基于静力响应面的结构有限元模型修正方法

提出了基于静力响应面的结构有限元模型修正方法.运用响应面方法,将结构静力响应和结构参数之间复杂的隐式关系用显式函数近似表达出来;在此响应面模型(函数)基础上,通过优化计算对结构有限元模型参数进行修正.阐述了基于静力响应面的结构有限元模型修正方法的基本理论和一般实现过程.对两跨连续梁结构的静力模型修正数值算例分析结果表明:基于静力响应面的有限元模型修正方法可以减少结构有限元计算的次数、提高模型修正的优化效率,结构有限元模型修正结果具有可接受的精度.     

基于振动响应的耦合弦系统损伤检测

为解决具有相近频率和相重频率特征的多跨耦合弦系统的损伤检测问题,建立了耦合弦系统在外激励作用下的有限元运动方程.利用直接积分法计算了系统强迫振动响应,将弦的局部损伤模拟为单元面积的减少,推导了振动响应对弦单元面积的灵敏度,并利用此响应灵敏度进行弦的局部损伤识别.数值算例表明:此方法能快速准确地识别出耦合弦的局部损伤,并且对模拟的人工噪声不敏感.     

结构损伤的非概率区间识别方法

基于结构时域加速度响应,利用区间分析方法对具有外界激励和测量数据不确定性的结构系统进行损伤识别.不确定性量被处理为有界区间数,基于参考有限元模型和被测加速度响应,经过提出的两步模型参数的区间修正方法分别得到了未损伤和损伤结构区间模型,进而通过定义的PoDE(Possibility of Damage Existence)确定了结构各单元的损伤可能性.最后以十杆平面桁架系统为例,对区间方法与概率方法的损伤识别结果进行对比,讨论了损伤程度和不确定度对识别结果的影响,结果表明了本文方法的可行性与有效性.     

基于Kriging模型的频响函数有限元模型修正方法

针对使用频响函数进行有限元模型修正的问题,提出了一种基于Kriging模型的修正方法,用于检测结构由损伤引起的在单元刚度特性上的衰减。本文方法可以在不需要推导修正参数与频响函数残差代数关系的前提下,通过少量测点提供的有效数据快速求解;还可以通过控制算法的终止准则来提高对未知区域的探索程度,降低结果收敛到局部解上的可能。使用Kriging模型可以有效地减少原有限元模型的计算次数,保证计算效率的同时,为对结构进行更准确精密的有限元建模提供了便利。     

A COMPLEX PARAMETER MODEL UPDATING METHOD FOR DAMPING CHARACTERISTICS OF FINITE ELEMENT MODELS

阻尼对于结构动力学响应具有重要的影响,但有限元模型一般很难对阻尼特性进行精确建模.基于实测频响函数,研究了一种有限元模型阻尼特性的复参数修正方法.以待修正区域各单元质量、刚度矩阵的比例修正系数为复修正参数,建立了单元矩阵比例修正的灵敏度方程直接算法,并对比分析了复修正参数与不同阻尼特性之间的数学关系.以六自由度集中参数模型和25杆平面桁架模型为例,验证了复参数修正方法在阻尼特性修正中的有效性.     

适用于几何非线性气动弹性分析的结构动力学降阶模型方法研究

几何非线性是壁板颤振和大展弦比机翼气动弹性等问题的一个主要特征,在进行数值仿真分析时往往需要采用商业非线性有限元求解器,存在计算量大和耦合迭代策略不易控制等问题。本文发展了一种适用于几何非线性的结构动力学降阶模型(CSD-ROM),利用广义坐标的非线性多项式表征非线性内力,采用参数识别方法获取多项式系数,并通过增加额外的线性模态来改善模型预测精度。基于此方法,分别针对壁板颤振、切尖三角翼的CFD/CSD-ROM非线性颤振问题开展了时域响应分析。计算结果表明,通过CSD-ROM计算出的壁板颤振速度为590 m/s,颤振频率为174 Hz,与有限元结果误差分别为0.8%和1.7%。马赫数0.879时切尖三角翼的颤振动压预测结果为2.25 psi,与非线性有限元相比的误差为3.8%。本文采用的非线性和线性模态基底组合方法,在保证计算精度的基础上可有效降低训练样本数量,一定程度上可替代非线性有限元开展气动弹性分析。     

Damage detection using a new regularization method with variable parameter

In this research, a sensitivity approach to finite element model updating is used to determine stiffness reduction factors from measured structural response. The used method causes a set of nonlinear ill-conditioned equations that need to be linearized and regularized in order to find the solution. A new approach to solve the problem is presented using variable regularization parameter. Utilization of variable regularization parameter eliminates dependency on the number of iterations and prevents the loss of regularization effect due to iterations. A new stopping criteria is used which is based on the difference between mean and variance of last iterations. Furthermore the results show that using wavelet transform to update the model yields better results than modal parameters. Expedient performance of the proposed method is shown through a numerical simulation.     

Identification of the plastic behavior of aluminum plates under free air explosions using inverse methods and full-field measurements

This article describes an inverse method for the identification of the plastic behavior of aluminum plates subjected to sudden blast loads. The method uses full-field optical measurements taken during the first milliseconds of a free air explosion and the finite element method for the numerical prediction of the blast response. The identification is based on a damped least-squares solution according to the Levenberg–Marquardt formulation. Three different rate-dependent plasticity models are examined. First, a combined model based on linear strain hardening and the strain rate term of the Cowper–Symonds model, secondly, the Johnson–Cook model and finally, a combined model based on a bi-exponential relation for the strain hardening term and the strain rate term of the Cowper–Symonds model. A validation of the method and its sensitivity to measurement uncertainties is first provided according to virtual measurements generated with the finite element method. Next, the plastic behavior of aluminum is identified using measurements from real free air explosions obtained from a controlled detonation of C4. The results show that inverse methods can be successfully applied for the identification of the plastic behavior of metals subjected to blast waves. In addition, the material parameters identified with inverse methods enable the numerical prediction of the material’s response with increased accuracy.     

Parameters identification of cable stayed footbridges using Bayesian inference

Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy).

     

Fluid–structure interaction modelling of nonlinear aeroelastic structures using the finite element corotational theory

The application of the finite element corotational theory to model geometric nonlinear structures within a fluid–structure interaction procedure is proposed. A dynamic corotational approximately-energy-conserving algorithm is used to solve the nonlinear structural response and it is shown that this algorithm's application with a four-node flat finite element is more stable than the nonlinear implicit Newmark method. This structural dynamic algorithm is coupled with the unsteady vortex-ring method using a staggered technique. These procedures were used to obtain aeroelastic results of a nonlinear plate-type wing subjected to low speed airflow. It is shown that stable and accurate numerical solutions are obtained using the proposed fluid–structure interaction algorithm. Furthermore, it is illustrated that geometric nonlinearities lead to limit cycle oscillations.     

摄动有限元法在结构动力模型修改中的应用

本文将摄动理论与有限元法相结合,提出了用于小变参数结构分析的摄动有限元法(P-FEM),导出了在结构参数发生小变化的情况下,结构摄动单元矩阵的一般公式及结构的动特性随结构参数变化的二阶渐近展开式,并将这一结果运用于结构的动力模型修改中,提出了一种新的适合于工程应用的结构动力模型修改方法,把这一方法应用于实际的复杂结构动力模型修改中,获得了十分满意的结果.     

一种结构参数识别的两阶段方法

针对测量信息不完备的剪切型结构 ,建立了一种两阶段系统识别的复合反演方法 ,这种方法包括两部分 :子结构地震动反演和结构参数识别。首先 ,选取可观测的子结构 ,利用一维地震动作用于结构的力学特性 ,将子结构动力方程的有限元列式进行变换 ,得到适合于最小二乘法的简单形式 ,解决了测量信息不完备及结构参数未知条件下的地震动反演问题。其次 ,根据子结构反演得到的地震动输入 ,采用结构参数时域识别技术中的加权整体迭代 -广义卡尔曼滤波器方法 ,成功地识别出了有限测量条件下单元水平结构参数     

Restoring force and dynamic loadings identification for a nonlinear chain-like structure with partially unknown excitations

Most of the currently employed vibration-based identification approaches for structural damage detection are based on eigenvalues and/or eigenvectors extracted from dynamic response measurements, and strictly speaking, are only suitable for linear system. However, the inception and growth of damage in engineering structures under severe dynamic loadings are typical nonlinear procedures. Consequently, it is crucial to develop general structural restoring force and excitation identification approaches for nonlinear dynamic systems because the restoring force rather than equivalent stiffness can act as a direct indicator of the extent of the nonlinearity and be used to quantitatively evaluate the absorbed energy during vibration, and the dynamic loading is an important factor for structural remaining life forecast. In this study, based on the instantaneous state vectors and partially unknown excitation, a power series polynomial model (PSPM) was utilized to model the nonlinear restoring force (NRF) of a chain-like nonlinear multi-degree-of-freedom (MDOF) structure. To improve the efficiency and accuracy of the proposed approach, an iterative approach, namely weighted adaptive iterative least-squares estimation with incomplete measured excitations (WAILSE-IME), where a weight coefficient and a learning coefficient were involved, was proposed to identify the restoring force of the structure as well as the unknown dynamic loadings simultaneously. The response measurements of the structure, i.e., the acceleration, velocity, and displacement, and partially known excitations were utilized for identification. The feasibility and robustness of the proposed approach was verified by numerical simulation with a 4 degree-of-freedom (DOF) numerical model incorporating a nonlinear structural member, and by experimental measurements with a four-story frame model equipped with two magneto-rheological (MR) dampers mimicking nonlinear behavior. The results show the proposed approach by combining the PSPM and WAILSE-IME algorithm is capable of effectively representing and identifying the NRF of the chain-like MDOF nonlinear system with partially unknown external excitations, and provide a potential way for damage prognosis and condition evaluation of engineering structures under dynamic loadings which should be regarded as a nonlinear system.     

Monitoring structural damage of components using an effective modulus approach

This paper describes a novel nondestructive damage detection method that was developed to study the influence of a crack on the dynamic properties of a cantilever beam subjected to bending. Experimental measurements of transfer functions for the cracked cantilever beam revealed a change in the natural frequency with increasing crack length. A finite element model of a cracked element was created to compute the influence of severity and location of damage on the structural stiffness. The proposed model is based on the response of the cracked beam element under a static load. The change in beam deflection as a result of the crack is used to calculate the reduction in the global component stiffness. The reduction of the beam stiffness is then used to determine its dynamic response employing a modal analysis computational model. Euler–Bernoulli and Timoshenko beam theories are used to quantify the elastic stiffness matrix of a finite element. The transfer functions from both theories compare well with the experimental results. The experimental and computational natural frequencies decreased with increasing crack length. Furthermore the Euler–Bernoulli and Timoshenko beam theories resulted in approximately the same decrease in the natural frequency with increasing crack length as experimentally measured.     

Quantification of phase shift in the simulation of shallow water waves

Numerical simulation of nonlinear waves to reproduce the laboratory measurements has been a topic of great interest in the recent past. The results reported in the literature are mainly focused on qualitative comparison or on the relative errors between the numerical simulation and measurements in laboratory and hence lack in revealing the existence of phase shift in nonlinear wave simulation. In this paper, the simulation of nonlinear waves in mixed Eulerian and Lagrangian framework using finite element method (FEM) is investigated by applying two different velocity calculation methods viz, cubic spline and least squares (LS). The simulated wave surface elevation has been compared with the experimental measurements. The coherence analysis has been carried out using the wavelet transformation, which gives a better understanding between the numerical and the experimental results with respect to the time–frequency space, compared with the conventional Fourier transformation. It is observed that the application of cubic spline approach leads to a higher phase difference for steeper waves. The present study has shown that the phase difference exists at the higher modes rather than at the primary period. For waves with steepness (wave height/wave length) higher than 0.04, LS approach is found to be effective in capturing the higher‐order frequency components in the event of nonlinearity. In addition, the comparison of numerical simulations with that from PIV measurements for the tests with solitary waves is also reported. Copyright © 2009 John Wiley & Sons, Ltd.     

动力模型修正中逆特征值问题的数值解法

本文提出了一种参数型动力模型修正的方法．因为这种方法与经典的逆特征值问题的提法是一致的，所以先建立起与逆问题等价的关于设计参数的非线性方程组，然后构造出可以用Ｎｅｗｔｏｗ法求解的格式．数值仿真结果表明本文方法具有较好的收敛性和较高的计算精度．     

基于径向基函数的频响函数模型修正

针对使用频响函数进行有限元模型修正存在的时间成本和精度问题,结合模态参与变异系数法和模态动能法分别优化激励点和测点,使获得的模态信息更完整;然后,引入径向基函数(RBF)模型减少原有限元模型计算次数,并根据均方根误差准则对所构建代理模型的参数(spread)进行优选,提高模型预测精度;最后,选用一个36自由度的二维桁架模型进行可行性验证,对比有限元法、Kriging模型及二阶响应面模型的修正精度和迭代时间,结果表明,本文方法具有较好的优势。     

框架结构缺损识别的交错迭代法

对具有局部缺损刚度框架结构识别的逆分析问题进行了研究,在采用有限元最小二乘法的基础上,提出了非线性最小化过程的交错迭代方法。算例及分析表明,本文方法是一种精度高、收敛迅速、应用方便的逆分析方法。     

Research on the iterative method for model updating based on the frequency response function

Model reduction technique is usually employed in model updating process.In this paper,a new model updating method named as cross-model cross-frequency response function(CMCF) method is proposed and a new iterative method associating the model updating method with the model reduction technique is investigated.The new model updating method utilizes the frequency response function to avoid the modal analysis process and it does not need to pair or scale the measured and the analytical frequency response function,which could greatly increase the number of the equations and the updating parameters.Based on the traditional iterative method,a correction term related to the errors resulting from the replacement of the reduction matrix of the experimental model with that of the finite element model is added in the new iterative method.Comparisons between the traditional iterative method and the proposed iterative method are shown by model updating examples of solar panels,and both of these two iterative methods combine the CMCF method and the succession-level approximate reduction technique.Results show the effectiveness of the CMCF method and the proposed iterative method.     

基于能量辨识的非线性静电-结构系统的自由度缩减建模方法

给出了一种基于系统能量函数辨识的静电致动微薄板系统自由度缩减建模方法.从Von Karman应变-位移关系式出发,推导出以广义模态坐标为变量的系统动能、应变能以及电容函数的函数表达式.为了将应变能以及电容函数写成广义模态坐标的多变量多项式形式,利用一系列经静态非线性结构有限元计算的结果,拟合得到多变量多项式的未知系数.由Lagrangian方程获得原系统的自由度缩减模型.利用该模型对器件的静/动态特性进行仿真,其计算费用很低.与有限元结果比较,验证了建模方法的正确性.