OPTIMIZATION OF ADAPTIVE DIRECT METHOD FOR APPROXIMATE SOLUTION OF INTEGRAL EQUATIONS OF SEVERAL VARIABLES

This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.

Direct method of finding first integral of two-dimensional autonomous systems in polar coordinates

A direct method to find the first integral for two-dimensional autonomous system in polar coordinates is suggested. It is shown that if the equation of motion expressed by differential 1-forms for a given autonomous Hamiltonian system is multiplied by a set of multiplicative functions, then the general expression of the first integral can be obtained, An example is given to illustrate the application of the results.

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations （SIEs）, the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.

A Straightforward Direct Traction Boundary Integral Method for Two-Dimensional Crack Problems Simulation of Linear Elastic Materials

This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.

The efficiency of direct integration methods in elastic contact-impact problems

A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.

Structural Reliability Analysis Based on Support Vector Machine and Dual Neural Network Direct Integration Method

Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis.

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

Conservation Law Classification and Integrability of Generalized Nonlinear Second-Order Equation

This paper is concerned with the generalized nonlinear second-order equation.By the direct construction method,all of the first-order multipliers of the equation are obtained,and the corresponding complete conservation laws(CLs) of such equations are provided.Furthermore,the integrability of the equation is considered in terms of the conservation laws.In addition,the relationship of multipliers and symmetries of the equations is investigated.

A PREDICT-CORRECT NUMERICAL INTEGRATION SCHEME FOR SOLVING NONLINEAR DYNAMIC EQUATIONS

A new numerical integration scheme incorporating a predict-correct algorithm for solving the nonlinear dynamic systems was proposed in this paper. A nonlinear dynamic system governed by the equation v = F（v, t） was transformed into the form as v = Hv ＋ f（v, t）. The nonlinear part f（v, t） was then expanded by Taylor series and only the first-order term retained in the polynomial. Utilizing the theory of linear differential equation and the precise time-integration method, an exact solution for linearizing equation was obtained. In order to find the solution of the original system, a third-order interpolation polynomial of v was used and an equivalent nonlinear ordinary differential equation was regenerated. With a predicted solution as an initial value and an iteration scheme, a corrected result was achieved. Since the error caused by linearization could be eliminated in the correction process, the accuracy of calculation was improved greatly. Three engineering scenarios were used to assess the accuracy and reliability of the proposed method and the results were satisfactory.

Adaptive Reduced Basis Methods Applied to Structural Dynamic Analysis

The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

A two-step unconditionally stable explicit method with controllable numerical dissipations

A family of unconditionally stable direct integration algorithm with controllable numerical dissipations is proposed. The numerical properties of the new algorithms are controlled by three parameters α, β and γ. By the consistent and stability analysis, the proposed algorithms achieve the second-order accuracy and are unconditionally stable under the condition that α≥-0.5, β≤ 0.5 and γ≥-(1+α)/2. Compared with other unconditionally stable algorithms, such as Chang's algorithms and CR algorithm, the proposed algorithms are found to be superior in terms of the controllable numerical damping ratios. The unconditional stability and numerical damping ratios of the proposed algorithms are examined by three numerical examples. The results demonstrate that the proposed algorithms have a superior performance and can be used expediently in solving linear elastic dynamics problems.

A high order single step-βmethod for nonlinear structural dynamic analysis

A high order single step β algorithm, a new direct integration algorithm is proposed for solution of equations of motion. Whenβ=0.5, the accuracy of displacement, velocity and acceleration is of forth order (a truncation error of Δ t 5), and the algorithm is unconditionally stable and has no arithmetic damping and no overshooting. When >0.5, and an arithmetic damping is adopted, the algorithm is again unconditionally stable with a third order accuracy (a truncation error of Δ t 4). The analyses run with typical examples show that the algorithm proposed has higher speed, higher precision and better properties than other direct integration methods, such as Wilson θ method and Newmark β method in analysing linear elastic responses and nonlinear earthquake responses.

Improving the Angular Resolution of Coded-Mask Telescopes by Direct Demodulation

We develop a new procedure to improve the angular resolution of coded-mask telescopes by the Direct Demodulation Method （DDM）. DDM has been applied to both real and simulated data of INTEGRAL/IBIS. The angular resolution of IBIS/ISGRI has been improved from about 13＇ to 2＇.

近断层脉冲型随机地震动模拟方法及结构动力可靠度研究

以集集脉冲型地震动记录为数据集建立了一种改进的参数化近断层脉冲型随机地震动模型.首先,采用MP03模型和人工蜂群算法从实际地震动记录提取低频脉冲部分,建立随机低频脉冲模型;采用谱表示-随机函数法生成高频部分,二者叠加生成近断层脉冲型随机地震动.然后,采用蒙特卡罗模拟(MCS)法和直接概率积分法(DPIM)分别研究非线性单自由度体系和高层框架结构在不同类型地震动作用下的动力可靠度.结果表明:DPIM与MCS法计算结果相比基本吻合,但计算效率得到较大提升,可以很好地用于非线性结构的时变可靠度研究;脉冲型地震动与非脉冲型地震动相比能够对结构造成更大的变形,极大降低了结构的可靠度,且近断层距越小影响越显著,低频脉冲是使结构可靠度降低的主要因素,而高频部分对结构可靠度的影响较小.

考虑混凝土耐久性-地震随机性的高桩码头时变可靠度研究

为了研究高桩码头长期使用情况下,其结构性能出现的退化现象,利用时间相关的钢筋混凝土性能退化模型,综合考虑混凝土耐久性与地震随机性之间的相关性,结合直接概率积分(DPIM)方法对高桩码头进行随机动力分析和时变可靠度分析,获得不同运行年限下高桩码头在地震激励下的响应概率信息以及时变可靠度曲线。结果显示:随着运行年限的增加,码头上部结构的水平位移概率密度曲线(PDF)、累积分布曲线(CDF)峰值有所下降,动力可靠度随使用年限大幅下降,反映结构体系的性能退化逐渐加快,体现出钢筋混凝土退化对高桩码头地震安全性的显著影响。

考虑高阶振型效应的大跨度钢桁拱桥瑞利阻尼参数取值研究

为了解高阶振型效应对大跨度钢桁拱桥地震反应的影响机制,以及在采用直接积分法时构建合适的瑞利阻尼矩阵,以某490 m跨径钢桁拱桥为背景,采用SAP 2000软件建立全桥弹性动力计算模型。针对主拱圈上(下)弦杆轴力、弯矩,研究振型参与质量最大的7阶(第1、4、8、11、13、23、49阶)振型反应与总反应的占比关系,并对构建瑞利阻尼矩阵的特征频率选取方法展开研究。结果表明:主拱圈上、下弦杆拱脚区域的轴力主要由1阶振型(第1阶)控制,由拱脚向拱顶过渡,逐渐转变为由2~4阶振型控制,高阶振型效应显著;同一阶振型对主拱圈上、下弦杆轴力贡献率及分布规律的影响不同;对于复杂钢桁拱桥,采用振动方向上振型参与质量较大的2阶振型特征频率构建瑞利阻尼矩阵可能因高估了高阶振型阻尼比,导致除拱脚区域以外的拱圈弦杆杆件轴力计算结果偏小,结构偏于不安全;采用直接积分法对复杂钢桁拱桥进行地震反应分析时,建议选取多阶控制振型构建相应的瑞利阻尼工况,并对其计算结果取包络用于抗震设计。

高精度管道漏风量测试仪的设计及实验研究

现有的国产漏风量测试仪普遍存在测量精度低、自动化水平低的问题,为此,基于漏风量测试仪的原理,开展了漏风量测试仪的结构设计、系统设计及整机实验研究。首先,对漏风量的测量过程、喷嘴流量测量原理进行了研究,推导了喷嘴流量测量公式,并根据相关标准设计了角接取压方式的喷嘴结构,基于仪器操作便捷性要求,对整机结构进行了设计;其次,采用空气密度补偿公式完成了高精度流量自适应测量,设计了基于自锁式电磁阀的换向调零电路,采用换向调零法对压差传感器零点漂移进行了补偿,使用小波阈值去噪算法消除了信号噪声,提高了流量的测量精度;采用抗积分饱和比例积分微分(PID)算法对流量进行了闭环控制;最后,研制了管道漏风量测试仪样机,开展了压差与流量测量精度与重复性实验。实验及研究结果表明:该高精度漏风量测试仪工作状态稳定,压差测量精度为±0.4%,流量测量精度为±2%;该漏风量测试仪的测量精度优于国内同类仪器,符合国家标准要求,具有良好的市场前景。

考虑碳-绿证耦合机制的电-气-热综合能源系统分布式鲁棒低碳经济调度

为了保护综合能源系统中不同运营主体的信息隐私,权衡系统运行低碳性和经济性,解决天然气网络鲁棒模型难以求解的问题,提出了考虑碳-绿证耦合机制的电-气-热综合能源系统分布式鲁棒低碳经济调度方法。考虑天然气网络和热力网络的动态特性、碳-绿证耦合机制,构建综合能源系统动态低碳经济调度模型;为了保护各网络运营商的数据隐私,根据能量耦合关系对综合能源系统解耦,建立电-气-热网络的分布式协同优化模型;在此基础上,考虑风电出力和多能负荷的不确定性,提出基于一致性交替方向乘子法的分布式鲁棒优化框架,并利用二阶锥对偶理论与交替优化方法实现含二阶锥约束和二元变量的鲁棒子问题求解。以修改的IEEE 39节点电力网络、比利时20节点天然气网络和15节点热力网络为算例进行仿真分析,验证所提方法能够在源荷不确定性条件下实现综合能源系统各网络分散自治运行,同时兼顾系统运行的低碳性和经济性。

基于同步ADMM算法含P2G-CCS的多园区综合能源系统优化调度

多园区综合能源微电网系统交互需要解决每个微电网之间的协调优化调度的问题,文中通过引入交互耦合功率变量解耦的方法,来求解园区内微电网之间交互的电功率,将集中求解的复杂问题转换为各微电网之间相互合作而且可以内部管理的优化问题,于是文中考虑采用同步式交替向乘子法(alternating direction method of multipliers,ADMM)分布式求解方法来实现各个园区微电网系统的成本关系分配,系统只需要求解分布式优化方案所需的信息,可以最大限度地降低运行成本,同时为了保证多园区微电网系统的低碳运行和降低环境成本,在考虑单个电热冷综合能源微电网系统的基础上,采用碳捕集设备和电转气装置以及配合阶梯碳交易机制的方法,更进一步降低系统碳排放;最后,通过仿真算例来验证所提方法和模型的有效性。