深埋圆形巷道围岩和衬砌相互作用解析解

围岩采用Mohr-Coulomb屈服准则、衬砌采用双线性本构模型,提出广义荷载作用下深埋圆形巷道中围岩和衬砌相互作用体系弹塑性解的解析表达式.在此基础上,研究了围岩的位移、位移灵敏度和塑性区等随广义荷载的变化规律.根据参数分析和实例计算得到:1)围岩或衬砌由弹性进入塑性,位移灵敏度将发生突变;2)位移灵敏度在弹性区和塑...     

半正弦脉冲激励下双线性包装系统位移损坏边界确定的解析方法

运用包装动力学中的位移损坏边界新理论，选择简化自典型缓冲系统的双线性动力学模型，用解析方法首次获得了半正弦脉冲激励下的位移损坏边界。论文的分析思路与方法，为从理论上探讨不同力学特征缓冲系统的防护规律可能有所启迪。     

单自由度双线性隔震装置地震反应研究

本文用多条具有相同反应谱的人工地震波，对单自由度双线性系统进行了大量的非线性时程反应分析，讨论了采用双线性隔震装置结构的地震反应特点，研究了双线性隔震装置的刚度比、初始屈服位移等因素对结构地震反应的影响。研究结果对工程设计中合理选择双线性隔震装置的刚度比、初始屈服位移等设计参数有一定的参考价值。     

缓冲包装跌落仿真误差分析

目的研究Ansys/LS-DYNA DTM模块跌落仿真分析与经典缓冲包装设计方法之间的误差,并分析阻尼及摩擦因数对仿真结果的影响。方法基于经典缓冲包装设计方法,分别设计线弹性与双线性材料为缓冲材料的产品-衬垫系统;利用Ansys/LS-DYNA DTM模块对线弹性与双线性缓冲材料的产品-衬垫系统进行跌落分析,对比分析理论设计与仿真分析结果。结果对于线弹性材料与双线性缓冲材料的产品-衬垫系统,Ansys/LS-DYNA DTM模块跌落仿真分析与经典缓冲包装理论设计之间的误差均在5%以内。系统阻尼的增加导致所受最大冲击加速度减小;摩擦因数对所受最大冲击加速度影响较小;线性粘滞系数的增加导致所受最大冲击加速度增加。结论对于一般的工程应用,Ansys/LS-DYNA DTM模块跌落仿真分析方法与经典缓冲包装设计方法之间的误差在允许范围内。     

一类双线性系统受零均值平稳高斯白噪声激励时的FPK解

本文首先在文献[1]的基础上进一步分析研究了具有一般形式对称双线性恢复力的非线性系统受零均值平稳高斯白噪声激励时的FPK解（即位移响应的概率密度函数）；在此基础上，针对一类特殊的双线性系统给出了相应的FPK解。     

筏体和基础弹性对设备冲击响应影响的有限元分析

带有限位器的浮筏隔振系统是非线性系统,利用ANSYS建立了这一非线性系统的有限元模型,计算了带有限位器的浮筏隔振系统模型的冲击响应,分析了筏体弹性、基础弹性和限位器参数对冲击响应的影响.计算结果表明筏体弹性和基础弹性对系统的冲击响应均有一定程度的影响,它们使得机组的最大加速度响应减小,筏体和机组的最大位移响应增大.对于刚性浮筏隔振系统和弹性浮筏隔振系统,限位器间隙与冲击响应之间的关系是相同的,即随着限位器间隙的减小,筏体和机组的最大加速度响应增大,而最大位移响应都减小.     

等效线性的基础隔震建筑的动力响应

利用随机等儿线性化方法,本文分析了地震激励下多隔震建筑结构的动力响应。文中采用的地震波为过滤高斯白噪声,上部结构及叠层橡胶隔震器为线弹性,铅阻尼器为双线性恢复力模型,对隔震系统线性化后,推导了隔震结构的相对位移及绝对加速度的响应有达式,并通过算例讲座了地震波输入功率谱密度及场地卓越频率对结构响应的影响。     

等强残余位移系数谱研究

针对双线性单自由度体系定义了残余位移系数,然后选取100条地震波,通过弹塑性动力时程分析,建立了等强残余位移系数谱,分析了其影响因素,并建立了拟合公式,最后对残余位移和最大位移之间的关系进行了研究。结果表明:在总体上,结构周期越小,强度越低,屈服后刚度系数越小,其残余位移系数越大;结构周期较大时,残余位移系数和周期之间关系不大;结构周期越小,结构强度对残余位移系数的影响越大;残余位移和最大位移基本呈线性关系。     

物品包装系统位移损坏边界

Ｒ．Ｅ．Ｎｅｗｔｏｎ提出的基于物品易损度的加速度损坏边界概念及其表达式仅反映了为保护物品安全，对其加速度响应的限制，未考虑缓冲衬垫压缩变形范围有限的制约条件。本文对物品的相位位移响应引入约束条件，首次定义了物品包装位移易损度及位移损坏边界，与加速度损坏边界相结合，用以确定物品包装系统的安全区，讨论了两类损坏边界的关系。并推导了后峰锯齿脉冲及矩形脉冲作用下，双线性及线性包装系统损坏边界的表达式。     

限位器对隔振系统抗冲击性能的影响

水面舰艇特别是潜艇在战斗条件下的主要威胁来自水中爆炸物的非接触性爆炸,选用抗冲击性能好的设备和对设备采取冲击防护措施可以保证艇上设备的安全性,使用隔振装置就是一种较好的冲击防护措施。对于通常的隔振装置,在一定的冲击作用下,设备的相对位移响应较大,可能超过了设备外接管线的变形能力,甚至超过了隔振器本身的极限变形能力。在隔振装置中使用限位器可以有效地限制设备的最大相对位移。通过对弹性限位器各参数(工作间隙和刚度)对隔振系统抗冲击性能(设备的最大加速度和最大相对位移)的影响的探讨,提出了限位器各参数的确定方法。对浮筏隔振系统中限位器的参数进行设计,应用MSC.NASTRAN 软件对具有限位器和没有限位器的浮筏隔振系统冲击响应进行计算,分析了限位器对浮筏隔振系统抗冲击性能的影响。     

Computation of upper and lower bounds to the frequencies of elastic systems by the method of Lehmann and Maehly

A method, called the Lehmann-Maehly method, for determining upper and lower bounds for eigenvalues, which was introduced by Bazley and Fox⁴ in 1964, is applied to the determination of bounds to the frequencies of elastic systems. In reviewing the fundamental theory involved, the present paper emphasizes the physical significance of the adjoint operators T and T* employed. An error in the paper by Bazley and Fox is noted and it is pointed out that with the corrected theory it is possible to use the Lehmann-Maehly method as a procedure for computing converging sequences of upper and lower bounds merely by varying a constant, the shifting constant. Thus, sequences of bounds are shown to be easily obtainable without prior knowledge of rough bounds, and the procedure for obtaining the bounds is not significantly more difficult to apply than the familiar Rayleigh-Ritz method for upper bounds. Since displacements and stresses are independently varied, the displacement functions used in the approximation procedure are only required to satisfy prescribed displacement boundary conditions while the stress functions only need satisfy the natural (stress) boundary conditions. Operators are derived for a non- uniform beam based on Timoshenko beam theory. Tables of bounds computed by the Lehmann-Maehly method and also the Rayleigh-Ritz method are given as an illustrative example.     

A hierarchy of upper bounds on the response of stochastic systems with large variation of their properties: random variable case

This paper is the first of a two-part series that constitutes an effort to establish spectral- and probability-distribution-free upper bounds on various probabilistic indicators of the response of stochastic systems. In this first paper, the concept of the variability response function (VRF) is discussed in some detail with respect to its strengths and its limitations. It is the first time that various limitations of the classical VRF are discussed. The concept of associated fields is then introduced as a potential tool for overcoming the limitations of the classical VRF. As a first step, the special case of material property variations modeled by a single random variable is examined. Specifically, beam structures with the elastic modulus being the only stochastic property are studied. Results yield a hierarchy of upper bounds on the mean, variance and exceedance values of the response displacement, obtained from zero-mean U-shaped beta-distributed random variables with prescribed standard deviation and lower limit. In the second paper that follows, the concept of the generalized variability response function is introduced and used with the aid of associated fields to extend the upper bounds established in this paper to more general problems involving stochastic fields.     

Optimal Operation of Integrated Heat and Electricity Systems: A Tightening McCormick Approach

Combined heat and electricity operation with variable mass flow rates promotes flexibility, economy, and sustainability through synergies between electric power systems (EPSs) and district heating systems (DHSs). Such combined operation presents a highly nonlinear and nonconvex optimization problem, mainly due to the bilinear terms in the heat flow model—that is, the product of the mass flow rate and the nodal temperature. Existing methods, such as nonlinear optimization, generalized Benders decomposition, and convex relaxation, still present challenges in achieving a satisfactory performance in terms of solution quality and computational efficiency. To resolve this problem, we herein first reformulate the district heating network model through an equivalent transformation and variable substitution. The reformulated model has only one set of nonconvex constraints with reduced bilinear terms, and the remaining constraints are linear. Such a reformulation not only ensures optimality, but also accelerates the solving process. To relax the remaining bilinear constraints, we then apply McCormick envelopes and obtain an objective lower bound of the reformulated model. To improve the quality of the McCormick relaxation, we employ a piecewise McCormick technique that partitions the domain of one of the variables of the bilinear terms into several disjoint regions in order to derive strengthened lower and upper bounds of the partitioned variables. We propose a heuristic tightening method to further constrict the strengthened bounds derived from the piecewise McCormick technique and recover a nearby feasible solution. Case studies show that, compared with the interior point method and the method implemented in a global bilinear solver, the proposed tightening McCormick method quickly solves the heat–electricity operation problem with an acceptable feasibility check and optimality.     

Assessment of the local stress state through macroscopic variables

Macroscopic quantities beyond effective elastic tensors are presented that can be used to assess the local state of stress within a composite in the linear elastic regime. These are presented in a general homogenization context. It is shown that the gradient of the effective elastic property can be used to develop a lower bound on the maximum pointwise equivalent stress in the fine-scale limit. Upper bounds are more sensitive and are correlated with the distribution of states of the equivalent stress in the finescale limit. The upper bounds are given in terms of the macrostress modulation function. This function gauges the magnitude of the actual stress. For 1 相似文献   

Porosity-dependence of elastic properties and ultrasonic velocity in polycrystalline alumina — a model based on cylindrical pores

Effective elastic moduli and ultrasonic velocity of materials having aligned cylindrical pores have been derived using a series expansion in terms of the difference between the upper and lower bounds of elastic moduli obtained by the variational method. The theoretical results for polycrystalline alumina agree well with the experimental data, confirming the suggestion of previous researchers that a matrix containing parallel cylindrical pores orientated perpendicular to the applied stress, provide a better model than a spherical one in describing the porosity-dependence of elastic moduli in sintered specimens.     

Practical methods for a posteriori error estimation in engineering applications

This work presents an extension of the goal‐oriented error estimation technique to the engineering analysis of three‐dimensional linear elastic bodies. In the series of examples shown, the errors are estimated with respect to local displacement and stress components. The paper also introduces novel means to compute lower bounds on the error in the energy norm based on a cost‐effective postprocessing of the upper bound error estimates. The numerical results indicate that the method can be used effectively for complex engineering applications. Copyright © 2003 John Wiley & Sons, Ltd.     

筏体和基础弹性对船舶设备冲击响应影响的试验分析

试验研究是船舶机械设备冲击隔离性能分析的主要方法之一。为了分析筏体弹性、基础弹性和限位器间隙对冲击响应的影响，设计制作了可以考虑筏体弹性和基础弹性的带有限位器的浮筏隔振系统试验模型。试验结果表明筏体弹性和基础弹性对系统的冲击响应均有一定程度的影响，它们使得机组的最大加速度响应减小，提高系统的抗冲击隔离效果。对于刚性浮筏隔振系统和弹性浮筏隔振系统，限位器与冲击响应之间的关系是相同的，即安装限位器之后将使得筏体和机组的加速度响应增大，随着限化器间隙的减小，筏体和机组的最大加速度响应进一步增大。     

Computing a-posteriori bounds for stress intensity factors in elastic fracture mechanics

This paper mainly focuses on computing the lower and upper bounds on stress intensity factors in elastic fracture mechanics with an efficient finite element output bound procedure on quantities of interest in engineering. The bounds procedure is obtained by minimizing the quadratic energy functional of output with constraints of equilibrium conditions of mechanics and continuity conditions of finite element space. The computation is based on solving the elemental Neumann residual problems for the bounds on energy norm of error in finite element solutions. The lower and upper bounds on the intensity factors of an open mode and a shear mode elastic fracture problems are computed in this paper.     

Finite element analysis of elastic property bounds of a composite with randomly distributed particles

The bounds of the elastic properties of an E-glass particle reinforced BISGMA/TEGDMA composite were predicted by a random unit cell model. Two means of tensile loading were used: iso-displacement loading and iso-stress loading. The iso-displacement loading predicts the upper bound of Young’s modulus, while iso-stress loading predicts the practical lower bound of Young’s modulus. The results showed that Young’s modulus increases, while Poisson’s ratio decreases with increasing filler content for both loading conditions. For comparative purposes, the upper and practical lower bounds were also calculated by Hashin’s method, a periodic three-dimensional single-particle, and two-particle unit cells. Analytical solutions using the Mori–Tanaka model and experiments were also conducted for verification purpose. The results showed that the random unit cell predicts better overall bounds for elastic properties.