省了存储空间和减少了计算量。算例表明该方法是有效的。     

基于能量极值原理的单晶体塑性滑移的有限变形分析

对FCC单晶体的率无关弹塑性力学响应的本构关系进行了数值模拟。用一个基于能量极值原理的数值计算方法来处理复杂的多面塑性问题，这种算法可以有效地模拟单晶体多滑移系的启动，在这一理论框架下，增量的应力应变关系可以从所构造的能量函数中推导出来。对于滑移系激活情况的判定则可转化为求解活动约束的非线性数学规划问题，通过对时间的离散，此问题又可细化为逐步二次规划问题，并采用有效集法来搜索启动滑移系，进而求得弹塑性本构关系，数值结果表明该方法具有稳定、收敛、可行的特点，在数值计算的基础上研究了单轴拉伸下晶体的不同取向对单晶体硬化程度和滑移系激活情况的影响。     

组合截面工程结构离散变量优化设计的通用模型及启发式算法

建立了组合截面离散变量优化设计的通用模型;提出了一种启发式求解算法。通过对截面设计变量的合并,把截面整体作为一个设计变量;将约束条件按其作用范围分为三类:局部约束、全局约束、中间约束,即介于局部和全局约束之间的约束;根据离散结构实体杆件在结构中受力和传力的特点,将杆件分为5类。针对三类约束的不同特点,分别给出了启发式求解算法。最后通过一个三维的空间结构实例给出验证,优化效率高,效果明显。六个工程实例的优化结果比经验设计可节省材料5.0～19.0%。实践表明本文提出的模型通用性强,启发式求解方法效率高且实用,适合大规模离散变量工程结构最轻设计问题。     

飞机壁板结构的动特性分析与计算

本文以“修正的变分方法”为基础推导了一种新的飞机壁板结构动力分析方法.该法不需要将结构理想化或离散化而直接对复杂的飞机壁板结构进行特征分析或响应分析,方法的实质是将一个复杂结构划分为一个参考结构和一些附加结构,而把这些附加结构视为作用在该参考结构上的广义力,这些广义力由系统能量的变分求得.同时,本文还将有限条法与各向异性壳法相结合,发展了新的有限条分析方法.文中通过固有频率的计算,对这种方法的计算精度和应用场合等问题进行了讨论.     

一种新的实时相关极值匹配算法设计与仿真

对传统相关极值匹配算法局限性进行了分析,并利用二维高斯样条函数张量积方法对局部重力异常离散格网基准图进行逼近以获取该局部基准图的连续解析表达式,在此基础上对相关极值匹配算法进行重新建模并采用拟牛顿BFGS非线性寻优方法对该模型进行解算。考虑到相关极值算法存在实时性差的缺点,采用固定初始序列长度的方式对初始序列采样结构进行改善,推导出了刚性变换中心从序列质心到原点的转换公式,最终完成能够实现单点迭代的基于局部重力异常基准图实时相关极值匹配算法设计,该匹配算法突破了传统离散匹配算法受限于基准图分辨率的局限。最后在2′×2′卫星测高反演重力异常数据基础上进行了两组仿真实验进行对比分析,实验结果表明,在重力测量噪声和初始定位误差较大的情况下,通过该匹配算法获得的匹配定位仍能以较高的精度实时跟踪真实航迹。     

含非理想约束多柔体系统递推建模方法

基于多体系统中邻接物体运动学递推关系,可以证明树状多体系统中末端物体的作用体现为传递给其内接物体的惯性和外力. 由于闭环系统切断铰约束反力和非理想约束反力可看作为系统外力,任何复杂系统都可以转化为等效的树系统,并且系统约束方程中所涉及的广义加速度可以系统化地用描述约束反力的拉氏乘子替换. 基于以上结果,提出了针对含非理想约束多柔体系统递推建模方法. 利用该方法可以将复杂多体系统动态减缩为单个物体,从而在求解系统加速度时不需对整个系统的质量矩阵进行求逆运算,同时大幅度地降低了非理想约束反力方程的维数. 通过一个算例具体说明了所提方法的求解过程,算例结果与现有商业软件所得结果一致.      

基于局部连续场的重力匹配辅助导航

重力匹配辅助惯性导航是一种在惯性导航系统定位信息基础上利用地球重力场特征获取载体位置信息的组合导航技术。一般匹配辅助导航方法都是建立在格网化离散场的基础上,考虑到用局部连续场逼近离散散场的可行性,提出了利用连续场实现相关极值匹配算法,建立了基于局部连续场的相关极值匹配算法模型,采用随机初值迭代方式改进拟牛顿方法以实现在置信范围内全局寻优。最后在三组不同仿真条件下对该算法进行了仿真实验。从实验结果可以看出,在观测误差、初始定位误差较大的情况下,通过该算法获得的匹配航迹仍能以较高的精度跟踪真实航迹,从而验证了算法的有效性。     

能量释放率G的两种解法的统一

在线弹性断裂力学中,从能量的观点考察裂纹的扩展过程是研究破坏机理的一条有效途径.如果裂纹扩展过程中系统所释放出的能量,足以提供裂纹扩展所需要的能量,则裂纹便发生扩展.能量释放率G 就是描述裂纹扩展物体能量变化的一个参数,它是线弹性断裂力学中一个很重要的概念.在一些文献和断裂...     

非高斯风压的极值计算方法

以经典极值理论为基础,发展了一种基于单个标准样本的非高斯风压的极值计算方法. 首先介绍了风洞试验及试验数据处理的基本概况;然后在阐述经典Gumbel极值理论的基础上,根据观察极值的相互独立性推导了短时距下极值分布参数和长时距下极值分布参数的关系式,给出了一种由短时距样本推算长时距下的极值估算方法; 最后基于风洞试验数据,将常用极值估算方法(峰值因子法、改进峰值因子法和Sadek-Simiu法)和该方法的计算结果进行了比较. 得到如下结论:将一个标准长度的非高斯风压时程数据划分成若干等长的子段,可以通过子段的极值分布规律准确地估算出母段的极值期望值,子段的最佳分段长度可以通过自相关分析给出;与常用的极值估算方法相比,该方法更能准确估计非高斯风压的极值.      

The combined energy variational principles in linear elasticity

In this paper, a new kind of mixed energy variational principles in linear elasticity—the combined energy variational principles is presented. First, we define the conjugate body of an elastic body, which is obtained by changing the boundary conditions of the elastic body. Next, we decompose the conjugate body into two component-states, construct functionals of potential energy and complementary energy, respectively, for the component-states and define the additional hybrid energy between the component-states. Thus the functionals of combined energy can be constructed. Three typical combined energy variational principles are demonstrated and the other forms of combined energy variational principles are given. The application of the proposed principles to the calculation of thin plates with complicated boundaries is shown.     

Some energetic properties of smooth solutions in rate-type viscoelasticity

A free energy function compatible with the second law of thermodynamics is constructed for the semilinear rate-type viscoelasticity. Under physically acceptable conditions this energy function is a positive and convex function of stress and strain.

It is shown that for a class of one dimensional initial-boundary value problems, the total energy at any time is bounded by the sum of the total energy of the initial data and the energy supplied to the body by nonvanishing body forces. A Maxwell type viscosity approach to non-linear elasticity for an isolated body is also discussed.

The stability in total energy and uniqueness of the smooth solutions of some initial-boundary value problems is discussed for the one dimensional case as well as for the three dimensional case of small deformations.     

流致振动能量收集的钝头体几何设计研究

流致振动蕴含着可观的能量, 通过能量收集技术可将其转化为电能. 为提高低速流场中能量转化效率, 本文实验研究了不同截面下钝头体以及它们的宽厚比(W/T)对流致振动能量收集特性的影响, 并通过计算流体动力学(computational fluid dynamic, CFD)仿真分析了尾流特性. 流致振动能量收集装置由压电悬臂梁和不同截面的钝头体构成. 首先搭建了流致振动能量收集风洞实验平台, 钝头体的截面分别设置为矩形、三角形和D形, 宽厚比分别设定为1, 1.3, 1.8和2.5. 然后利用实验方法分析不同形状钝头体的宽厚比(W/T)对位移响应和电压响应的影响规律. 最后通过计算流体动力学模拟揭示实验结果的内在力学机理. 实验结果表明, 当钝头体截面为矩形时, 增大宽厚比可以显著提高电压输出峰值; 当钝头体为三角形和D形时, 增加宽厚比将使系统呈现“驰振”→“驰振 + 涡激振动”→“涡激振动”响应特性变化趋势, 提高了低风速时的能量收集效果. CFD结果解释了实验现象, 即随着宽厚比增加, 钝头体尾流会产生更加强劲的涡街, 显著提高流致振动能量收集效果. 相关结果可优化流致振动能量收集装置结构, 为提高低速流场的能量收集效果提供理论和实验依据.      

Experimental investigations on the effect of energy deposition in hypersonic blunt body flow field

We describe here an experimental study on the effect of energy deposition in the flow field of a 120° blunt cone, carried out in a hypersonic shock tunnel. The energy deposition is realised using an electric arc discharge generated between two electrodes placed in the free stream, and various parameters influencing the effectiveness of this technique is studied. The experimental observations suggest that the location of energy deposition has a vital role in dictating the flow structure, with no noticeable effects being produced on the flow field when the discharge was located close to the body (0.416 times body diameter). In addition, the nature of the test gas and the free stream density are also identified as important parameters. In these experiments, a maximum drag reduction of ~50% and ~84% reduction in stagnation point heating rate has been observed as a result of energy addition. The experimental evidence also indicates that the relaxation of the internal degrees of freedom plays a major role in the alteration of the hypersonic blunt body flow structure and that under the specific conditions encountered in our experiments, the energy deposition is not strong enough to create a shock on its own, but the heated region behind the energy source interacts with the blunt body shock resulting in the flow field alteration.      

在质量块冲击作用下刚架大挠度响应的实验研究

本文报道刚架跨中受到以不同速度运动的质量块冲击时动态大挠度响应的实验研究工作,实验测取了冲击点位移、速度随时间变化的曲线及某些关键点的动态应变历史,由此描述了在响应过程中,质量块与刚架间动量动能的传递过程,找出了塑性区域形成和扩展的规律。研究表明:初始撞击接近于理想非弹性,动态荷载不宜简化为瞬时冲量,此时初始冲击动能与刚架所能吸收的最大弹性能之比即便很大,响应中弹性成分仍占有很大的比例,能量比率作为判断是否宜于采用刚塑性解答的条件已不再充分;刚架在初始撞击中吸收的能量和冲量与初始动能和动量之比,仅与刚架承受初始撞击的相当质量和冲击物质量之比有关,而与冲击速度无关,文中给出了二者的关系式。     

The variational principles of coupled systems in photoelasticity

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Features of Movement of a Rotational Body

Vertical motion of a rotational body in an air environment as a mechanical model of a rotochute is considered. It is assumed that, in the process of motion, the symmetry axis of the rotational body remains vertical and the rotational body itself rotates relative to this axis. The aerodynamic impact model is based on a quasistatic approach. Steady regimes of motion are identified, their stability is analyzed, and certain features of transition regimes are explored, including those related to the exchange between the energy of rotational motion and the energy of translational motion.     

Thermodynamic potential of free energy for thermo-elastic-plastic body

The procedure of derivation of thermodynamic potential of free energy (Helmholtz free energy) for a thermo-elastic-plastic body is presented. This procedure concerns a special thermodynamic model of a thermo-elastic-plastic body with isotropic hardening characteristics. The classical thermodynamics of irreversible processes for material characterized by macroscopic internal parameters is used in the derivation. Thermodynamic potential of free energy may be used for practical determination of the level of stored energy accumulated in material during plastic processing applied, e.g., for industry components and other machinery parts received by plastic deformation processing. In this paper the stored energy for the simple stretching of austenitic steel will be presented.     

On Sanders' energy-release rate integral and conservation laws in finite elastostatics

Sanders showed in 1960, within the framework of two-dimensional elasticity, that in any body a certain integral I around a closed curve containing a crack is path-independent. I is equal to the rate of release of potential energy of the body with respect to crack length. Here we first derive, in a simple way, Sanders' integral I for a loaded elastic body undergoing finite deformations and containing an arbitrary void. The strain energy density need not be homogeneous nor isotropic and there may be body forces. In the absence of body forces, for flat continua, and for special forms of the strain energy density, it is shown that I reduces to the well-known vector and scalar path-independent integrals often denoted by J, L, and M.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.