Continuum topology optimization considering uncertainties in load locations based on the cloud model

Few researchers have paid attention to designing structures in consideration of uncertainties in the loading locations, which may significantly influence the structural performance. In this work, cloud models are employed to depict the uncertainties in the loading locations. A robust algorithm is developed in the context of minimizing the expectation of the structural compliance, while conforming to a material volume constraint. To guarantee optimal solutions, sufficient cloud drops are used, which in turn leads to low efficiency. An innovative strategy is then implemented to enormously improve the computational efficiency. A modified soft-kill bi-directional evolutionary structural optimization method using derived sensitivity numbers is used to output the robust novel configurations. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed algorithm.     

弱非线性和不确定性对结构动力学分析的影响

局部连接引起的弱非线性和加工制造公差引起的参数变化不确定性是许多工程结构的常见现象。针对弱非线性和参数变化不确定性对结构动力学分析的影响进行了讨论,提出了一种通过恒位移和恒速度响应的振动试验进行非线性建模,并用统计分析来处理不确定性,建立尽可能精确的数学模型进行结构动力学分析的处理方法。仿真实例是在对美国Sandia国家实验室2006年提出的"结构动力学问题的模型确认挑战"研究的基础上,建立的具有非线性刚度和非线性阻尼以及参数变化不确定性的三自由度集中质量模型,仿真结果验证了方法的有效性。     

Improved dynamic analysis of structures with mechanical uncertainties under deterministic input

This paper addresses the dynamic analysis of linear systems with uncertain parameters subjected to deterministic excitation. The conventional methods dealing with stochastic structures are based on series expansion of stochastic quantities with respect to uncertain parameters, by means of either Taylor expansion, perturbation technique or Neumann expansion and evaluate the first- and second-order moments of the response by solving deterministic equations. Unfortunately, these methods lead to significant error when the coefficients of variation of uncertainties are relatively large. Herein, an improved first-order perturbation approach is proposed, which considers the stochastic quantities as the sum of their mean and deviation. Comparisons with conventional second-order perturbation approach and Monte Carlo simulations illustrate the efficiency of the proposed method. Applications are discussed in order to investigate the influence of mass, damping and stiffness uncertainty on the dynamic response of the system.     

随机荷载下陡波形立管的非线性动力分析EI北大核心CSCD

对陡波形立管在随机荷载作用下的非线性动力响应进行了数值分析。考虑内部流体,基于柔性杆理论建立了陡波形立管(SWR)的数值模型,采用Newmark-β法求解立管动力响应,利用MATLAB软件编写相应计算程序DRSWR,将DRSWR的计算结果与OrcaFlex进行对比验证,然后对陡波形立管在随机波浪、顶部浮体随机运动共同激励下的应力响应进行了参数敏感性分析。结果表明:浮子段应力水平、应力变化幅值最高;应力极值点为拱弯点和垂弯点;大波高、低周期的波浪会导致立管整体应力水平急剧升高;平均静偏移增大导致立管应力极值减小;大幅高频的慢漂运动会使悬挂点应力显著增大;高密度、高流速内部流体会使陡波形立管处于高应力状态。     

Optimum load time history for non-linear analysis using dynamic relaxation

A modification of the dynamic relaxation method is proposed which facilitates static analysis of non-linear problems. Continuous loading in time is adopted instead of the ordinary step function of time. Inertia and damping forces arising during the loading process are kept at a minimum using an optimum load time history. This results from the stationary condition of an appropriate functional. The equation of motion is included as a subsidiary condition. Continuous load—deflection curves can be obtained. An incremental solution is avoided. Application of the method is extremely simple. Existing programs based on explicit time integration schemes can be easily adapted for it. Sample solutions are presented.     

Nonlinear stability analysis of a perforated FGM plate under thermal load

The nonlinear thermal stability analysis of a perforated Ni/Al₂O₃ FGM plate with temperature-dependent thermoelastic material properties is carried out through a finite element approach based on the first-order shear deformation theory and the von-Karman's nonlinear kinematics. The thermoelastic material properties of the FGM plate are varied in the thickness direction, and the Mori-Tanaka homogenization scheme is applied to evaluate these properties. After validating the results of the current formulation, parametric studies are conducted to examine the effects of temperature-dependent material properties, material in-homogeneity, cutout shape and size, edge boundary conditions, aspect and slenderness ratios on the thermal buckling and postbuckling response of perforated FGM plate.     

Dynamic sensitivity analysis of material and load parameters in nonlocal elasticity

Dynamic sensitivity analysis of a general performance functional in nonlocal elasticity is performed with respect to material parameters and loading functions. The adjoint variable method is employed in order to evaluate the first variation of the functional with respect to the decision variables. It is found that, in an iterative solution procedure, while the primary problem is solved forward in time, an adjoint problem must be integrated backwards.     

Parametric uncertainties for dynamic response evaluation of offshore structures

The dynamic characteristics involved in the loading process in the ocean environment are extremely complicated and difficult for exact evaluation. In this paper, parametric studies are presented to assess the influence of uncertainties associated with various assumptions and approximations, involved in modelling the dynamic loading processes of ocean environment, for the evaluation of dynamic response of offshore structures. These uncertainties are represented by the inertia coefficient and the drag coefficient of the Morison equation which defines the wave forcing function, the mean height of the input sea waves and the shear wave velocity of the soil. The results show that the effects of uncertainties are closely related to the natural frequency of the structure and the predominant frequency of the wave force. These uncertainties, except the variation in the shear wave velocity in the soil, contribute significantly to the dynamic response and the first passage probability evaluation of the offshore structure systems.     

The dynamic analysis of a suspended cable due to a moving load

The dynamic behaviour of a saggy suspension cable under a moving load was investigated. First of all, the updated Lagrangian formulation and the finite element method were used to derive the property matrices of a saggy suspension cable in order to define the discretized equations of motion. Then, the Jacobi method was applied to the determination of the natural frequencies and the mode shapes of the suspended cable. The moving-load-induced dynamic responses of the saggy suspended cable were obtained by using the Newmark direct integration method incorporated with the Newton–Raphson iteration technique. The influence of some pertinent factors, such as speed of moving load, ratio of axial rigidity to total cable weight (AE/⁰m?g⁰L) and ratio of moving load mass to total cable mass, is the key point of the dynamic analysis.     

Finite element procedures for the nonlinear dynamic stability analysis of arbitrary shell structures

The objective is the development of numerical algorithms for the dynamic stability analysis of strongly nonlinear shell structures subjected, in particular, to parametric excitations. The finite-element discretization is achieved by displacement models of high accuracy. The basis for the stability analysis is Ljapunow's first approximation equation obtained from a finite-rotation shell theory by a variational method. The operator formulation used for this purpose shows the mathematical requirements imposed on consistent formulations. In close connection with Floquet's theory, a semi-analytical criterion is finally given for the stability analysis of parametric instability phenomena. The numerical results presented demonstrate the efficiency of the numerical algorithms.     

考虑三维圆柱铰间隙碰撞的空间机构柔性多体动力学分析方法

三维圆柱铰的动态性能对空间机构的运动精度和动力学特性有着重要的影响。基于多体动力学方法和刚体有限元方法,提出考虑三维圆柱铰的间隙碰撞和动态接触作用的空间机构柔性多体接触动力学方法。采用圆柱-圆柱的线接触力学模型和切片法,计算圆柱-圆柱的接触变形量和接触力,建立三维圆柱铰的轴销与轴套之间的间隙碰撞作用和三维动态接触关系。以等效刚体单元和Timoshenko梁单元描述柔性杆件的刚性有限元模型,建立柔性连杆和三维圆柱铰的具有多刚体系统的统一形式的动力学方程。计算分析了含三维圆柱铰的空间机构的运动精度和动力学特性,获得空间机构的位移响应,三维圆柱铰的相对运动轨迹和动态作用力等动力学响应。采用三维圆柱-圆柱动态线接触方法,能有效地预测空间机构系统的三维圆柱铰持续接触、间隙碰撞状态和摩擦作用下的动力学特性。计算结果表明三维圆柱铰的间隙碰撞作用对空间机构的运动精度和动态特性的影响较为显著。动力学模型和计算结果对复杂工况下高精度多间隙的空间机构的动态设计和动力学研究具有重要的理论意义。     

Representative static load models for transient stability analysis: development and examination

Load representation has a significant impact on power system analysis and control results. Currently, static load models are still popular in power industry for transient stability analysis. Dynamic load models are recommended in both industry and academia for possible improvement in analysis accuracy. The accuracy of using static (nonlinear) load models with suitably identified parameters for transient stability analysis is examined. Numerical studies conducted using on-line measurement data indicate that static load models, as compared with induction motor load models, are acceptable for modelling real power behaviours during disturbances and hence are adequate for transient stability analysis. Using multiple sets of on-line measurements, representative model parameters of five static nonlinear load models are derived and their performance in modelling dynamic behaviours of both real and reactive powers is compared. A method is presented to determine a representative set of parameters of static (nonlinear) load models for each loading condition     

Numerical solution of the dynamic stability problems

A novel integral equation technique is employed for the analysis of dynamic stability problems. The governing equation of the linearized parametric resonance problem is transformed into an integral equation. The kernel of the integral equation is computed as the influence function for the deflection and/or bending moment of a corresponding beam. The highest derivative of the governing function (in our case fourth derivative of the displacement function) is chosen as the basic unknown. Using the formal analogy with the differential equation of the beam flexure this highest derivative is comprehended as some unknown transverse ‘load’. The distribution of this ‘load’ is a priori assumed to be polygonal. Using elementary methods of structural analysis, the displacements due to the assumed ‘load’ are determined. These displacements, arrayed into a square matrix, approximate the kernel of the governing integral equation. The subsequent procedure via Hill's determinant is a conventional one. The results prove to be accurate enough even for a very modest number of points of integration. This reflects the fact that the method is based on numerical integration rather than on numerical differentiation.     

The stability of the Johnson-Mehl-Avrami equation parameters

The stability of the parameters of the Johnson-Mehl-Avrami equation was studied using two parametrizations of the sigmoidal function and its fit to some kinetic data. The results indicate that one of the forms of the function has more stable parameters and only for this form it is reasonable to use, as an approximation, the linear regression theory to analyse the parameters.     

Composite load models based on field measurements and their applications in dynamic analysis

The composite load model with an induction motor in parallel with a static load has been studied and applied in analysis of dynamics of power systems for a long time. However, the load parameters from field tests are still very limited. Based on the theoretical results of identifiability and estimation methodology of load parameters that have been achieved in the previous work, a project of load modelling based on field measurements is described. Eight sets of equipment for load modelling were installed in HeNan Electric Power Grid (HNEPG) Corporation, and the dynamics of the load were recorded and a dynamic index is proposed to evaluate the dynamic characteristics of the data measured. The load models derived from the field measurements are applied to stability analysis of HNEPG. The critical clearing time and power transfer capability analyses illustrate the enhancement of the stability analysis of the power grid using the load parameters derived from the field measurements and show the benefits of application of such model parameters in power system dynamic analysis.     

Analytical formulation of small signal stability analysis of power systems with nonlinear load models

It is now recognized that both load dynamics and generating unit dynamics contribute significantly to the limitation of loadability of power systems. In this paper, we take a static nonlinear load representation and different combinations of machine and exciter dynamic models to develop a comprehensive linearized model to study small signal stability. In particular we monitor the Hopf bifurcation instability and through participation factor analysis we identify the relevant state variables.     

悬停状态带磁流变减摆器直升机的动稳定性分析

建立了适用于直升机悬停状态动稳定性的磁流变减摆器模型,悬停状态下动力入流模型采用动量理论模型,与直升机旋翼/机体耦合动力学方程组联立,采用Simulink时域仿真的方法计算得到磁流变减摆器对悬停状态下直升机动稳定的影响,对比了不同电压下磁流变减摆器对桨叶挥舞摆振运动的影响.结果表明:对于磁流变减摆器,施加不同电压可得到不同的阻尼力,该性质可以抑制直升机悬停状态动不稳定性.