Equivalent Linearization Method Based on Energy-to-cth-Power Difference Criterion in Nonlinear Stochastic Vibration Analysis of Multi-Degree-of-Freedom Systems

Basic equations of energy-to-cth-power difference criterion were derived for multi-degree-of-freedom (MDOF) systems subjected to stationary Gaussian excitations with non-zero mean. Modal transform technique was used in order to reduce unknowns. Main computational formulae were presented and suggested values of c were given. Numerical results show that the method of this paper prevails over equation difference criterion both in accuracy and in simplicity.     

基于解析解和新准则的深埋隧道断面形状优化

针对深埋隧道断面形状优化问题,考虑复杂受力下洞周可能存在拉应力情况,提出基于摩尔-库伦屈服准则的新的优化准则,基于解析解用模拟退火法获得洞周最小破坏范围的最优断面形状．优化模型中,以断面映射函数系数为优化的设计变量,利用混合罚函数使优化孔形满足一定的约束条件,设立孔边最大有效应力（与屈服准则相关）最小的优化准则．针对存在内压的深埋隧道断面形状优化问题,对不同内压、不同侧压系数、不同宽高比限制等情况进行优化计算,并对比两种优化准则在该情况下优化结果的异同．结果表明,对压应力主导优化的情况,新准则与原准则没有差别;对可能出现拉应力的复杂应力情况,新准则有更好的适应性,可以获得更优断面形状．     

45#钢的损伤演化方程和层裂准则研究

通过唯象分析和细观物理统计相结合的方法建立了一种韧性材料的损伤演化方程。在试验结果和内变量理论的基础上得到了45#钢的含损伤热—粘塑性本构关系。用有限差分方法计算了45#钢平板撞击所产生的应力波传播规律、损伤演化规律及层裂进程。通过自由面速度历史的数值模拟,并基于计算结果与试验结果间的最佳一致性,得到了损伤演化方程中的材料参数和极限损伤数值,并以此为依据建立了材料的应力率层裂准则。     

高静水压力下Mohr–Coulomb准则的拓展研究

深部开采时极端环境下的岩体高应力和高地压是影响工程安全的主要因素。本文指出了Mohr–Coulomb准则（简称M–C准则）在高静水压力下无法判断岩石材料发生屈服破坏的问题,开展了岩样在高应力下的三轴压缩实验,观察了高静水压力下岩石材料的破坏现象,推导了高静水压力条件下M–C准则的拓展方程。研究结果显示,与现有M–C准则不同的是,材料剪切强度随轴压和围压之差增大到某一峰值时将逐渐减小,岩样在高静水压力下也可发生屈服破坏,M–C准则拓展方程与实验结果基本吻合。同时,本文探讨了低静水压力下M–C屈服面的下限和高静水压力下M–C屈服面的上限。研究成果可为深部工程的安全高效开展提供理论参考。

     

On the criteria of the absolute convective stability for compressible fluids

The conditions under which natural convection is absent from compressible fluids are investigated. It is shown that in the parameter “Rayleigh number-given temperature difference” plane there is a domain in which convection occurs for neither Rayleigh numbers. It is proposed to refer to this domain as the absolute convective stability region and to name the criterion determining the boundary of this region the absolute convective stability criterion. The necessary, sufficient, and necessary and sufficient conditions of the absolute convective stability for a viscous compressible fluid are derived. It is shown that in the particular case in which the thermal properties of the fluid and the adiabatic gradient are constant, these conditions coincide with the Schwarzschild criterion.     

Periodic solutions of a difference equation that depends on two indices

We obtain a criterion for the existence of a unique periodic solution of a linear two-parameter difference equation in a Banach space.     

Hybrid determination of equivalent characteristics of perforated plates

In this paper, we have adopted the hybrid method, which combines experimental and numerical methods, to investigate the dynamic behavior of perforated plates. It was found that the modal assurance criterion is a useful criterion to judge the degree of similarity between experimental and numerical models. The difference between the experimental and numerical models can be reduced via sensitivity testing and by checking the correlation coefficient. The equivalent material properties of the perforated plates were also obtained by the hybrid method. In addition, the curve-fitting technique was utilized to find the relationship of the mass remnant ratio with the parameter ratio. The functions obtained from the curve fitting can be used to predict accurately the equivalent material properties and resonant frequencies of perforated plates of the diagonal array.     

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC-based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.     

水下爆炸载荷作用下加筋板的毁伤模式

为研究加筋板结构在水下爆炸载荷作用下的破坏模式,进行了一系列模型试验。通过对试验结果的分析,将加筋板的毁伤模式总体分为塑性大变形（模式I）、拉伸破坏（模式II）和剪切破坏（模式III）等3大类。又根据载荷强弱和加强筋的相对强度,将每种破坏模式细分为3种子模式。提出了一个量纲一的损伤因子,作为预报毁伤模式的判据。     

Elasto-plastic postbuckling of damaged orthotropic plates

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion related to spherical tensor of stress is proposed to describe the mixed hardening of damaged orthotropic materials. Its dimensionless form is isomorphic with the Mises criterion for isotropic materials. Furthermore, the incremental elasto-plastic damage constitutive equations and damage evolution equations are established. Based on the classical nonlinear plate theory, the incremental nonlinear equilibrium equations of orthotropic thin plates considering damage effect are obtained, and solved with the finite difference and iteration methods. In the numerical examples, the effects of damage evolution and initial deflection on the elasto-plastic postbuckling of orthotropic plates are discussed in detail.     

Phase equilibrium in non-fluids and non-fluid mixtures

A criterion of phase equilibrium for mixtures of materials with arbitrary symmetry (e.g. between solid and fluid or two solid mixture phases) is deduced using a rational thermodynamics approach. This criterion, known also as Maxwell relation, is expressed via the difference of chemical potential tensors (Eshelby tensors) on the singular surface dividing the bulk phases.The thermomechanical balance equations, the entropy inequality and the Maxwell relation for phase equilibrium are given first for the case of pure (one-constituent) materials of arbitrary symmetry and then for the case of mixtures (including chemically reacting ones) of arbitrary symmetry.In the special case of fluids it is shown that the chemical potential tensors reduce to the classical scalar chemical potentials and the Maxwell relations to the classical thermodynamic criterion for the phase equilibrium.     

Deformation and long-term damage of particulate composites under thermal loads

A theory of long-term damage of particulate composite materials under thermal load is proposed. The damage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a single microvolume is determined by its stress-rupture strength, which, in turn, is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which characterizes the ultimate strength according to the Schleicher–Nadai criterion. The damage (porosity) balance equation is derived for an arbitrary time, taking the thermal effect into account. Algorithms for calculating microdamage and macrostresses as functions of time are developed     

单步Newmark预测-校正算法无条件稳定的充分必要条件的论证

应用判别差分方程稳定性的Schur－Cohn准则，研究用于一般耦合系统动力响应分析的单步Newmark预测－校正算法的稳定性问题；给出了算法无条件稳定的充分必要条件的严格理论证明。     

A choked-flow calculation criterion for nonhomogeneous, nonequilibrium, two-phase flows

This study applies the theory of characteristics to a one-dimensional transient model, in order to analyze the conditions for a choked, two-phase flow. The basic hydrodynamic model analyzed is a two-fluid model that includes relative phasic acceleration terms and a nonequilibrium, derivative-dependent exchange of mass.

The analytical results provide an algebraic, choked-flow criterion analogous to that for a single-phase flow, except that terms pertaining to relative phase motion and nonequilibrium mass transfer are included.

This paper discusses the numerical implementation of the choked-flow criterion in a nonhomogeneous and nonequilibrium finite difference scheme. The use of a mass-transfer model having a derivative dependence is shown to be necessary if self-choking is expected.     

Stability analysis of annular flow structure, using a discrete form of the “two-fluid model”

The differential form of the “two-fluid model” for annular flow, neglecting surface tension, is ill-posed, and it is not suited for examining the stability of the steady-state solutions with respect to the average film thickness. It is shown here that a discrete (difference) representation of the two-fluid model may lead to an appropriate criterion for the stability of the steady-state solutions. Exactly the same criterion is obtained from the requirement that the kinematic waves will propagate in the downstream direction. The suggested discrete form of the “two-fluid model” is used to perform transient simulation and for examining the system response to finite disturbances.     

On the constitutive equations for cyclic plasticity under nonproportional loading

Experimental results on 316 stainless steel, at room temperature, under strain controled axial-torsion loadings, point out a large difference in strengthening between proportional and nonproportional loadings. The maximum difference is produced by 90° out of phase straining. In this paper we discuss the possibility of describing this additional hardening, without any new internal variable, by only modifying the expression for the yield criterion.     

基于S准则发展的混凝土动态多轴强度准则

通过对经典强度理论或准则的强度参数分析,将强度参数转化为由混凝土的单轴压缩和单轴拉伸强度表示,结合S准则给出的混凝土单轴强度的率效应规律,得出了强度参数受应变率影响的率效应函数,进而将常用的静态多轴强度准则摩尔-库伦强度理论、松岗-中井强度理论、德鲁克-普拉格强度理论、拉得-邓肯强度准则和胡克-布朗强度准则发展为动态多轴强度准则.利用混凝土动态单轴压缩和动态单轴拉伸试验结果统计分析给出的S准则率效应参数,分析了5种强度准则中强度参数随应变率的变化规律以及取值范围.基于混凝土单轴压缩和单轴拉伸强度,分别给出了5种强度准则在子午面、偏平面和平面应力条件下的强度曲线与主应力空间中的强度曲面,对比分析了5种强度准则间的异同,以及每种强度准则随应变率的变化规律.利用混凝土材料的动态双轴和动态真三轴强度试验结果,分析评价了5种动态多轴强度准则,并且阐述了各动态多轴强度准则的应变率适用范围.德鲁克-普拉格强度理论与试验结果相差甚远,不适于描述混凝土材料的强度规律.动态双轴加载时,在拉压区各强度准则差别不大,都可较好地描述试验规律;在压压区各强度准则差别较大,松岗-中井强度理论与试验结果吻合最好.在动态真三轴比例加载时,摩尔-库伦强度理论和胡克-布朗强度准则无法考虑中主应力的影响;松岗-中井强度理论和拉得-邓肯强度准则都可较好地描述试验规律.      

Coupled processes of deformation and long-term damage of layered materials under thermal loading

The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle fracture on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Schleicher–Nadai failure criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the layers at an arbitrary time is formulated taking into account the thermal component. Algorithms of calculating the time dependence of microdamage and macrostresses are developed. Corresponding curves are plotted. The effect of temperature on the deformation and microdamage of the layers is studied     

Is There Chaotic Synchronization in Space Extend Systems?

Based on coupled map lattice (CML), the chaotic synchronous pattern in space extend systems is discussed. Making use of the criterion for the existence and the conditions of stability, we find an important difference between chaotic and nonchaotic movements in synchronization. A few numerical results are presented.