Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

FURTHER IMPROVEMENT ON FUNDAMENTAL SOLUTIONS OF PLANE PROBLEMS FOR ORTHOTROPIC MATERIALS

On the basis of the existing fundamental solutions ofdisplacements, further improvement is made, and then the generalfundamental solutions of both plane elastic and plane plasticproblems for ortho- tropic materials are obtained. Two parametersbased on material constants a_1, a_2 are used to derive the rele-vant expressions in a real variable form. Additionally, an analyticalmethod of solving the singular integral for the internal stresses isintroduced, and the corresponding result are given. If a_1=a_2=1, allthe expres- sions obtained for orthotropy can be reduced to thecorresponding ones for isotropy. Because all these expres- sions andresults can be directly used for both isotropic problems andorthotropic problems, it is convenient to use them in engineeringwith the boundary element method (BEM).

AN EFFECTIVE BOUNDARY METHOD FOR THE ANALYSIS OF ELASTOPLASTIC PROBLEMS

In this paper, a series of effective formulae of the boundary element method is presented. In these formulae, by using a new variable, two kernels are only of the weaker singularity of Lnr (where r is the distance between a source point and a field point). Hence, the singularities in the conventional displacement formulation and stress formulation at internal points are reduced respectively so that the 'boundary-layer'' effect which strongly degenerates the accuracy of stress calculation by using original formulae is eliminated. Also the direct evaluation of coefficients C (boundary tensor), which are difficult to calculate, is avoided. This method is used in elastoplastic analysis. The results of the numerical investigation demonstrate the potential advantages of this method.

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modem structural engineering. This paper introduces the boundary element method （BEM） into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic me- dia with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media.

Almost periodic solutions of memristive multidirectional associative memory neural networks with mixed time delays

Traditional biological neural networks cannot simulate the real situation of the abrupt synaptic connections between neurons while modeling associative memory of human brains.In this paper,the memristive multidirectional associative memory neural networks(MAMNNs)with mixed time-varying delays are investigated in the sense of Filippov solution.First,three steps are given to prove the existence of the almost periodic solution.Two new lemmas are proposed to prove the boundness of the solution and the asymptotical almost periodicity of the solution by constructing Lyapunov function.Second,the uniqueness and global exponential stability of the almost periodic solution of memristive MAMNNs are investigated by a new Lyapunov function.The sufficient conditions guaranteeing the properties of almost periodic solution are derived based on the relevant definitions,Halanay inequality and Lyapunov function.The investigation is an extension of the research on the periodic solution and almost periodic solution of bidirectional associative memory neural networks.Finally,numerical examples with simulations are presented to show the validity of the main results.

CLOSED-FORM SOLUTIONS FOR ELASTOPLASTIC PURE BENDING OF A CURVED BEAM WITH MATERIAL INHOMOGENEITY

The elastoplastic pure bending problem of a curved beam with material inhomo- geneity is investigated based on Tresca＇s yield criterion and its associated flow rule. Suppose that the material is elastically isotropic, ideally elastic-plastic and its elastic modulus and yield limit vary radially according to exponential functions. Closed-form solutions to the stresses and radial displacement in both purely elastic stress state and partially plastic stress state are presented. Numerical examples reveal the distinct characteristics of elastoplastic bending of a curved beam composed of inhomogeneous materials. Due to the inhomogeneity of materials, the bearing capac- ity of the curved beam can be improved greatly and the initial yield mode can also be dominated. Closed-form solutions presented here can serve as benchmark results for evaluating numerical solutions.

DYNAMICS OF NEW CLASS OF HOPFIELD NEURAL NETWORKS WITH TIME-VARYING AND DISTRIBUTED DELAYS

In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.

考虑弹性模量劣化的洞室围岩弹塑性分析

洞室开挖伴随岩体参数的劣化,描述参数的劣化对指导工程实践具有重要意义。为描述变形参数的劣化,基于霍克-布朗准则,利用损伤门槛值表征弹性模量劣化程度,通过泰勒级数简化求解含损伤门槛值的平衡方程得到塑性区半径解析解并给出损伤门槛值的取值方式,结合有限差分软件FLAC^(3D)对比验证了公式合理性。基于常弹性应变和变弹性应变2种假设,联合非关联流动准则获得了含损伤门槛值的塑性区位移表达式。最后,通过算例分析了不同参数下塑性区半径及洞壁位移变化规律。结果表明:劣化越严重,洞室越容易失稳;随着损伤门槛值增大,2种假设下的位移差值和塑性区半径逐渐增加,常弹性应变假设得到的位移偏小。为避免洞室失稳破坏,要重视支护的施作。

寒区隧道应力和位移弹塑性统一解及对比分析

选择合理的屈服准则分析寒区隧道弹塑性解能为寒区隧道稳定性分析提供理论基础。为此,结合Mohr-Coulomb准则(即M-C准则)和外接圆Drucker-Prager准则(即D-P准则)分析得到考虑中间主应力效应的统一强度准则,建立寒区隧道弹塑性力学计算模型,基于线性非关联准则推导得出考虑围岩不均匀冻胀特性的寒区隧道应力场及位移场的弹塑性统一解,并对所得统一解答式进行算例及参数分析。研究表明:采用M-C准则计算偏于保守,而利用外接圆D-P准则计算偏于危险,考虑中间主应力效应能充分发挥围岩承载潜能,有效缩小塑性半径,缓解衬砌冻胀变形;统一强度理论参数b保持常数时,初始地应力、衬砌强度、不均匀冻胀系数及围岩体积冻胀率等参数的变化对寒区隧道应力及塑性半径变化影响显著。该研究成果可丰富寒区隧道工程设计理论。

三维主应力条件下隧道应变软化围岩弹塑性解

为探究隧道在三维主应力作用下的围岩应变及位移,将塑性区内相等的径向应力增量划分为有限个相同数量的同心圆环,通过平衡微分方程和差分进化算法,利用三维H-B屈服准则确定每一环的应力。基于求解的应力和相关联流动法则可以获得塑性区的塑性应变及位移。将计算结果与有限元软件的数值模拟结果进行对比验证其可靠性。结果表明,笔者所建立的三维主应力条件下隧道应变软化围岩弹塑性解是一种可以同时求解3个主应力及位移数值解的新方法,且与数值模拟结果拟合良好,证明了该方法的可靠性与准确性。相对于二维平面应变假设,该方法更好地考虑了岩体三维主应力状态下的应力应变关系,对复杂岩层条件下的隧道围岩稳定性分析具有重要参考价值。

隧洞式内衬储气库极限储存压力解析解

隧洞式内衬储气库是一种新型能源储存方法,有助于平衡供需,推动国家由化石能源向绿色能源的持续过渡,有利于国家“碳中和、碳达峰”目标的实现.本文采用极限平衡方法和弹塑性分析方法推导隧洞式内衬储气库极限储存压力的解析解.在极限平衡方法中,考虑上覆围岩自重、破裂面受力和极限储存压力,选用刚性锥模型,推导了上限压力表达式;在弹塑性分析方法中,根据围岩中应力分布规律和剪切、抗拉强度,推导获得了弹塑性条件下上限与下限压力表达式.最终综合考虑两方法求得的结果,确定极限储存压力解析解.结果表明:极限平衡方法求得上限压力与埋深呈二次函数关系,且随着侧压力系数的增大而增大;弹塑性分析方法确定的上限压力和下限压力与埋深呈线性关系,下限压力随着侧压力系数的增大而减小,且Ⅰ级围岩条件下的内衬储气库不用考虑下限压力.在侧压力系数λ=1.2时上限压力最大,因此应尽量在侧压力系数为1.2的围岩条件下修建隧洞式储气库.最后根据典型工况下上限和下限压力曲线给出内衬洞室推荐压力范围.

Periodic Solution to BAM-type Cohen-Grossberg Neural Network with Time-varying Delays

By using the continuation theorem of Mawhin＇s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays.

Existence and exponential stability of weighted pseudo-almost periodic solutions for genetic regulatory networks with time-varying delays

The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.

应变软化围岩受轴向力作用的弹塑性解

为有效解决轴向力作用下应变软化岩体扩孔问题,以渝昆高铁云贵段的乐业隧道工程为依托,基于M-C和广义H-B屈服准则,考虑轴向应力的影响,提出了应变软化岩体扩孔问题弹塑性解。通过将塑性区按径向应力从内向外依次按照有限同心圆环进行划分,并基于平衡方程和屈服准则确定塑性区的应力和塑性半径,同时依据非关联的三维塑性势函数,可以得到圆孔扩张的弹塑性应变和位移。该计算方法不仅考虑了中主应力和轴向塑性应变的作用,而且可以进一步得到扩孔问题的极限扩孔压力、扩孔过程中应力和位移的变化及分布情况。最后通过简化方法,将该方法计算结果与Vesic的理论结果进行对比,验证了考虑轴向力作用下的应变软化岩体扩孔问题弹塑性解的合理性。

考虑围岩软化特性和应力释放的圆形隧道黏弹塑性解

将围岩的塑性应变软化特性引入到考虑应力释放的圆形隧道黏弹塑性解中,并且在围岩的软化和残余强度阶段考虑围岩的塑性体积膨胀特性,提出了考虑塑性软化以及塑性体积膨胀和围岩应力释放的圆形隧道弹塑性解。当软化系数k=∞、膨胀系数h=s时,该解转化为黏弹-脆塑性解;当k=0、h=s时,则转化为黏弹-理想塑性解,进一步令h=s=1,则转化为不考虑塑性体积膨胀的黏弹-理想塑性解。通过具体实例计算,分析了掌子面与研究断面间距x、围岩的软化系数k、膨胀系数h和s、支护结构等对围岩塑性区、破碎区半径和变形的影响。当开挖面与研究断面间距x在（0~4）D（D为隧道直径）范围内,随着时间增加塑性圈和破碎区迅速增大;超过4D,塑性区和破碎区半径增量逐渐变小,趋于稳定值;围岩中包含塑性区和破碎区时,二者半径的比值只取决于围岩的性质,与支护结构无关,但支护结构可以限制塑性区及破碎区的范围;考虑应变软化和塑性体积膨胀时,围岩径向位移和塑性区及破碎区半径均大于不考虑应变软化和塑性体积膨胀时的结果;软化系数k增大,围岩位移、塑性区和破碎区半径增加、塑性区半径和破碎区半径之间的比值变小。得到的结果对于隧道工程设计和施工具有一定的指导性和参考价值。

考虑脆性损伤和渗流的圆形水工隧洞解析解

针对脆性岩石的损伤特性引入脆性损伤模型,导出三维各向同性损伤情况下的损伤变量表达式。在考虑损伤、不同工况主应力对应关系和渗流作用影响下,推导出圆形水工隧洞洞周围岩的弹塑性应力和塑性半径的解析解。对岩石的脆性特性的研究表明,考虑脆性损伤时的洞周围岩塑性半径比不考虑时有一定程度提升;围岩脆性特征越明显,塑性半径越大。无论洞周围岩应力状态如何,考虑渗流影响后,洞周围岩塑性区范围均会有所扩展。在内水压从0逐渐增加过程中,塑性半径随内水压增加而逐渐减小,直至塑性区消失,在超出临界内压后,塑性区重新出现,塑性半径逐渐增大。

基于幂强化本构模型的轴对称圆巷弹塑性解

轴对称圆巷的弹塑性求解的关键是选择合适的屈服准则。已经有诸多学者选择Mohr-Coulomb准则、Drucker-Prager准则和Hoek-Brown准则等,进行了相应的求解。为了探讨更符合工程实际需要的准则和求解,在考虑岩石材料的应变强化效应的条件下,建立了轴对称圆巷的幂强化本构模型和基于Drucker-Prager屈服准则的幂强化-理想塑性模型,并进行了弹塑性求解。以工程实例为计算条件,将幂强化-理想塑性模型的计算结果与基于Mohr-Coulomb准则、Drucker-Prager准则的理想塑性模型和幂强化模型的计算结果分别进行了对比,分析幂强化参数对围岩弹塑性解的影响。研究表明,应变强化效应对围岩稳定性有较大影响,对于应变强化效应较强的岩石材料,采用幂强化模型分析更接近工程实际。

考虑地下水、注浆及衬砌影响的深埋隧洞弹塑性解

对于深埋隧洞,地下水-围岩-注浆圈-衬砌共同形成了一个水压平衡体系,传统的隧洞应力与塑性区计算方法均未同时考虑上述4个因素的共同作用。以深埋隧洞为研究对象,将围岩、注浆圈、衬砌视为均质各向同性连续弹塑性介质,基于地下水动力学、弹塑性力学及摩尔-库仑屈服准则,推导了4个因素共同作用下深埋隧洞轴对称问题的应力弹塑性解与塑性区计算公式;利用Matlab编制程序对某隧洞工程进行了计算,并与传统计算方法进行了对比,验证了公式的正确性,指出了传统计算方法的缺陷;讨论了注浆参数对塑性区的影响规律,提出了最优注浆圈厚度的确定方法。

考虑膨胀应力和剪胀的深埋隧道弹塑性解

基于湿度应力场理论,推导了考虑膨胀应力和剪胀特性的圆形隧道开挖后围岩力学响应的弹塑性解。将隧道软弱围岩遇水膨胀现象视为湿度-应力耦合过程,基于Fick第二定律,推导了圆形隧洞围岩内湿度扩散非稳态解。采用非关联流动法则,获得了隧道高膨胀势区的应力和位移解答。以两种不同质量岩体开挖的隧洞为例,分析了膨胀围岩应力和变形的影响因素。结果表明,考虑膨胀应力(取决于围岩含水率变化和湿度膨胀系数)时,塑性区扩大,松动圈厚度增加,应力收敛变慢。当膨胀应力增大到一定程度时,塑性区将出现拉应力区。膨胀岩隧洞开挖遇水作用,膨胀应力增加的围岩变形远大于地应力引起的围岩变形。同时,应力剪胀对膨胀性围岩的变形影响不容忽视,尤其是在支护抗力较小的情况下,洞壁处径向位移增加显著。

圆形巷道围岩应变软化弹塑性分析

岩土类材料广义上都呈应变软化力学行为,考虑峰后岩石应变软化过程中引起后继强度面收缩的特性,认为岩体在足够小的局部范围内材料特性保持不变,将后继破坏岩体分为多个塑性区,给出基于平面应变和Mohr-Coulomb准则的围岩准应变软化弹塑性应力解析式,并给出符合围岩后继强度和变形演变规律的各软化区半径求解方程组。洞室围岩变形特征曲线是地下工程支护设计的重要依据,考虑岩体破裂过程中变形参数不断劣化的特性,分析剪切模量劣化对围岩变形、软化半径及破裂半径的影响。最后通过算例对模型进行验证,计算结果可以对地下工程的优化支护设计及安全性评价提供理论依据。