关于时标上的适应Nabla分数阶导数

本文研究了时标上的适应Nabla分数阶导数的问题.利用时标理论,获得了关于适应Nabla分数阶导数的若干重要性质.这些结果推广并改进了文献[9,10]中的有关结论以及一般Nabla导数的性质.     

关于时标上的适应Nabla分数阶导数（英文）

本文研究了时标上的适应Nabla分数阶导数的问题.利用时标理论,获得了关于适应Nabla分数阶导数的若干重要性质.这些结果推广并改进了文献[9,10]中的有关结论以及一般Nabla导数的性质.     

基于粒子群优化的分数阶PFGM(1,1)模型在建筑物沉降预测中的应用

针对传统的灰色预测模型对建筑物沉降预测精度不高、拟合数据较差的问题,在传统的GM(1,1)模型基础上提出了分数阶建模的思想,采用粒子群优化算法求解最优分数阶次,建立基于粒子群优化的分数阶PFGM(1,1)模型.实例计算表明,分数阶FGM(1,1)模型可以提高建筑物沉降的预测精度,通过粒子群优化算法选取最优阶次可以进一步提高预测精度和误差检验等级.由此可见,基于粒子群优化的分数阶PFGM(1,1)模型对建筑物的沉降控制有着重要的指导作用.     

圆形均布荷载作用下分数导数型黏弹性土基变形分析

土体的蠕变特性是影响工后沉降和工程安全的重要因素.基于半空间弹性土基受圆形均布荷载作用弹性理论解,根据弹性与黏弹性理论的对应原理,建立了分数导数型黏弹性土基在竖向圆形均布荷载作用下的地表位移与分数阶导数等参数的关系,并分析了不同分数阶下地表变形的时效特性.结果表明,与经典黏弹性本构模型相比,分数导数黏弹性模型能够在较宽的范围内描述黏弹性土基变形的特性,采用分数导数Kelvin黏弹性本构模型计算的地表沉降较经典的Kelvin黏弹性模型小,土基的蠕变特性与分数导数的阶数有关,具有更为广泛的适用性和应用前景.     

分数阶模糊时滞神经网络模型解的存在唯一性和有限时间稳定性

本文介绍了一类分数阶模糊时滞神经网络模型.利用压缩映射原理,讨论了带时滞的分数阶神经网络模型解的存在性和唯一性,并根据Gronwall不等式结合分数阶微分方程的性质,证明了分数阶神经网络模型平衡点的有限时间稳定性,给出了有限时间稳定性的判断准则.最后,给出数值仿真说明了理论结果的正确性.     

带有边界值问题的脉冲分数阶微分方程正解的存在性

本文研究了具有边界值条件的脉冲分数阶微分方程.利用Kuratowski非紧性测度理论和Sadovskii不动点定理,得到了脉冲分数阶微分方程正解的存在性的结果,推广了已有文献的结论.     

带有边界值问题的脉冲分数阶微分方程正解的存在性（英文）

本文研究了具有边界值条件的脉冲分数阶微分方程.利用Kuratowski非紧性测度理论和Sadovskii不动点定理,得到了脉冲分数阶微分方程正解的存在性的结果,推广了已有文献的结论.     

一类分数阶Kirchhoff型方程非平凡解的存在性

利用临界点理论中的山路引理,研究一类分数阶Kirchhoff型方程在次临界增长条件下非平凡解的存在性,进一步统一和丰富了已有文献的相关结果.     

分数阶力学系统的正则变换理论

应用分数阶模型可以更准确地描述复杂系统的力学与物理行为,随着分数阶微积分在科学和工程的诸多领域的成功应用,传统的分析力学理论和方法需要拓展到含有分数阶微积分的系统.变换是分析力学研究的一个重要手段.本文研究分数阶力学系统的变换理论.基于Cuputo分数阶导数的定义,定义力学系统的Lagrange函数和Hamilton函数,在H(o|¨)lder交换关系下建立了分数阶Hamilton原理,并由分数阶Hamilton原理通过变分运算导出分数阶Hamilton正则方程;建立了分数阶力学系统的正则变换理论,给出了四种基本形式的分数阶正则变换,并通过算例说明母函数在分数阶正则变换中的作用.     

移动热源作用下基于分数阶应变的三维弹性体热-机响应

基于分数阶应变理论,研究了移动热源作用下三维弹性体的热 机动态响应.将分数阶应变理论下的控制方程应用于三维半空间模型,通过Laplace积分变换、双重Fourier变换及其数值反变换对控制方程进行求解,得到了不同热源速度和不同分数阶参数下,无量纲温度、应力、应变和位移的分布规律.结果表明,分数阶应变参数对机械波影响显著而对热波影响有限,热源速度对热 机械波影响显著.     

饱和粘土非线性渗流规律与径向固结

以多孔介质等效渗流概念得出粘土平均孔隙微尺度数量级范围在0.01 μm至0.1μm,与测试结果一致．实验结果表明饱和粘土微尺度孔隙渗流为非线性流．理论推导表明固液界面作用与渗透率平方根或孔隙半径成反比,固液界面相互作用是导致饱和粘土非线性渗流的重要原因．提出了精确描述饱和粘土微尺度孔隙非线性渗流基本规律的数学模型,其参数量纲明确,物理意义清楚．建立了饱和粘土非线性渗流新定律,统一描述了从较低到较高水力梯度全过程渗流曲线特征,达西定律是其特例．基于新定律,建立了饱和粘土非线性渗流定流量径向固结数学模型．以粘性边界层思想与稳态依序替换法及积分方程法,导出了粘土非线性渗流平均质量守恒方程及活动边界运动方程,给出了饱和粘土非线性渗流超孔隙水压力分布公式与平均固结度计算公式,获得了粘土层压力分布规律和平均固结度随时间变化规律．结果表明:饱和粘土非线性渗流使活动边界运动速度减小．研究结果为粘土地质工程与岩土工程应用提供了新的科学依据．达西渗流径向固结计算是新的非线性渗流固结计算的特例．     

Mathematical modelling and study of the consolidation of an elastic saturated soil with an incompressible fluid by FEM

The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the stability of the method as well as the estimation of the error by using semi-discretization in time. Finally, we then solved this one by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data.     

任意荷载下成层粘弹性地基的一维固结

针对成层粘弹性地基模型,运用Laplace变换及矩阵传递法求解了任意荷载下成层粘弹性地基一维变形问题,得到了频域内的通解,通过Laplace逆变换,即可计算成层粘弹性地基在任意荷载下的一维变形.Terzaghi一维固结理论解是本文的一个特例.结合三层地基的算例,可以看到粘弹性地基的固结相对于弹性地基有个滞后过程,但随时间最终趋于一致;循环荷载下粘弹性多层地基固结时,其有效应力和变形都呈振荡增长,且不与荷载同步,而要相对滞后.此外,通过一工程实例,对该方法的可靠性进行论证,以证明该法确能指导工程实践.     

结构—饱和土壤相互作用的固结有限元分析

讨论了结构与饱和土壤相互作用的固结分析问题.对于结构利用多重子结构分析技术实现向饱和土交界面上的凝聚.从而建立了结构与饱和土壤相互作用的固结控制方程.文中给出了问题求解的一次性算法方案,采取压力主从关系的手段处理边界上的不排水条件.文末给出数值算例.本文工作为大型结构与土体相互作用固结分析研究工作的深入创造了条件.     

Large-strain numerical solution for coupled self-weight consolidation and contaminant transport considering nonlinear compressibility and permeability

Based on the one-dimensional (1D) consolidation equation and advection-dispersion transport equation, this paper presents a large-strain numerical solution for coupled self-weight consolidation and contaminant transport in saturated deforming porous media considering nonlinear compressibility and permeability relationships. The finite difference method is used to solve the governing equations for consolidation and transport. The proposed numerical solution for consolidation accounts for vertical strain, soil self-weight, and nonlinearly changing compressibility and hydraulic conductivity during consolidation. The solution for solute transport accounts for advection, diffusion, mechanical dispersion, linear and nonlinear equilibrium sorption, and porosity-dependent effective diffusion coefficient. The proposed numerical solution is verified against a self-weight consolidation field tank test, an analytical solution in the literature, and the CST1 numerical model. Using the verified solution, a series of parametric study is conducted to investigate the effect of several important parameters on the contaminant transport process for confined disposal of dredged contaminated sediments. The results indicate that the consolidation process and contaminant transport process induced by soil self-weight- can be very different from those induced by the more traditional external surcharge loading. Treating the self-weight loading as traditional external surcharge loading can underestimate the rate of contaminant outflow, especially in the early times. The compressibility and permeability relationships of sediment and the type of loading (i.e., self-weight loading versus external surcharge loading) can all significantly affect the contaminant transport process for confined disposal of dredged contaminated sediment.     

非饱和土一维固结的半解析解

首先对Fredlund的非饱和土一维固结理论进行简化,由得到的液相及气相的控制方程、Darcy定律及Fick定律,经Laplace变换及Cayley-Hamilton定理构造了顶面状态向量与任意深度处状态向量间的传递关系;通过引入边界条件,得到了大面积瞬时加荷情况多种边界条件下Laplace变换域内的超孔隙水压力、 超孔隙气压力及土层沉降的解;采用Crump方法编制程序实现Laplace逆转换,得到了时间域内的超孔隙水压力、超孔隙气压力、土层沉降的半解析解;引用典型算例,对单面排水排气情况,与已有的解析解进行对比,验证其正确性;对单面排气不排水情况,与差分法结果进行对比进一步证明半解析解的正确性,并进行固结特性分析．该研究对非饱和土一维固结的研究具有重要的意义．     

Numerical optimization applying trust-region reflective least squares algorithm with constraints to optimize the non-linear creep parameters of soft soil

Determination of the creep model parameters is a challenging task particularly when a non-linear elastic visco-plastic (EVP) model is adopted, mainly due to the limited test duration as well as the assumption of the reference time. Therefore, this paper presents an innovative numerical solution to find the EVP model parameters applying the trust-region reflective least square optimization algorithm. The developed approach involves several available laboratory consolidation test results in the optimization procedure with the adopted commencing time to creep as a unit of time. In this paper, the laboratory results of Ottawa clay were employed to demonstrate the limitation of the recent method to obtain model parameters. Furthermore, the developed method is verified against Skå-Edeby clay in the laboratory conditions. The EVP model parameters are obtained by applying the developed method to the available laboratory consolidation results of clay samples. The analysis results of vertical strains and excess pore water pressures demonstrate that the developed method can be a feasible tool to estimate the settlement properties of clays.     

Numerical solution of a one-dimensional problem of filtration consolidation of saline soils in a nonisothermal regime

A mathematical model of a problem of filtration consolidation of saline soils in a nonisothermal regime with allowance for the presence of salts in the liquid and solid phases is constructed. A numerical solution of the corresponding one-dimensional boundary-value problem is found by the method of finite differences. As an example, we investigate a problem of filtration consolidation of a massif of clay soil of finite thickness. Results of numerical investigations and their analysis are presented. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 197–204, January–March, 2008.     

Numerical simulation of nonlinear consolidation problems by models based on the network method

The nonlinear consolidation problem in saturated soils, for any type of constitutive dependences of the hydraulic permeability and the void ratio on the effective pressure, has been numerically simulated by the network method. Three different network models, based on logarithmic and/or potential constitutive dependences, called the Davis and Raymond, Juárez-Badillo and Cornetti and Battaglio models, as well as a fourth one with dependences in tabulated form, are solved. In addition, new network models that delete the two restrictive hypotheses assumed by these authors are presented. These hypotheses are the influence of the void ratio changes in the term of contraction of the governing equation and the influence of the thickness change of the volume element as consolidation progresses. Only a few rules based on elementary theory of circuits are required for the design of the models, whose solution is reliable with relatively small grids and computational times. After verifying the results of the network method with the solutions of the classic authors, the extended models have been used to address a real case of consolidation.     

Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM

Research interest in the mechanical behaviour of soils is growing as a result of an increasing number of geomechanical problems involving consolidation effects. The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid and variable permeability. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the convergence of the method using a technique based on the proof of solution’s existence. Finally, we then solved this constitutive model by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data. Therefore, the model can be used for quantitative predictions of consolidation behaviour of soils with permeability dependent on the settlement.