Comparative study of granular solid-structure interaction in a uni-axial compression system

Interaction between granular solids and confining structures is an elementary problem encountered in subsurface structural design and bulk solids storing and handling. A classic scenario is uni-axial compression of granular solids in a deformable cylindrical container. Despite being apparently simple in loading condition, the understanding of this scenario remains limited, mainly due to complex interactive deformation between the two components via frictional interfaces. This paper comparatively examines such a uni-axial compression particulate system by a laboratory experiment and two different numerical approaches, namely, continuum finite element method (FEM) and linked discrete-finite element method (linked DEM-FEM). In the continuum FEM approach, two intendedly chosen simple material models, linear elastic and porous elastic models, are attempted. The comparative study reveals that the majority of resultant characteristics show satisfactory agreement amongst the numerical predictions and the experimental measurements. The simple elastic continuum FEM models can hence be a useful alternative in modelling such problems with mild structural flexibility under a monotonic loading scenario. However, precise prediction of some characteristics, such as lateral pressure ratio, may demand more elaborated material model or parameter selection. The enhancements needed for each numerical approach in order to achieve an improved result are further discussed.     

Self‐regularized pseudo time‐marching schemes for structural system identification with static measurements

We explore the application of pseudo time marching schemes, involving either deterministic integration or stochastic filtering, to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response. Solutions of such non‐linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping, an important, yet inadequately understood, aspect in dynamic system identification problems. The usual method of least‐square solution is through a regularized Gauss–Newton method (GNM) whose results are known to be sensitively dependent on the regularization parameter and data noise intensity. Finite time, recursive integration of the pseudo‐dynamical GNM (PD‐GNM) update equation addresses the major numerical difficulty associated with the near‐zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration. Therefore, we also propose a pseudo‐dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo‐dynamic ensemble Kalman filter (PD‐EnKF). For multiple sets of measurements involving various load cases, we expedite the speed of the PD‐EnKF by proposing an inner iteration within every time step. Results using the pseudo‐dynamic strategy obtained through PD‐EnKF and recursive integration are compared with those from the conventional GNM, which prove that the PD‐EnKF is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small. Copyright © 2009 John Wiley & Sons, Ltd.     

Detection of stiffness degradation in laminated composite plates by filtered noisy impact testing

The purpose of this paper is to detect damage (stiffness degradation) of laminated composite plates from noisy impact response data. The combined finite element method (FEM) with five degrees of freedom (DOF) and the advanced noise filtering algorithm described in this paper may allow us not only to detect the deteriorated elements but also to find their locations and the extents. A first order shear deformation theory (FSDT) is used to predict the structural behavior and to detect damage of laminated composite plates. The filtering procedure is designed by means of a wavelet decomposition together with a selection of the measuring points, and the optimization criterion is constructed on an estimate of the probability of detection using genetic algorithms. All these techniques are applied for the first time to composites. The effects of filtered noise associated with the uncertainty of measurements due to the complex nature of composites are considered for different layup sequences, number of layers, and length–thickness ratios. Several numerical results show that the noise filtering system is computationally efficient in identifying stiffness degradation for complex structures such as laminated composites.     

A scaled unscented transformation based directed Gaussian sum filter for nonlinear dynamic system identification

Impoverishment of particles, i.e. the discretely simulated sample paths of the process dynamics, poses a major obstacle in employing the particle filters for large dimensional nonlinear system identification. A known route of alleviating this impoverishment, i.e. of using an exponentially increasing ensemble size vis-à-vis the system dimension, remains computationally infeasible in most cases of practical importance. In this work, we explore the possibility of unscented transformation on Gaussian random variables, as incorporated within a scaled Gaussian sum stochastic filter, as a means of applying the nonlinear stochastic filtering theory to higher dimensional structural system identification problems. As an additional strategy to reconcile the evolving process dynamics with the observation history, the proposed filtering scheme also modifies the process model via the incorporation of gain-weighted innovation terms. The reported numerical work on the identification of structural dynamic models of dimension up to 100 is indicative of the potential of the proposed filter in realizing the stated aim of successfully treating relatively larger dimensional filtering problems.     

A uniform multiscale method for 2D static and dynamic analyses of heterogeneous materials

A uniform extended multiscale finite element method is developed for solving the static and dynamic problems of heterogeneous materials in elasticity. To describe the complex deformation, a multinode two‐dimensional coarse element is proposed, and a new approach is elaborated to construct the displacement base functions of the coarse element. In addition, to improve the computational accuracy, the mode base functions are introduced to consider the effect of the inertial forces of the structure for dynamic problems. Furthermore, the orthogonality between the displacement and mode base functions is proved theoretically, which indicates that the proposed multiscale method can be used for the static and dynamic analyses uniformly. Numerical experiments show that the mode base functions almost do not work for the static problems, while they can improve the computational accuracy of the dynamic problems significantly. On the other hand, it is also found that the number of the macro nodes of the multinode coarse element has a great influence on the accuracy of the numerical results for both the static and dynamic analyses. Numerical examples also indicate that the uniform extended multiscale finite element method can obtain sufficiently accurate results with less computational cost compared with the standard FEM. Copyright © 2012 John Wiley & Sons, Ltd.     

Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity

A methodology for analyzing the large static deformations of geometrically nonlinear structural systems in the presence of both system parameters uncertainties and model uncertainties is presented. It is carried out in the context of the identification of stochastic nonlinear reduced-order computational models using simulated experiments. This methodology requires the knowledge of a reference calculation issued from the mean nonlinear computational model in order to determine the POD basis (Proper Orthogonal Decomposition) used for the mean nonlinear reduced-order computational model. The construction of such mean reduced-order nonlinear computational model is explicitly carried out in the context of three-dimensional solid finite elements. It allows the stochastic nonlinear reduced-order computational model to be constructed in any general case with the nonparametric probabilistic approach. A numerical example is then presented for a curved beam in which the various steps are presented in details.     

Damage model and implementation in nonlinear dynamic problems

Microcracking, damage and subsequent softening in materials introduce higher levels of nonlinearity than those for materials characterized by nonlinear elastic or classical plasticity models. Hènce, implementation of such advanced models that allow for the foregoing effects require special considerations in terms of the analysis of the characteristics of the model, convergence during plastic deformations, and time integration schemes that consider the nonlinearity.This paper describes a damage model, a special scheme involving drift correction and the generalized time finite element (GTFEM) scheme for time integration for dynamic analysis. The main objective is to examine the model and develop schemes that can lead to consistent and reliable predictions from computational procedures. Toward this aim, (1) the damage model is analyzed with respect to its convergence behavior with mesh refinement, (2) a special drift correct scheme is implemented for the plasticity based model, (3) the generalized time finite element method (GTFEM) is implemented in the nonlinear dynamic finite element procedure for time integration and compared with the Newmark method, and (4) the damage model, the drift correction scheme and the GTFEM are verified by solution of representative static and dynamic problems involving a material (concrete) that experiences damage and softening, including verification with respect to behavior of concrete in the laboratory.     

Reliability models for existing structures based on dynamic state estimation and data based asymptotic extreme value analysis

The problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations is considered. The study assumes that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. In all these studies, the governing stochastic differential equations are discretized using the strong forms of Ito–Taylor’s discretization schemes. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low-dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on a limited amount of pertinent Monte Carlo simulations.     

Generalized Wishart distribution for probabilistic structural dynamics

An accurate and efficient uncertainty quantification of the dynamic response of complex structural systems is crucial for their design and analysis. Among the many approaches proposed, the random matrix approach has received significant attention over the past decade. In this paper two new random matrix models, namely (1) generalized scalar Wishart distribution and (2) generalized diagonal Wishart distribution have been proposed. The central aims behind the proposition of the new models are to (1) improve the accuracy of the statistical predictions, (2) simplify the analytical formulations and (3) improve computational efficiency. Identification of the parameters of the newly proposed random matrix models has been discussed. Closed-form expressions have been derived using rigorous analytical approaches. It is considered that the dynamical system is proportionally damped and the mass and stiffness properties of the system are random. The newly proposed approaches are compared with the existing Wishart random matrix model using numerical case studies. Results from the random matrix approaches have been validated using an experiment on a vibrating plate with randomly attached spring-mass oscillators. One hundred nominally identical samples have been created and separately tested within a laboratory framework. Relative merits and demerits of different random matrix formulations are discussed and based on the numerical and experimental studies the recommendation for the best model has been given. A simple step-by-step method for implementing the new computational approach in conjunction with general purpose finite element software has been outlined.     

Application of finite element method and SPICE simulation fordesign optimization of oven-controlled crystal oscillators

Thermal finite element method (FEM) calculations and SPICE-based dynamic thermal models are used to simulate and optimize the static and dynamic performance of miniaturized oven-controlled crystal oscillators (OCXOs). FEM can be used to generate the values of the SPICE circuit elements. Good agreement is achieved between simulation and measurement. Several application examples, including directly heated OCXOs, are discussed     

Bonded particle modeling of grain size effect on tensile and compressive strengths of rock under static and dynamic loading

The effect of grain (particle) size on the strength is an interesting subject in the rock engineering. Some investigations about the impact of particle size on static strength of rock have been conducted and reported in the literature. However, this issue has not received enough attention when high loading rates are involved. In this work, by utilizing the CA3 bonded particle - finite element computer program, the combined influence of loading rate and particle size on the compressive and tensile strengths of rock is examined. The bonded particle model is used to simulate the crack initiation and failure of the rock specimen and the finite element is utilized to model the elastic bars in the Split Hopkinson Pressure Bar (SHPB) apparatus employed for the dynamic testing. Specimens with four different particle sizes were prepared. The results suggest that the particle size does not affect the rock strength under static and dynamic loading. However, the particle size modifies the nominal tensile strength of the notched Brazilian specimens. For the intact Brazilian specimens under high stress rates, the particle size contributes to the tensile strength and this contribution can be justified based on the principles of fracture mechanics. The theoretical reason for these observations is derived for a 3D bonded particle system and discussed.     

Coupling finite element and reliability analysis through proper generalized decomposition model reduction

The FEM is the main tool used for structural analysis. When the design of the mechanical system involves uncertain parameters, a coupling of the FEM with reliability analysis algorithms allows to compute the failure probability of the system. However, this coupling leads to successive finite element analysis of parametric models involving high computational effort. Over the past years, model reduction techniques have been developed in order to reduce the computational requirements in the numerical simulation of complex models. The objective of this work is to propose an efficient methodology to compute the failure probability for a multi‐material elastic structure, where the Young moduli are considered as uncertain variables. A proper generalized decomposition algorithm is developed to compute the solution of parametric multi‐material model. This parametrized solution is used in conjunction with a first‐order reliability method to compute the failure probability of the structure. Applications to multilayered structures in two‐dimensional plane elasticity are presented.Copyright © 2013 John Wiley & Sons, Ltd.     

粒子滤波和独立分量分析的含噪信号盲分离算法研究

研究了两阶段含噪独立分量分析算法来解决含噪信号盲分离问题。第一阶段,通过粒子滤波实现对不含噪混合信号的估计,将含噪独立分量分析转化为不含噪的独立分量分析;第二阶段用现有的FastICA算法从估计的不含噪混合信号中提取出源信号。不含噪混合信号的时变自回归模型和含噪与不含噪混合信号之间的关系构造了动态的状态．空间方程。该方程的特点是多变量、过程和观测噪声不限于高斯分布,粒子滤波是解决该问题的有效方法。提出了解决含噪独立分量分析的PF＋FastICA算法,仿真试验表明所提出的算法性能优于相关文献的结果。     

Parameters identification of excitation system models using genetic algorithms

A methodology is presented to identify parameters of non-linear models of excitation systems (ESs). Based on the use of genetic algorithms (GAs), the proposed methodology carries out simultaneous parameter identification of linear and non-linear model components. The computational algorithm allows to adequately identify model parameters and it is not affected by the noise present in the measurements. The application of this methodology was developed to identify and validate ES models of different technologies that are used in stability studies through dynamic simulations. First, model parameters of DC1A and ST1A type ES were determined in a simulation environment. The performance of two identifiers based on a GA paradigm is analysed: GA with arithmetic and intermediate recombination operators (GA-BASE) and GA based on differential evolution (GA-DE) mutation. Then the GA-DE identifier is applied to estimate parameters of a static ES (EXE) model of a Brazilian hydro power plant utilising measurements corrupted by noise and registered during field tests. The results obtained are satisfactory and the responses of the identified models are close to real system measurements.     

一类周期结构的部分组集有限元法及静动力分析

本文分析了周期结构经有限元离散所形成系数矩阵的元素分布，提出部分组集的有限元法；随后将块ＳＯＲ、块共轭梯度等方法用于求解相应的线性代数方程组，并以此改造求解大型特征值问题的Ｌａｎｃｚｏｓ算法。这些工作使得在一类周期结构静动力分析中能够避免对大规模代数方程组的直接计算。算例表明这些工作大大降低了所需内外存空间     

The scaled boundary finite element method in structural dynamics

The scaled boundary finite element method is extended to solve problems of structural dynamics. The dynamic stiffness matrix of a bounded (finite) domain is obtained as a continued fraction solution for the scaled boundary finite element equation. The inertial effect at high frequencies is modeled by high‐order terms of the continued fraction without introducing an internal mesh. By using this solution and introducing auxiliary variables, the equation of motion of the bounded domain is expressed in high‐order static stiffness and mass matrices. Standard procedures in structural dynamics can be applied to perform modal analyses and transient response analyses directly in the time domain. Numerical examples for modal and direct time‐domain analyses are presented. Rapid convergence is observed as the order of continued fraction increases. A guideline for selecting the order of continued fraction is proposed and validated. High computational efficiency is demonstrated for problems with stress singularity. Copyright © 2008 John Wiley & Sons, Ltd.     

基于信息熵与谱有限元法的传感器优化布置

为从测量数据中获得尽可能多信息,减少待识别模型参数的不确定性,提出面向结构模型参数识别的传感器优化布置方法。为避免用静态形函数传统有限元方法建模对结构动力特性及传感器优化布置影响,采用高精确动力学法即谱有限元法对结构进行动力学建模。以结构模型参数识别结果的不确定性最小作为传感器优化布置准则,该不确定性程度通过信息熵标量指标量化,用贝叶斯统计系统识别法进行识别。采用整数编码遗传算法在所有可能的传感器配置组合中极小化信息熵指标,获得给定数目的传感器最优布置位置。通过弹性地基带弹性接头的周期管梁模型数值仿真及模型试验验证所提方法。     

Genetic particle swarm parallel algorithm analysis of optimization arrangement on mistuned blades

This article introduces a method of mistuned parameter identification which consists of static frequency testing of blades, dichotomy and finite element analysis. A lumped parameter model of an engine bladed-disc system is then set up. A bladed arrangement optimization method, namely the genetic particle swarm optimization algorithm, is presented. It consists of a discrete particle swarm optimization and a genetic algorithm. From this, the local and global search ability is introduced. CUDA-based co-evolution particle swarm optimization, using a graphics processing unit, is presented and its performance is analysed. The results show that using optimization results can reduce the amplitude and localization of the forced vibration response of a bladed-disc system, while optimization based on the CUDA framework can improve the computing speed. This method could provide support for engineering applications in terms of effectiveness and efficiency.     

Finite element analysis of non-linear static and dynamic response

The paper presents the theoretical and computational procedures which have been applied in the design of a general purpose computer code for static and dynamic response analysis of non-linear structures. A general formulation of the incremental equations of motion for structures undergoing large displacement finite strain deformation is first presented. These equations are based on the Lagrangian frame of reference, in which constitutive models of a variety of types may be introduced. The incremental equations are linearized for computational purposes, and the linearized equations are discretized using isoparametric finite element formulation. Computational techniques, including step-by-step and iterative procedures, for the solution of non-linear equations are discussed, and an acceleration scheme for improving convergence in constant stiffness iteration is reviewed. The equations of motion are integrated using Newmark's generalized operator, and an algorithm with optional iteration is described. A solution strategy defined in terms of a number of solution parameters is implemented in the computer program so that several solution schemes can be obtained by assigning appropriate values to the parameters. The results of analysis of a few non-linear structures are briefly discussed.     

Adhesion study between micron-scale graphite particles and rough walls using the finite element method

The characteristics of how graphite particles adhere to the walls of high-temperature gas-cooled reactors are very important for analyzing reactor source terms. In the present study, atomic force microscopy (AFM) is used to measure the particle adhesion force and the wall morphology, then Lennard-Jones potential theory and the finite element method (FEM) are coupled to calculate the adhesion force between different particles and rough walls. The obvious deviations between the AFM measurements and the theoretical models are due to the contact hypothesis of a sphere with a smooth flat plane in the latter. The FEM results reveal the formation of maximum adhesion at the pull-off point of the particle and the corresponding stress distribution. For aspherical particles, the local curvature of the particle contact interface is the main factor affecting the adhesion force. In addition, for rough walls, different contact regimes correspond to different adhesion trends. When discrete wall roughness with hemispheres and truncated cones is used, the FEM predictions are closer to the AFM measurements, indicating that roughness dominates the adhesion weakening.