A HYBRID GRANULARITY PARALLEL ALGORITHM FOR PRECISE INTEGRATION OF STRUCTURAL DYNAMIC RESPONSES

Precise integration methods to solve structural dynamic responses and the corresponding time integration formula are composed of two parts： the multiplication of an exponential matrix with a vector and the integration term. The second term can be solved by the series solution. Two hybrid granularity parallel algorithms are designed, that is, the exponential matrix and the first term are computed by the fine-grained parallel algorithra and the second term is computed by the coarse-grained parallel algorithm. Numerical examples show that these two hybrid granularity parallel algorithms obtain higher speedup and parallel efficiency than two existing parallel algorithms.

ANALYSIS OF THE LARGE DEFLECTION DYNAMIC RESPONSE OF RIGID-PLASTIC CIRCULAR PLATE RESTING ON FLUID

A study is presented for the large deflection dynamic response of rigid- plastic circular plate resting on potential fluid under a rectangular pressure pulse load. By virtue of Hankel integral transform technique,this interaction problem is reduced to a problem of dynamic plastic response of the plate in vacuum.The closed-form solutions are derived for both middle and high pressure loads by solving the equations of motion with the large deflection in the range where both bending moments and membrane forces are important.Some numerical results are given.

A COMBINED PARAMETRIC QUADRATIC PROGRAMMING AND PRECISE INTEGRATION METHOD BASED DYNAMIC ANALYSIS OF ELASTIC-PLASTIC HARDENING/SOFTENING PROBLEMS

The objective of the paper is to develop a new algorithm for numerical solution of dynamic elastic-plastic strain hardening/softening problems. The gradient dependent model is adopted in the numerical model to overcome the result mesh-sensitivity problem in the dynamic strain softening or strain localization analysis. The equations for the dynamic elastic-plastic problems are derived in terms of the parametric variational principle, which is valid for associated, non-associated and strain softening plastic constitutive models in the finite element analysis. The precise integration method, which has been widely used for discretization in time domain of the linear problems, is introduced for the solution of dynamic nonlinear equations. The new algorithm proposed is based on the combination of the parametric quadratic programming method and the precise integration method and has all the advantages in both of the algorithms. Results of numerical examples demonstrate not only the validity, but also the advantages of the algorithm proposed for the numerical solution of nonlinear dynamic problems.

Dynamic response of cylindrical cavity to anti-plane impact load by using analytical approach

The transient response of an unlimited cylindrical cavity buried in the infinite elastic soil subjected to an anti-plane impact load along the cavern axis direction was studied.Using Laplace transform combining with contour integral of the Laplace inverse transform specifically,the general analytical expressions of the soil displacement and stress are obtained in the time domain,respectively.And the numerical solutions of the problem computed by analytical expressions are presented.In the time domain,the dynamic responses of the infinite elastic soil are analyzed,and the calculation results are compared with those from numerical inversion proposed by Durbin and the static results.One observes good agreement between analytical and numerical inversion results,lending the further support to the method presented.Finally,some valuable shear wave propagation laws are gained: the displacement of the soil remains zero before the wave arrival,and after the shear wave arrival,the stress and the displacement at this point increase abruptly,then reduce and tend to the static value gradually at last.The wave attenuates along the radial,therefore the farther the wave is from the source,the smaller the stress and the displacement are,and the stress and the displacement are just functions of the radial distance from the axis.

An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom （SDOF） system, and then is generalized for a multiple-degree of freedom （MDOF） system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.

基于Duhamel积分的车桥耦合动力分析方法

为了缩短求解车桥耦合系统动力响应的计算时间,利用振型分解法对车桥耦合系统的桥梁子系统和车辆子系统解耦,假定在每一时间步长内车桥相互作用力线性变化,借助Duhamel积分解析解,通过迭代得到系统的动力响应,提出了一种新型的车桥耦合动力分析方法.以一节四轴客车匀速通过32 m简支梁为例进行了实验研究,结果表明：本文方法得到的车桥耦合系统的动力响应结果与Newmark-β方法的结果接近,各极值点相对误差均不超过1%;在保证相同的计算精度前提下,本文方法将积分步长提高至原来的5~10倍,提高了求解速度.

关于Duhamel积分的进一步讨论

本文对求解线性振动系统任意激励响应的Duhamel积分法作进一步讨论。基于将任意外激励分解成无穷多个脉冲激励的基本思想,以串行累计与并行叠加两种方式对各脉冲激励的作用过程作进一步地分析和阐释,给出了各自的理论依据,揭示出Duhamel积分的并行叠加计算本质。另外,基于微积分运算给出了Duhamel积分的严格数学验证,加深了对Duhamel积分的理论认知。

Duhamel积分的高精度递推格式

本文以二次式来逼近每个时间步中的激励变化,给出了计算Duhamel积分的递推公式。用线性插值时,就是熟知的Nigam—Jennings算法。分析了算法的传递函数误差,并计算了几个数值例子,从而阐明本文推荐的二次插值算法优于Nigam—Jennings算法。

DYNAMIC ANALYSIS TO INFINITE BEAM UNDER A MOVING LINE LOAD WITH UNIFORM VELOCITY

Based on the principle of linear superposition, this paper proves generalized Duhamel's integral which reserves moving dynamical load problem to fixed dynamical load problem. Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam. The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem. Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed. Additionally, the authors also present definition of moving dynamic coefficient which reflects moving effect.

PATH INTEGRAL SOLUTION OF NONLINEAR DYNAMIC BEHAVIOR OF STRUCTURE UNDER WIND EXCITATION

A numerical scheme for the nonlinear behavior of structure under wind excitation is investigated. With the white noise filter of turbulent-wind fluctuations, the nonlinear motion equation of structures subjected to wind load was modeled as the Ito＇ s stochastic differential equation. The state vector associated with such a model is a diffusion process. A continuous linearization strategy in the time-domain was adopted. Based on the solution series of its stochastic linearization equations, the formal probabilistic density of the structure response was developed by the path integral technique. It is shown by the numerical example of a guyed mast that compared with the frequency-domain method and the time-domain nonlinear analysis, the proposed approach is highlighted by high accuracy and effectiveness. The influence of the structure non-linearity on the dynamic reliability assessment is also analyzed in the example.

Experimental study of suppressing the unbalanced response vibration of rotor system with a G-type integral squeeze film damper

Conventional squeeze film dampers have numerous challenges including lock up,bistable response and incoordinate precession.In order to resolve these nonlinear problems,a novel G-type integral squeeze film damper(GISFD)is proposed in this research.The experimental test rig is provided to investigate the rotor system with an unbalanced single disk.Numerical simulation results show that the structural design of GISFD is reasonable,which can ensure its safe and stable operation.The influence of different support stiffnesses on the first-order speed of the rotor system is analyzed.Experimental results show that GISFD can effectively suppress the unbalanced response vibration of the rotor.In a certain range,it is found that the suppression effect of GISFD increases with the increase in the kinematic viscosity of the damping fluid.When the silicone oil with kinematic viscosity coefficients v=30.0 cm^(2)/s is employed,the vibration reduction of GISFD is approximately 71.51%.Furthermore,the experimental results show that with the increase of the unbalance,there is a linear relationship between the unbalance and the corresponding amplitude of the unbalanced response.It is concluded that GISFD has excellent linear damping characteristics and reduces the sensitivity of the rotor system to the unbalanced mass.

Dynamics of mechanical system for electromechanical integrated toroidal drive under electric disturbance

Based on electromagnetics and mechanics, electromechanical coupled dynamic equations for the drive were developed. Using method of perturbation, free vibrations of the mechanical system under electric disturbance were investigated. The forced responses of the mechanical system to mechanical excitation under electric disturbance were also presented. It is known that for the system with electric disturbance, as time grows, beat occurs. When electric disturbing frequency is near to the natural frequencies of the mechanical system or their integer multiple, resonance vibrations occur. The forced responses of the mechanical system to mechanical excitation under electric disturbance are compound vibrations decided by mechanical excitation, electric disturbance and parameters of the system. The coupled resonance vibration caused by electric disturbance and mechanical excitation was discussed as well. The conditions under which above coupled resonance occurs were presented. The results show that when the difference of the excitation frequency and the perturbation frequency is equal to some order of natural frequency, coupled resonance vibrations occur.

Lamb's integral formulas of two-phase saturated medium for soil dynamic with drainage

When dynamic force is applied to a saturated porous soil, drainage is common. In this paper, the saturated porous soil with a two-phase saturated medium is simulated, and Lamb＇s integral formulas with drainage and stress formulas for a two-phase saturated medium are given based on Biot＇s equation and Betti＇s theorem （the reciprocal theorem）. According to the basic solution to Biot＇s equation, Green＇s function Gij and three terms of Green＇s function G4i, Gi4, and G44 of a two-phase saturated medium subject to a concentrated force on a spherical coordinate are presented. The displacement field with drainage, the magnitude of drainage, and the pore pressure of the center explosion source are obtained in computation. The results of the classical Sharpe＇s solutions and the solutions of the two-phase saturated medium that decays to a single-phase medium are compared. Good agreement is observed.

STOCHASTIC OPTIMAL CONTROL FOR THE RESPONSE OF QUASI NON-INTEGRABLE HAMILTONIAN SYSTEMS

A strategy is proposed based on the stochastic averaging method for quasi non- integrable Hamiltonian systems and the stochastic dynamical programming principle.The pro- posed strategy can be used to design nonlinear stochastic optimal control to minimize the response of quasi non-integrable Hamiltonian systems subject to Gaussian white noise excitation.By using the stochastic averaging method for quasi non-integrable Hamiltonian systems the equations of motion of a controlled quasi non-integrable Hamiltonian system is reduced to a one-dimensional av- eraged It stochastic differential equation.By using the stochastic dynamical programming princi- ple the dynamical programming equation for minimizing the response of the system is formulated. The optimal control law is derived from the dynamical programming equation and the bounded control constraints.The response of optimally controlled systems is predicted through solving the FPK equation associated with It stochastic differential equation.An example is worked out in detail to illustrate the application of the control strategy proposed.

STUDY ON DYNAMIC J-INTEGRAL OF MECHANICAL HETEROGENEOUS WELDED JOINT

Welded joint is a mechanical heterogeneous body, and mechanical heterogeneity has great effect on dynamic fracture behaviour of welded joints. In the present investigation, dynamic response curve and dynamic J-integral of practical undermatched welded joint and whole base and whole weld three-point-bend (TPB) models containing longitudinal crack are com- puted. Dynamic J-integral is evaluated using virtual crack extension (VCE) method and the computation is performed using MARC finite element code. Because of the effect of inertia, dynamic load response curve of computed model waves periodically. Dynamic J-integral evaluated by VCE method is path independent. The effect of inertia has little influence on dynamic J-integral curve. The value of dynamic J-integral of undermatched welded joint is lower than that of whole base metal and higher than that of whole weld metal. The results establish the foundation of safety evaluation for dynamic loaded welded structures.

考虑超碳需求响应的综合能源系统低碳优化调度

西北地区新能源发展迅速,充分利用当地独有的光热资源优势,同时结合火电低碳化改造与新能源协同运行,有利于推动当地能源系统绿色低碳转型。为尽最大限度地提升系统的减碳能力,提出一种基于源荷协同降碳的超碳需求响应模型,将动态碳排放因子作为分时电价的惩罚因子,从而将源侧碳信号传递至荷侧,驱使用户侧进行低碳性状态转移。首先,在日前调度阶段,构建预调度-再调度两阶段调度运行机制,再调度根据预调度的系统状态信息进行超碳需求响应,来深度降低系统碳排量。其次,将光热电站引入综合能源系统,与风电场、碳捕集电厂协同运行,从而构建高比例新能源场景,来验证超碳需求响应在此场景下的减碳效益。最后,建立了基于超碳需求响应的预调度-再调度两阶段低碳调度模型。经算例仿真分析表明,所提源荷协同降碳的新思路能有效提高系统的减碳能力,深入挖掘系统的降碳空间,提升系统的经济效益。

静动力边界转换及其合理性验证方法的研究

繁琐复杂的静动力边界转换处理是进行静动力耦合模拟的关键步骤,为了研究黏弹性边界条件下传统静动力边界转换的合理性及其验证方法的适用性,本文首先根据弹性叠加原理提出了一种验证静动力耦合模拟分析中静动力边界转换合理性的方法(参考解法);然后基于有限元软件ABAQUS,并结合自行研发的适用于成层介质的黏弹性边界施加和等效节点力计算程序VBEA2.0,对多土层自由场静动力耦合模型和土-地下结构静动力耦合模型进行了地震反应分析,对参考解法的适用性进行了探究;最后使用本文提出的参考解法,对一种典型的未进行合理静动力边界转换的自由场模型进行了分析,探讨了静动力边界转换产生振荡的原因和机理。研究结果表明:用于验证静动力边界转换合理性的参考解法,既适用于多土层自由场静动力耦合计算模型,又适用于土-结构相互作用的静动力耦合模型;静动力边界转换后产?生的振荡是静动力耦合计算模型静力不平衡所导致,一般是因为未合理施加边界反力或单元应力。

公轨合建盾构隧道振动荷载的动力响应特性

为了探究汽车-列车振动荷载对公轨合建盾构隧道内部结构及周围土体的动力响应特性,采用有限元软件ABAQUS对某公轨合建盾构隧道内部结构及周围土体进行数值模拟,通过ABAQUS软件的Dload子程序对汽车、列车振动荷载进行耦合,分别将单一振动荷载及汽车-列车振动荷载作用引入公轨合建盾构隧道,分析公轨合建盾构隧道内部结构及周围土体在不同工况时加速度、位移、应力、应变的变化。结果表明:汽车、列车振动荷载频率不同,共同作用后产生拍频现象,导致相同方向合成荷载的振幅可能小于分荷载的振幅,当频率相同时所合成荷载的振幅最大;管片上方的土体以及非封闭弧形内衬外侧土体发生较大的应变,最大塑性应变发生于拱顶偏右侧,达到7.032×10^(-6);公轨合建盾构隧道内部结构中的预制箱涵牛腿柱、顶板处出现较大拉、压应变,在长期运营期间需要对预制箱涵牛腿柱、顶板位置进行定期检查和必要支护。

考虑接入电动汽车充电站的虚拟电厂低碳经济调度

风光出力不确定背景下,为解决电动汽车充电站接入虚拟电厂后两者之间的利益协调问题,构建以虚拟电厂运营商为上层,电动汽车充电站为下层的双层规划模型。首先,结合氢能系统以及电热负荷需求响应特性,设计一种源荷协调响应机制,提升系统整体灵活运行的能力。其次,结合虚拟电厂能源-负荷分布情况、碳排放情况以及电动汽车充电站运行计划等因素,制定一种动态定价策略,引导下层电动汽车充电站参与虚拟电厂调度,优先消纳新能源,协调上下层之间的利益关系。此外,引入阶梯型碳交易机制和碳捕集设备,进一步提升系统低碳运行能力。最后,采用CPLEX商用求解器对双层规划模型迭代求解,同时引入联合最优判别机制获取联合最优解,算例结果验证了所提模型及方法在协调不同利益主体的利益关系和降低系统碳排方面的有效性。

考虑源荷互动的综合能源系统多目标双层规划

随着综合能源系统建设的不断推进,传统的“源随荷动”模式转向“源荷互动”已成为发展趋势。为此,提出了一种考虑源荷互动的综合能源系统多目标双层规划方法。首先,引入电–热–冷可中断负荷和可转移负荷参与综合需求响应,并制定了一种基于新能源发电与等效负荷相匹配的动态定价策略。然后,构建了含电动汽车充电站的综合能源系统多目标双层规划与运行模型,在上层规划模型中以经济成本、碳排放量、自主性为目标,在下层模型中以综合能源系统和电动汽车充电站的总运行成本最小为目标。最后,利用非支配排序遗传算法(non-dominated sorting genetic algorithm Ⅱ,NSGA-Ⅱ)算法和商业求解器CPLEX求解获得Pareto前沿解集,并利用Topsis法选择最优解。算例表明,该方法可以有效降低经济性成本、减少碳排放量、提高系统自主性。