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主要研究了分数阶混合随机泛函微分方程的能控性.在无限维空间下,假设所考虑方程线性部分生成半群不是紧的,使用非紧性测度技术和Mönch不动点定理,给出了方程能控性充分条件,并通过一个例子说明了结论的有效性. 相似文献
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In this paper, the ability of a material rate‐independent system to evolve toward another mechanical state from an equilibrium configuration, with no change in the control parameters, is investigated. From a mechanical point of view, this means that the system can spontaneously develop kinetic energy with no external disturbance from an equilibrium state, which corresponds to a particular case of bifurcation. The existence of both conjugate incremental strain and stress such that the second‐order work vanishes is established as a necessary and sufficient condition for the appearance of this bifurcation phenomenon. It is proved that this fundamental result is independent of the constitutive relation of the rate‐independent material considered. Then the case of homogeneous loading paths is investigated, and, as an illustration, the subsequent results are applied to interpret the well‐known liquefaction observed under isochoric triaxial loading conditions with loose granular materials. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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王水球 《成都信息工程学院学报》2009,24(3)
运用泛函分析性质以及Fourier变换的方法研究带有周期边界条件的非线性k-s方程在有限时间区间上的精确控制.首先研究线性化k-s方程的精确控制,证明对于任意给定的函数u0∈Hs,uT∈Hs,总能找到一个控制函数h使得线性化k-s方程有解u且满足u(x,0)=u0,u(x,T)=uT;然后结合线性化k-s方程的精确控制,通过定义Fredholm算子并应用Fredholm算子的一些理论找到非线性化k-s方程的控制函数,使其可精确控制. 相似文献
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François Nicot Noel Challamel Jean Lerbet Florent Prunier Félix Darve 《国际地质力学数值与分析法杂志》2011,35(13):1409-1431
The concept of bifurcation has been widely discussed, based, for example, on homogeneous tests in soil mechanics. Essentially two‐dimensional (axisymmetric) conditions have been considered. This paper aims at deriving a bifurcation criterion in geomechanics, independently of the problem's dimension. This criterion is related to the vanishing of the determinant of the symmetric part of the material's (or the discrete system's) constitutive (or stiffness) matrix. The derivation is essentially based on the notion of loading parameters (controlling the loading). Basically, a bifurcation occurs when the existence of a unique solution to the quasistatic problem, involving a given set of loading parameters, is lost. Interestingly, the criterion is shown to be independent of the choice of loading parameters. As a possible extension, the context of structure mechanics is considered, and the close connection between both soil and structure analysis is discussed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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This paper concerns the hydromechanical stability of partially saturated soils during wetting. The response of a loose silty sand is numerically/theoretically investigated with the main aim of identifying both triggering mechanisms and predisposing factors to instability. This latter is testified by both a rapid increase in the pore water pressure and an unexpected loss of numerical convergence. The study has been conducted at different scales from laboratory tests to boundary value problems, and in both cases, the controllability theory has been employed to both interpret and justify the numerical results. 相似文献
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In this paper, the onset of mechanical instability in time‐sensitive elasto‐viscoplastic solids is theoretically analyzed at the constitutive level and associated with the occurrence of ‘spontaneous accelerations’ under stationary external perturbations. For this purpose, a second‐order form of Perzyna's constitutive equations is first derived by time differentiation, and a sufficient stability condition is identified for general mixed loading programs. These loading conditions are in fact the most general in both laboratory tests and real boundary value problems, where a combination of certain stress and strain components is known/prescribed. The theoretical analysis leads to find precise stability limits in terms of material hardening modulus. In the case of constitutive relationships with isotropic strain‐hardening, no instabilities are possible while the hardening modulus is larger than the so‐called ‘controllability modulus’ defined for (inviscid) elasto‐plastic materials. It is also shown that the current stress/strain rate may also directly influence the occurrence of elasto‐viscoplastic instability, which is at variance with elasto‐plastic inviscid media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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开敞式TBM工法施工时,钻遇突涌水灾害后易造成严重的工程事故,堵漏浆液注浆止水处理措施是常用的技术手段。本文在分析了工程中常用浆液存在不足的基础上,结合室内试验,研制适用于开敞式TBM工法的堵漏浆液配方,并通过正交试验确定了优化配方为水灰比为0.59、酒石酸为0.25%、水解聚丙烯酰胺溶液为3%、铝酸钠为1.6%。在可控性（可泵期等）满足要求的基础上,对优化配方进行了包括析水性、抗压强度等各项性能的测试及室内模拟试验,经正交试验后测得配方浆液形成的结石体具有良好的抗压强度和抗渗能力,能够满足工程现场的需要。实际工程的涌水点注入研制的可控浆液后,短时间内达到停泵条件,相比传统浆液,可大幅减少堵漏浆液用量。结果表明,该可控配方浆液对吉林省内某隧道工程施工中钻遇的涌水灾害具有良好的治理效果,能够满足实际工程的需要。 相似文献
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The volumetric compaction due to wetting processes is a phenomenon observed quite often in unsaturated soils. Under certain circumstances, saturation events can result into a sudden and unexpected collapse of the system. These phenomena are usually referred to as wetting‐induced collapses, without providing any detailed theoretical justification for this terminology. In order to predict in a general fashion the occurrence of coupled instabilities induced by saturation processes, a generalization of the theoretical approaches usually employed for saturated geomaterials is here provided. More specifically, this paper addresses the problem of hydro‐mechanical instability in unsaturated soils from an energy standpoint. For this purpose, an extension of the definition of the second‐order work is here suggested for the case of unsaturated porous media. On the basis of some examples of numerical simulations of laboratory tests, coupled hydro‐mechanical instabilities are then interpreted in the light of this second‐order energy measure. Finally, the implications of the theoretical results here presented are commented from a constitutive modelling perspective. Two possible alternative approaches to formulate incremental coupled constitutive relations are indeed discussed, showing how the onset of hydro‐mechanical instabilities can be predicted using an extended form of Hill's stability criterion. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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The question of diffuse failure in granular media such as soils is treated by numerical modelling with a discrete element
model. Two numerical samples are considered, one dense and the other loose. A criterion based on the sign of the second-order
work is applied to the numerical model to detect bifurcation points related to diffuse failure. The notions of loss of controllability
and loss of sustainability are taken into account to simulate diffuse failure at bifurcation points detected. Therefore, the
failures predicted based on the second-order work criterion are numerically verified. 相似文献
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