Application of thermodynamics-based rate-dependent constitutive models of concrete in the seismic analysis of concrete dams

This paper discusses the seismic analysis of concrete dams with consideration of material nonlinearity. Based on a consistent rate-dependent model and two thermodynamics-based models, two thermodynamics-based rate-dependent constitutive models were developed with consideration of the influence of the strain rate. They can describe the dynamic behavior of concrete and be applied to nonlinear seismic analysis of concrete dams taking into account the rate sensitivity of concrete. With the two models, a nonlinear analysis of the seismic response of the Koyna Gravity Dam and the Dagangshan Arch Dam was conducted. The results were compared with those of a linear elastic model and two rate-independent thermodynamics-based constitutive models, and the influences of constitutive models and strain rate on the seismic response of concrete dams were discussed. It can be concluded from the analysis that, during seismic response, the tensile stress is the control stress in the design and seismic safety evaluation of concrete dams. In different models, the plastic strain and plastic strain rate of concrete dams show a similar distribution. When the influence of the strain rate is considered, the maximum plastic strain and plastic strain rate decrease.

Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry.To study the mechanical behavior of a typical ductile cast iron(GJS-450)with nodular graphite,uni-axial quasi-static and dynamic tensile tests at strain rates of 10^(-4),1,10,100,and 250 s^(-1)were carried out.In order to investigate the influence of stress state on the deformation and fracture parameters,specimens with various geometries were used in the experiments.Stress strain curves and fracture strains of the GJS-450 alloy in the strain rate range of 10^(-4)to 250 s^(-1)were obtained.A strain rate-dependent plastic flow model was proposed to describe the mechanical behavior in the corresponding strain-rate range.The available damage model was extended to take the strain rate into account and calibrated based on the analysis of local fracture strains.Simulations with the proposed plastic flow model and the damage model were conducted to observe the deformation and fracture process.The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys.The predictions with the proposed plastic flow and damage models at various strain rates agree well with the experimental results,which illustrates that the rate-dependent plastic flow and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.The proposed plastic flow and damage models can be used to describe the deformation and fracture analysis of materials with similar properties.

DISSIPATION-BASED CONSISTENT RATE-DEPENDENT MODEL FOR CONCRETE

An energy-dissipation based viscoplastic consistency model is presented to describe the performance of concrete under dynamic loading. The development of plasticity is started with the thermodynamic hypotheses in order that the model may have a sound theoretical background. Independent hardening and softening and the rate dependence of concrete are described separately for tension and compression. A modified implicit backward Euler integration scheme is adopted for the numerical computation. Static and dynamic behavior of the material is illustrated with certain numerical examples at material point level and structural level, and compared with existing experimental data. Results validate the effectiveness of the model.

Modelling and Analysis of Bacteria Dependent Infectious Diseases with Variable Contact Rates

In this research,we proposed a non-linear SIS model to study the effect of variable interaction rates and non-emigrating population of the human habitat on the spread of bacteria-infected diseases.It assumed that the growth of bacteria is logistic with an intrinsic growth rate is a linear function of infectives.In this model,we assume that contact rates between susceptibles and infectives as well as between susceptibles and bacteria depend on the density of the non-emigrating population and the total population of the habitat.The stability theory has been analyzed to analyzed to study the crucial role played by bacteria in the increased spread of an infectious disease.It is shown that as the density of non-emigrating population increases,the spread of an infectious disease increases.It is shown further that as the emigration increases,the spread of the disease decreases in both the cases of contact mentioned above rates,but this spread increases as these contact rates increase.It suggested that the control of bacteria in the human habitat is very useful to decrease the spread of an infectious disease.These results are confirmed by numerical simulation.

Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

A Generalized Gibbs Potential Model for Materials Degradation

It is well known that work done on a material by conservative forces (electrical, mechanical, chemical) will increase the Gibbs Potential of the material. The increase in Gibbs Potential can be stored in the material and is free/available to do work at some later time. However, it will be shown in this paper that while in this state of higher Gibbs potential, the material is metastable and the material will degrade spontaneously/naturally with time in an effort to reach a lower Gibbs Potential. A generalized Gibbs Potential Model is developed herein to better understand its impact on a materials degradation rate. Special attention will be given to dielectrics degradation.

GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.

The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors

We study the parameter estimation in a nonlinear regression model with a general error's structure,strong consistency and strong consistency rate of the least squares estimator are obtained.

Intelligent modeling and control for nonlinear systems with rate-dependent hysteresis

A new modeling approach for nonlinear systems with rate-dependent hysteresis is proposed. The approach is used for the modeling of the giant magnetostrictive actuator, which has the rate-dependent nonlinear property. The models built are simpler than the existed approaches. Compared with the experiment result, the model built can well describe the hysteresis nonlinear of the actuator for input signals with complex frequency. An adaptive direct inverse control approach is proposed based on the fuzzy tree model and inverse learning and special learning that are used in neural network broadly. In this approach, the inverse model of the plant is identified to be the initial controller firstly. Then, the inverse model is connected with the plant in series and the linear parameters of the controller are adjusted using the least mean square algorithm by on-line manner. The direct inverse control approach based on the fuzzy tree model is applied on the tracing control of the actuator by simulation. The simulation results show the correctness of the approach.

Viscosity Transient Phenomenon during Drop Impact Testing and Its Simple Dynamics Model

Most soft materials behave as if they were hardened when subjected to an impact force. The strain rate dependence of viscosity resistance is the reason for this behavior. The authors carried out drop impact tests on several types of soft materials under the condition of a flat frontal impact. The impact force waveform of soft materials was found to consist of a thorn-shaped waveform and a succeeding mountain-shaped waveform. Based on our experimental observations, we believe that a large viscosity resistance is rapidly changed to a small resistance in the course of the impact. In the present study, the cause of this distinct waveform is discussed based on a dynamics model. The study applies a standard linear solid (SLS) model in which the viscosity transient phenomenon is considered is applied. Three types of impact force waveforms of actual soft materials are simulated using the SLS model. Some features of the impact force waveform of soft materials can be explained using the SLS model.

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional(fractional-order)derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic(FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly.The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature(KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Timedependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894(2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Analysis of SIRVI model with time dependent coefficients and the effect of vaccination on the transmission rate and COVID-19 epidemic waves

COVID-19 epidemic models with constant transmission rate cannot capture the patterns of the infection data in the presence of pharmaceutical and non-pharmaceutical interventions during a pandemic.Because of this,a new modification of SIR model that contain the vaccination compartment with time dependent coefficients and weak/lossimmunity is explored.Literature review confirms that the effect of vaccination on the time dependent transmission rate is still an open problem.This study answers this open problem.In this study,we first prove the well-posedness and investigate the model dynamics to show their continuous dependence on the model parameters.We then provide an algorithm to derive the time-dependent transmission function for the epidemiologic model and the data of the infected cases.The derived coupled nonlinear differential equations show the effect of vaccination on the transmission rate.Unlike previous studies,we first filter the published data and solve the nonlinear coupled differential equations using the finite difference technique,where the coefficient of the coupled nonlinear differential equations is a function of given data.We then show that time-dependent transmission function can be represented by linear combinations of Gaussian radial base function.We then validate the prediction of our models using numerical simulations,where we used the published data of COVID-19 confirmed cases by the Ministries of Health in Saudi Arabia and Poland.Finally,the numerical solutions of a SIRVI model with time dependent transmission rate show that the waves for currently active cases are in good agreement with the data of Saudi Arabia and Poland.

Modeling and H_∞ Robust Control of a Smart Structure with Rate-dependent Hysteresis Nonlinearity

The performance of smart structures in trajectory tracking under sub-micron level is hindered by the rate-dependent hysteresis nonlinearity.In this paper,a Hammerstein-like model based on the support vector machines(SVM)is proposed to capture the rate-dependent hysteresis nonlinearity.We show that it is possible to construct a unique dynamic model in a given frequency range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set of signals for the linear dynamic subsystem of the Hammerstein-like model.Subsequently,a two-degree-of-freedom(2DOF)H∞robust control scheme for the ratedependent hysteresis nonlinearity is implemented on a smart structure with a piezoelectric actuator(PEA)for real-time precision trajectory tracking.Simulations and experiments on the structure verify both the efectiveness and the practicality of the proposed modeling and control methods.

An improved Prandtl-Ishlinskii model for compensating rate-dependent hysteresis in fast steering mirror system

To solve the rate-dependent hysteresis compensation problem in fast steering mirror(FSM) systems, an improved Prandtl-Ishlinskii(P-I) model is proposed in this paper. The proposed model is formulated by employing a linear density function into the STOP operator. By this way, the proposed model has a relatively simple mathematic format, which can be applied to compensate the rate-dependent hysteresis directly. Adaptive differential evolution algorithm is utilized to obtain the accurate parameters of the proposed model. A fast steering mirror control system is established to demonstrate the validity and feasibility of the improved P-I model. Comparative experiments with different input signals are performed and analyzed, and the results show that the proposed model not only suppresses the rate-dependent hysteresis effectively, but also obtains high tracking precision.

服役高速列车车体铝合金材料率相关剩余强度预测

高速列车结构与材料在长期服役过程中因受复杂边界条件的影响将逐渐趋于劣化,存在潜在的安全风险。本文以高速列车常用铝合金6005A-T6为对象,首先将材料细观微结构解耦为基体相与空洞相,推导符合微结构连续度Weibull分布特征的损伤演化方程;继而提出一种考虑应变率的试验−数值方法,识别材料颈缩后损伤的加速演化行为,进而推导得到覆盖空洞相萌生、生长、聚合全过程的损伤演化方程,并得出基体相的无损本构;最后结合细观物理机制提出损伤顺序交互作用模型,以实现仅测量材料表观弹性模量即可获取含先前服役损伤材料在后续延性变形中的损伤演化方程,准确预测含服役损伤材料的率相关剩余强度。研究结果表明:预测值与试验值的平均相对误差不超过1%。损伤随延性发展由应变率正敏感性转变为负敏感性;对于疲劳−延性机制,空洞在先前疲劳损伤发展的空洞基础上继续生长。

基于Maxwell模型的压电驱动系统前馈控制方法

为了提高外腔可调谐半导体激光器的测量精度,基于Maxwell模型提出了用于消除其压电驱动系统迟滞非线性的前馈控制方法.基于经典Maxwell力学模型,建立了描述非凸、非对称迟滞环的静态迟滞模型;根据频率与位移幅值的关系建立了率相关系数矩阵,与静态迟滞模型耦合得到率相关迟滞模型,实现了不同频率下压电驱动系统迟滞非线性的精准预测;构建了迟滞逆模型,对压电驱动系统进行前馈补偿控制.实验结果表明,率相关迟滞模型具有较高的精度,1 Hz下模型均方根误差为0.049μm, 50 Hz下模型均方根误差为0.252μm.基于迟滞逆模型的前馈控制方法能够明显提高系统输出位移的线性度,增大线性度范围,线性相关系数R2由0.971 58提高到了0.999 77.

Asymptotics for partly linear regression with dependent samples and ARCH errors:consistency with rates

Partly linear regression model is useful in practice, but littleis investigated in the literature to adapt it to the real data which are dependent and conditionally heteroscedastic. In this paper, the estimators of the regression components are constructed via local polynomial fitting and the large sample properties are explored. Under certain mild regularities, the conditions are obtained to ensure that the estimators of the nonparametric component and its derivatives are consistent up to the convergence rates which are optimal in the i.i.d. case, and the estimator of the parametric component is root-n consistent with the same rate as for parametric model. The technique adopted in the proof differs from that used and corrects the errors in the reference by Hamilton and Truong under i.i.d. samples.

压电陶瓷驱动器迟滞非线性的修正Rayleigh模型建模及实验验证

针对压电陶瓷驱动器建模复杂的技术难点,本文提出了一种基于修正Rayleigh模型的动态迟滞非线性建模方法。首先,针对压电陶瓷材料的机电响应特性,构建了压电驱动器的线性本构方程;然后,基于迟滞效应成因及其微观机理研究,提出了采用Rayleigh模型的非线性建模方法;在此基础上,采用一阶线性方程描述压电驱动器频率相关特性并通过实验验证其有效性;之后,采用双Rayleigh系数,构建了非对称Rayleigh模型;最后,实验验证了Rayleigh模型在压电陶瓷驱动器次环响应中的适用性。

具有密度依赖出生率的非选择性半封闭捕获离散偏害系统动力学行为

本文提出了具有密度依赖出生本的非选择性半封闭捕获离散偏害模型,运用整分力程的遗代方法和比软原理,得出了系统持久性及灭绝性的-系列条件.通过构造适当的Lypuov函数,得到-个系统全局吸引的充分条件。本研究结果表明,通过控制种群中可用于相获的种群比例m(这与密度依赖的出生率有很大关系),系统可能是持久的、灭绝的。全局吸引的。或者个种群持久间另一个天绝,系统的动志行为变得复杂。通过数值模拟验证了主要结果的可行性。