An unconditionally stable calculation scheme for the dynamic response of structures by the method of spline collocation

In this paper, by the method of collocation, using the cubic β-spline function as the trial function in the time domain and putting zero residuals of the differential equation of motion of the structure at two points of time, the authors obtain an unconditionally stable calculation scheme for the dynamic response of the structure. When a parameter σ in the scheme is within the interval 0.15<σ <0.5 the scheme is absolutely stable. It is shown that the accuracy of the scheme, as may be measured by AD (the decay of the amplitudes), PE (the elongation of periods) and the algorithmic damping ratio, is better than that of traditional methods—the Wilson-σ's method, the Newmark's method and the Houbolt's method. A numerical example is given in which a certain dynamic response problem is solved by the method of this paper and results are compared with that of the traditional methods and the analytic method showing that the accuracy of the method by this paper is superior to the other ones. The computational scheme for the dynamic response of structures by this paper may be regarded as an effective, convenient and accurate method for dynamic response of structures.     

λ-PDF AND GEGENBAUER POLYNOMIAL APPROXIMATION FOR DYNAMIC RESPONSE PROBLEMS OF RANDOM STRUCTURES

A bounded, mono-peak, and symmetrically distributed probability density function, called λ-PDF, together with the Gegenbauer polynomial approximation, is used in dynamic response problems of random structures. The λ-PDF can reasonably model a variety of random parameters in engineering random structures. The Gegenbauer polynomial approximation can be viewed as a new extension of the weighted residual method into the random space. Both of them can be easily used by scientists and engineers, and applied to a variety of response problems of random structures. The numerical example shows the effectiveness of the proposed method to study dynamic phenomena in random structures.     

Full field analysis of an anti-plane interface crack subjected to dynamic body forces

In this study, the transient full field response of an interface crack between two different media subjected to dynamic body force at one material is investigated. For time t < 0, the bimaterial medium is stress free and at rest. At t = 0, a concentrated anti-plane dynamic point loading is applied at the medium as shown in Fig. 1. The total wave field is due to the effect of this point loading and the scattering of the incident waves by the interface crack. An alternative methodology that is different from the conventional superposition method is used to construct the reflected, refracted and diffracted wave fields. A useful fundamental solution is proposed in this study and the full field solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying an exponentially distributed traction (in the Laplace transform domain) on the interfacial crack faces. The Cagniard–de Hoop method of Laplace inversion is used to obtain the transient solution in time domain. Exact transient closed form solutions for stresses and stress intensity factors are obtained. Numerical results for the time history of stresses and stress intensity factors during the transient process are discussed in detail.     

Constitutive relationship of brittle rock subjected to dynamic uniaxial tensile loads with microcrack interaction effects

A micromechanical model is proposed to describe both stable and unstable damage evolution in microcrack-weakened brittle rock material subjected to dynamic uniaxial tensile loads. The basic idea of the present model is to classify the constitution relationship of rock material subjected to dynamic uniaxial tensile loads into four stages including some of the stages of linear elasticity, pre-peak nonlinear hardening, rapid stress drop, and strain softening, and to investigate their corresponding micromechanical damage mechanisms individually. Special attention is paid to the transition from structure rearrangements on microscale to the macroscopic inelastic strain, to the transition from distribution damage to localization of damage and the transition from homogeneous deformation to localization of deformation. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress-strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to consistent with the experimental results.     

基于模糊相似优先比的湿陷性黄土强夯有效加固深度预测范例推理研究

在大量已有湿陷性黄土地区强夯资料的基础上,采用频数统计的方法,根据变权的概念确定权重,从而构建了一个基于模糊相似优先比的湿陷性黄土强夯有效加固深度预测范例推理模型。该模型是将已有强夯实例作为源范例,将待分析实例作为目标范例,选取相应的评价指标作为模糊因子,通过源范例与目标范例之间模糊因子的相似度计算,得到目标范例与源范例之间的相似性序列,找到与强夯有效加固深度目标范例最相似的源范例,实现有效加固深度的预测。实例分析表明,有效加固深度预测值与实测值误差在10%以内,预测精度较高,具有一定的推广价值。     

Estimation of stochastic nonlinear dynamic response of rock-fill dams with uncertain material parameters for non-stationary random seismic excitation

This research investigates the effect of uncertain material parameters on the stochastic, dynamic response of a rock-fill dam-foundation system subjected to non-stationary random excitation. The uncertain material parameter of particular interest is the shear modulus, developed from a lognormal distribution model. The stochastic seismic response model of the dam-foundation system, with uncertain material parameters and subjected to random loads is the result of a Monte Carlo simulation method. The nonlinear behavior model arises from an equivalent linear method, which considers the nonlinear variation of soil shear modulus and soil damping as a function of shear strain. Specification of the non-stationary stochastic process arises from a simulation method, which generates artificial earthquake accelerograms obtained from the product of a deterministic function of time and a stationary process. The artificial earthquake ground acceleration records reflect the characteristics of soft, medium and firm soil types. Comparison of the numerical results from these approaches provides stochasticity in earthquake seismic excitation and randomness in material parameter (shear modulus) cases. Further, the results indicate that both these cases generally influence the nonlinear dynamic response of rock-fill dams to a non-stationary seismic excitation.     

Percolation with a limiting gradient in a medium with random inhomogeneities

The coverage of a medium by percolation and the effective permeability of a medium with stagnant zones are determined. It is shown that effective permeability is a function of external conditions, particularly the average pressure gradient. Three-, two-, and one-dimensional flows are discussed. The theory of overshoots of random functions and fields beyond a prescribed level [1, 2] is used for the investigation. Overshoots of elements of the percolation field in media with random inhomogeneities are studied. Overshoots of energy being dissipated in a volume are discussed in particular; this permits an approximate determination of the coverage of an inhomogeneous porous medium by migration during percolation with a limiting gradient, i.e., in the case of formation of stagnant zones chaotically disseminated in the flow region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 159–165, September–October, 1970.The authors thank V. M. Entov for discussing the article and useful comments.     

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation‐based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1‐D as well as the 3‐D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1‐D problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Statistical characteristics of the motion of a fluid particle in a medium with random porosity

In the study of flow of a neutral admixture in a porous medium, it is most often assumed in the stochastic formulation that the porosity is constant and a determinate quantity, and the velocity is a random function [1–4]. The velocity distribution is usually regarded as known. Flow in a porous medium with random porosity has been studied to a far lesser extent. We note [5], which studies the averaged equations obtained within the framework of the correlation approximation. We consider the model problem of one-dimensional motion of a fluid particle (position of the front for flow of a neutral admixture in a porous medium) in a medium with random porosity. For a particular form of random porosity field, expressions are obtained for the one- and two-point densities of the distribution of the position of the particle. A study is made of the dependences of the first four moments and the correlation function of the position of the particle as functions of the time. It is shown that for large values of the time the motion of the particle is asymptotically similar to Brownian motion. It is shown by means of numerical modeling that the results obtained transfer to the case of an arbitrary random porosity field. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 59–65, November–December, 1986.     

Determination of permeability in fibrous porous media using the lattice Boltzmann method with application to PEM fuel cells

The lattice Boltzmann method (LBM) is used to simulate the flow through an idealized proton exchange membrane fuel cell (PEMFC) porous transport layer (PTL) geometry generated using a Monte Carlo method. Using the calculated flow field, Darcy's law is applied and the permeability is calculated. This process is applied in both through‐ and in‐plane directions of the paper as both of these permeability values are important in computational fluid dynamics models of PEMFCs. It is shown that the LBM can be used to determine permeability in a random porous media by solving the flow in the microstructure of the material. The permeability in the through‐ and in‐plane directions is shown to be different and the anisotropic nature of the geometry creates anisotropic permeability. It is also found that fiber arrangement plays a large role in the permeability of the PTL. New correlations are presented for in‐ and though‐plane permeabilities of fibrous porous media with (0.6<ε<0.8). Copyright © 2008 John Wiley & Sons, Ltd.     

Dynamic response and reliability analysis of random structures

The finite element method determining dynamic response of random structuressubjected to random dynamic load is studied,the formulas for dynamic response ofrandom structures and reliability based on random resistibility are proposed in thispaper.     

饱和土中球空腔的瞬态动力响应

采用工程上通用的饱和土力学模型,考虑流体与固全之间的耦合作用,利用Ｌａｐｌａｃｅ变换求解了饱和土中球空腔的瞬态动力响应问题,得到了变换域内的解析解,借助数值Ｌａｐｌａｃｅ换求解了饱和土中球空腔瞬态动力响应的位移、应力及孔压的变化规律,为分析地下结构瞬态动力响应提供了一种有效的方法,模型符合工程实际,有一定的工程应用价值。     

挡土结构物随机地震响应分析及动力可靠度研究

本文提供了一种简单的确定性数值方法,来分析在平稳随机地震荷载作用下的结构随机地震响应及动力可靠度。该方法基于有限元动力分析软件,以单位加速度脉冲函数作为地震荷载的输入,当计算出结构的脉冲响应函数后,再运用傅立叶变换得到随机激励和结构响应之间的传递函数,由此来计算结构的均方根响应和峰值响应。基于此方法,分析了挡土结构物在平稳随机地震荷载作用下的位移、弯矩、基底水平合力、基底竖向合力以及沿墙高的土压力极值的随机地震响应及动力可靠度。从分析结果可以看出:用Kanai谱模型的计算值比欧进萍谱模型的计算值更趋保守,而把响应过程当作马尔可夫过程似比泊松过程更精确。     

Microcrack interaction brittle rock subjected to uniaxial tensile loads

A micromechanics-based model is proposed to describe unstable damage evolution in microcrack-weakened brittle rock material. The influence of all microcracks with different sizes and orientations are introduced into the constitutive relation by using the statistical average method. Effects of microcrack interaction on the complete stress–strain relation as well as the localization of damage for microcrack-weakened brittle rock material are analyzed by using effective medium method. Each microcrack is assumed to be embedded in an approximate effective medium that is weakened by uniformly distributed microcracks of the statistically-averaged length depending on the actual damage state. The elastic moduli of the approximate effective medium can be determined by using the dilute distribution method. Micromechanical kinetic equations for stable and unstable growth characterizing the ‘process domains’ of active microcracks are taken into account. These ‘process domains’ together with ‘open microcrack domains’ completely determine the integration domains of ensemble averaged constitutive equations relating macro-strain and macro-stress. Theoretical predictions have shown to be consistent with the experimental results.     

Local effective thermoelastic properties of graded random structure matrix composites

Summary  We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated. Received 11 November 1999; accepted for publication 4 May 2000     

时变参数时滞减振控制研究

时滞动力吸振器对谐波激励有着良好的减振控制效果,但对随机激励的减振控制效果却并不明显,具体表现为时滞动力吸振器对随机激励的减振控制效果与被动吸振器几乎相同。针对上述问题,本文提出了一种新的时变参数时滞减振控制方法。在原有时滞减振控制方法的基础上,首先将时滞增益系数由定值形式变为时间函数形式,然后通过时变优化得到多组时滞控制参数并使其以一定时间周期循环作用于减振控制过程,通过这种方法进一步改善了时滞动力吸振器减振性能。本文最后以二自由度时滞动力吸振器减振模型为例,以主系统的振动响应为仿真对象,运用精细积分法求解了具有时变时滞参数的时滞动力学方程,以此得到了在谐波激励和随机激励作用下主系统振动的时域仿真结果。研究结果表明,在时变参数时滞动力吸振器的控制下,主系统无论是受谐波激励作用还是受随机激励作用,其振动位移、振动速度和振动加速度均比在定值参数时滞动力吸振器控制下时有大幅的减少,时滞动力吸振器的减振性能有了明显的改善。      

场地地震响应随机动力可靠性分析

本文针对地震响应的随机不确定性,将地震作用简化为随机过程,基于土体材料在随机动荷载作用下的破坏是各应力水平荷载产生损伤的累积结果,与荷载施加的先后次序无关,结合可靠度民随机振动理论。提出了运用累积损伤模型的地震响应动力可靠性分析法,并针对上海地区某地的软土地基,进行实列计算,比较了以累积损伤量评价地基动力破坏与其他的可靠度指标β值法,孔隙水压力比评价地基液化的计算结果,得到一些有意义的结论。     

A THEORY OF EFFECTIVE THERMAL CONDUCTIVITY FOR MATRIX-INCLUSION- MICROCRACK THREE-PHASE HETEROGENEOUS MATERIALS BASED ON MICROMECHANICS

The effective thermal conductivity of matrix-inclusion-microcrack three-phase heterogeneous materials is investigated with a self-consistent micromechanical method (SCM) and a random microstructure finite element method(RMFEM). In the SCM, microcracks are assumed to be randomly distributed and penny-shaped and inclusions to be spherical, the crack effect is accounted for by introducing a crack density parameter, the effective thermal conductivity is derived which relates the macroscopic behavior to the crack density parameter. In the RMFEM, the highly irregular microstructure of the heterogeneous media is accurately described, the interaction among the matrix-inclusion-microcracks is exactly treated, the inclusion shape effect and crack size effect are considered. A Ni/ZrO₂ particulate composite material containing randomly distributed, penny-shaped cracks is examined as an example. The main results obtained are: (1) the effective thermal conductivity is sensitive to the crack density and exhibits essentially a linear relationship with the density parameter; (2) the inclusion shape has a significant effect on the effective thermal conductivity and a polygon-shaped inclusion is more effective in increasing or decreasing the effective thermal conductivity than a sphere-shaped one; and (3) the SCM and RMFEM are compared and the two methods give the same effective property in the case in which the matrix thermal conductivity λ₁ is greater than the inclusion one λ₂. In the inverse case of λ₁ < λ₂, the two methods agree as the inclusion volume fraction and crack density are low and differ as they are high. A reasonable explanation for the agreement and deviation between the two methods in the case of λ₁ < λ₂ is made. This work was supported by the National Natural Science Foundation of China and Chnese “863” High-Tech, Program.     

设防烈度下非比例阻尼结构地震随机响应峰值区间估计方法

建立与抗震规范设防水准相一致的地震动随机模型,给出了非比例阻尼结构体系地震反应运动方程,推导了非比例阻尼结构体系分析的复振型时域闭合解和地震随机响应的闭合解.通过随机响应的峰值因子和变异系数获得了非比例阻尼结构体系的地震随机响应峰值均值和方差,提出了设防烈度下非比例阻尼结构体系随机响应峰值区间估计方法.计算31条实际地震记录的复振型时域闭合解,并与地震随机响应的闭合解进行了比较,算例结果表明随机响应峰值区间估计方法的合理性和有效性.地震响应区间分析方法将是工程抗震设计的一个重要方法.