基于LiToSim平台的海上风机过渡段优化软件开发

针对海上风机过渡段结构,考虑风机多尺度优化模型和所受环境荷载采取极端情况下,引入双向渐进结构拓扑优化方法,以全局应力最小化为目标、体积为约束,对风机过渡段进行优化设计;并在自主研发的LiToSim平台基础上,嵌入风机优化数值计算程序,最终形成一款关于海上风机过渡段拓扑优化的定制化软件TUR/TOPT.借助定制化软件TUR/TOPT平台,对比过渡段传统柔度优化与应力优化结果,突显出应力优化在减材设计过程中结构应力明显降低且能有效避免应力集中等方面的优势;TUR/TOPT软件的生成在风机建设选型过程中具有重要指导价值.     

基于LiToSim平台的金属围护结构软件研发

直立咬合金属围护结构在风荷载作用下易发生风揭破坏,目前缺少能数值模拟金属围护结构的等效节点模型以及有限元分析软件.该文首先根据围护结构的非线性风致响应提出了直立咬合金属围护结构的弹塑性等效弹簧节点模型,并推导出了弹塑性等效弹簧单元的有限元算法;然后将算法嵌入平台LiToSim中,研发出了金属围护结构的定制化软件LiToSpr;最后建模分析了结构响应,并与抗风揭实验对比,验证了定制化软件LiToSpr的适用性.软件LiToSpr能够模拟直立咬合金属围护结构的非线性风致响应,为工程设计提供一定参考.     

危岩主控结构面疲劳断裂寿命计算方法

危岩的破坏机理和安全性受控于危岩主控结构面．通过计算危岩主控结构面在自重、裂隙水压力及地震力作用下的Ⅰ型及Ⅱ型应力强度因子,建立了主控结构面临界长度计算方法;把主控结构面内的裂隙水压力视作交变荷载,通过计算其对主控结构面应力强度因子的贡献,遵循P-M准则运用Paris疲劳方程建立了处于临界状态条件下主控结构面的疲劳断裂寿命计算方法,并通过疲劳断裂试验确定了三峡库区万州地区典型长石石英砂岩的疲劳系数C值和m值．     

回转窑滚圈多轴疲劳寿命预测及与轴线偏移关系研究

结合轴线偏移情况开展回转窑滚圈多轴疲劳寿命研究,采用了Wang和Brown提出的多轴疲劳准则和雨流计数法及Miner准则进行累积损伤评估．回转窑运行轴线偏移会导致滚圈承受的支承载荷分布严重不均,因此引入载荷比来描述轴线偏移程度以进一步定量分析滚圈应力．采用有限元软件ANSYS进行了各载荷比下滚圈的接触应力分析,并根据滚动接触区域情况计算得到了切向摩擦应力．以某回转窑滚圈为分析对象,计算得到了随载荷比变化的疲劳寿命曲线,揭示了轴线偏移对滚圈疲劳寿命的影响规律．研究对减少滚圈疲劳失效有重要意义,同时也可作为轴线调整和优化调窑的理论依据．     

PCB焊点热循环失效分析和改进设计

针对PCB（印制电路板）焊点在高低温热循环下的失效,建立了传统结构的三维模型和在芯片边角下加锡块的改进设计模型,通过实验测得FR-4的弹性模量和热膨胀系数,用ANSYS计算了PCB在高低温循环下的应力应变,并用修正的Coffin-Manson经验方程计算了焊点的热循环寿命。结果表明,通过在芯片边角下加锡块,PCB焊点的最大等效塑性应变显著降低,其热疲劳寿命得到明显提高.     

梯度折射率介质内瞬态辐射传递的扩散近似法

基于瞬态时域与频域扩散近似方程求解了一维梯度折射率介质内辐射传递问题.通过计算在不同梯度折射率分布下的穿透率与反射率,对扩散近似的适用性展开研究.结果表明:求解时域穿透率时,扩散近似法始终能够准确计算出平行光的时间延迟,而对漫射部分时间延迟的计算不准确;对时域反射率而言,扩散近似法在反射率出现峰值之前与间断有限元法结果相吻合,随着折射率梯度的增大,扩散近似结果在出现峰值后的时间内偏大,且有明显的时移.对于频域穿透率和反射率计算,扩散近似法精度几乎不受折射率梯度变化的影响,能够较为准确地预测频域穿透率,但是对于频域反射率计算误差较大.     

广义疲劳等寿命曲线与二维疲劳极限概率分布

基于传统等寿命曲线,提出了广义疲劳等寿命Sa-Sm曲线概念,并找出该曲线的普遍表达式;根据相关系数优化法建立了该表达式的参数估计公式,并给出了具有可靠度p的广义疲劳等寿命P-Sa-Sm曲线公式;以广义P-Sa-Sm曲线为基础,导出了二维疲劳极限概率分布;进行了3组不同应力均值下的LY11CZ铝合金材料的二维配对升降法试验,试验结果验证了广义疲劳等寿命Sa-Sm曲线的合理性和算法的拟合精度.     

基于对偶二次规划的大型框架结构优化方法

将准则法和数学规划相结合,对于不同的约束采用不同的处理方法:应力约束作为局部性约束,用0阶近似进行处理,借助满应力准则将其转化为动态尺寸下限;位移约束作为全局性约束,根据单位虚载荷法将其显式化,从而建立了满足应力和位移约束的框架结构截面优化的显式模型．为了提高模型的求解效率,根据对偶理论将大规模的框架结构优化问题转化为仅仅几个对偶变量的对偶问题,采用二次规划方法求解,算例证明该方法能极大的提高模型的求解效率．采用近似射线步既能减小计算量又能使迭代过程更加平稳,采用删除无效约束技术能减小优化模型的规模. 以MSC/Nastran软件为结构分析的求解器,以MSC/Patran软件为开发平台,完成了满足刚度和强度的多工况、多变量的框架截面优化软件．算例结果表明上述程序算法的高效性．     

An Asymptotic-Homogenization Explicit Time-Domain Method for Random Multiscale Vibration Analysis of Porous Material Structures北大核心CSCD

由于具有高比强、高比刚度等优点,多孔结构在土木工程、机械工程和航天航空工程等领域得到了广泛应用.在随机动力荷载作用下多孔结构的随机响应分析是值得关注的研究方向之一.采用多尺度渐近均匀化法,推导了周期性多孔结构动力问题的多尺度控制微分方程,并建立了多孔结构宏观和细观动力响应的时域显式表达式.在此基础上,结合结构随机振动时域显式法,实现了非平稳随机激励下多孔结构动力响应统计矩的计算.所提出的渐近均匀化-时域显式法,一方面可以发挥多尺度动力分析渐近均匀化法的计算优势,高效建立多孔结构宏观和细观动力响应的时域显式表达式;另一方面也可以利用随机振动时域显式法的计算特点,快速精确地求解非平稳随机激励下多孔结构的随机振动问题.通过数值算例,验证了所提方法在多孔结构非平稳随机振动问题求解中的计算精度和计算效率.     

描述低周疲劳裂纹扩展速率的循环J积分新参量

探讨了低周疲劳加载条件下的应力增量．应变增量关系，提出了模拟裂纹疲劳扩展的二维模型以建立新的循环．积分参量，详细阐述了该积分参量的定义、主要特点、物理意义以及数值计算方法，并通过紧凑拉伸试样的疲劳试验检验该积分参量的有效性．结果表明：该积分参量能够较好描述恒幅低周疲劳裂纹的扩展速率．此外，基于积分参量体系，从能量的角度解释了疲劳迟滞现象．     

Topology optimization considering the fatigue constraint of variable amplitude load based on the equivalent static load approach

In this research, a new layout optimization method is developed to consider high cycle fatigue constraints which occur due to variable amplitude mechanical loading. Although fatigue is a very important property in terms of safety when designing mechanical components, it has rarely been considered in topology optimization with the lack of concept and the difficulty of sensitivity analysis for fatigue constraints calculated from multiaxial cycle counting. For the topology optimization for fatigue constraint, we use transient stress analysis to extract effective stress cycles and Miner's cumulative damage rule to calculate total damage at every spatial element. Because the calculation of the exact sensitivities of a transient system is complex and time consuming for the topology optimization application, this research proposes to use the pseudo-sensitivities of fatigue constraints calculated by applying equivalent static load approach. In addition, as an aggregated fatigue constraint is very sensitive to the changes in stress value which causes some unstable convergences in optimization process, a new scaling approach of the aggregated fatigue damage constraint is developed. To validate the usefulness of the developed approaches, we solved some benchmark topology optimization problems and found that the present method provides physically appropriate layouts with stable optimization convergence.     

吴消元法在Lagrange和Hamilton方程中的应用

主要借鉴吴消元法,研究带约束动力学中多项式类型Lagrange方程和Hamilton方程,提出了一种求约束的新算法．与以前算法相比,新算法无需求Hessian矩阵的秩,无需判定方程的线性相关性,从而大为减少了计算步骤,且计算更为简单．此外,计算过程中膨胀较小,且多数情形下无膨胀．利用符号计算软件,新算法可在计算机上实现．     

Cycles of two-dimensional systems: Computer calculations,proofs, and experiments

One of the central problems in studying small cycles in the neighborhood of equilibrium involves computation of Lyapunov’s quantities. While Lyapunov’s first and second quantities were computed in the general form in the 1940s–1950s, Lyapunov’s third quantity was calculated only for certain special cases. In the present work, we present general formulas for calculation of Lyapunov’s third quantity. Together with the classical Lyapunov method for calculation of Lyapunov’s quantities, which is based on passing to the polar coordinates, we suggest a method developed for the Euclidian coordinates and for the time domain. The calculation of Lyapunov’s quantities by two different analytic methods involving modern software tools for symbolic computing enables us to justify the formulas obtained for Lyapunov’s third quantity. For quadratic systems in which Lyapunov’s first and second quantities vanish, while the third one does not, large cycles were calculated. In the calculations, the quadratic system was reduced to the Liénard equation, which was used to evaluate the domain of parameters corresponding to the existence of four cycles (three “small” cycles and a “large” one). This domain extends the region of parameters obtained by S.L. Shi in 1980 for a quadratic system with four limit cycles.     

Fatigue crack growth simulations of homogeneous and bi-material interfacial cracks using element free Galerkin method

In this paper, quasi-static fatigue crack growth simulations of homogeneous and bi-material interfacial cracks have been performed using element free Galerkin method (EFGM) under mechanical as well as thermo-elastic load. The thermo-elastic fracture problem is decoupled into thermal and elastic problems. The temperature distribution obtained by solving heat conduction equation is used as input in the elastic problem to get the displacement and stress fields. Discontinuities in the temperature and displacement fields are captured by extrinsic partition of unity enrichment technique. The values of stress intensity factors have been extracted from the EFGM solution by domain based interaction integral approach. The standard Paris fatigue crack growth law has been implemented for the life estimation of various model problems. The results obtained by EFGM under mechanical and thermo-elastic loads were compared with those obtained by FEM using remeshing approach.     

On parallel Branch and Bound frameworks for Global Optimization

Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.     

基于SA-GA混合算法的动车组车辆轮重分配优化

针对动车组车辆出厂前存在的轮重偏差问题,建立动车组车辆轮重调节力学模型,利用模拟退火算法(SA)的机制和遗传算法(GA)非均匀变异思想,提出了一种模拟退火遗传(SA-GA)混合算法,并利用该混合算法对车辆轮重调节力学模型进行数值求解,结果显示:轮重偏差降低到1.2％以下,符合GB/T 3317—2006的规定.同时使用...     

矩形到任意多边形区域的Schwarz-Christoffel变换数值解法

运用Schwarz-Christoffel变换方法，建立多边形区域到带状区域共形映射数学模型.对于模型中的约束条件和奇异积分问题，根据Riemann(黎曼)原理，建立复参数与实参数互逆变换，消除非线性系统的约束条件；经过合理积分路径的确定，模型中的奇异积分转化为Gauss-Jacobi(高斯 雅可比)型积分；采用Levenberg-Marquardt算法对非线性系统模型进行求解.根据第一类椭圆函数性质，建立了矩形区域到带状区域共形映射数学模型，通过复参数椭圆函数的计算，得到矩形边界与带状区域边界的关系.最后，对8点对称多边形区域与27点不规则条带状区域计算，将不规则封闭区域边界映射到矩形区域边界，矩形区域内的正交网格，通过变换之后在多边形区域内依然满足正交性，为研究不规则区域到规则区域映射的数值计算奠定基础.     

Effective Dynamic Material Properties of Foam-like Microstructures

The effective material parameters of a microstructured material can be found using homogenization procedures based on calculations of a Representative Volume Element (RVE) of the material. In our approach the RVE is calculated in frequency domain and inertia is taken into account, leading to a frequency dependent behavior of the RVE.With the frequency response of the RVE, effective dynamic properties of the material are calculated using an optimization procedure. Due to the frequency dependent material behavior on the microscale a viscoelastic constitutive equation is applied on the macroscale. An example calculation is presented for an auxetic 2-D foam-like microstructure which is modelled as a plane frame structure. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An algorithm for calculating the frequency dependence of the complex dielectric permittivity and the complex compliance

Conclusions 1. The algorithm developed for a numerical transform of the kernel in the Boltzmann — Volterra integral equation from the time domain to the frequency domain is suitable for calculating the complex dielectric permittivity from the polarization current or for calculating the complex compliance from the creep kernel.2. The algorithm is applicable to any distribution of relaxation times and has been based on changing the readings of the given function with time according to a geometrical progression. Its use requires that a certain number of coefficients be known and that readings of the given function be taken with the corresponding time coordinates.3. Calculations using expressions where the distribution of readings of the given function is shifted with respect to the time corresponding to the selected frequency makes it possible to extend the frequency range within which the sought function (complex dielectric permittivity or complex compliance) is to be determined.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 524–530, May–June, 1977.