3D digital-image correlation insight into generalized relaxation behavior of sandstone under stress and pore pressure coupling

The occurrence of geological hazards and the instability of geotechnical engineering structures are closely related to the time-dependent behavior of rock.However,the idealization boundary condition for constant stress in creep or constant strain in relaxation is not usually attained in natural geological systems.Therefore,generalized relaxation tests that explore the simultaneous changes of stress and strain with time under different stress levels with constant pore-water pressure are conducted in this study.The results show that in area I,area II,and area III,the stress and strain both change synchronously with time and show similar evolutionary laws as the strain-time curve for creep or the stress-time curve for relaxation.When the applied stress level surpasses the sci or scd threshold,the variations in stress and strain and their respective rates of change exhibit a significant increase.The radial deformation and its rate of change exhibit greater sensitivity in response to stress levels.The apparent strain deforms homogeneously at the primary stage,and subsequently,gradually localizes due to the microcrack development at the secondary stage.Ultimately,interconnection of the microcracks causes the formation of a shear-localization zone at the tertiary stage.The strain-time responses inside and outside the localization zone are characterized by local strain accumulation and inelastic unloading during the secondary and tertiary stages,respectively.The width of the shear-localization zone is found to range from 4.43 mm to 7.08 mm and increased with a longer time-to-failure.Scanning electron microscopy(SEM)reveals a dominant coalescence of intergranular cracks on the fracture surface,and the degree of physiochemical deterioration caused by water-rock interaction is more severe under a longer lifetime.The brittle sandstone’s time-dependent deformation is essentially controlled by microcrack development during generalized relaxation,and its expectancy-life is determined by its initial microstructural state and the rheological path.

A new method of new exact solutions and solitary wave-like solutions for the generalized variable coefficients Kadomtsev-Petviashvili equation

Using the solution of general Korteweg-de Vries （KdV） equation, the solutions of the generalized variable coefficient Kadomtsev-Petviashvili （KP） equation are constructed, and then its new solitary wave-like solution and Jacobi elliptic function solution are obtained.

SIMILARITY REDUCTIONS FOR 2+1-DIMENSIONAL VARIABLE COEFFICIENT GENERALIZED KADOMTSEV-PETVIASHVILI EQUATION

With the aid of MATHEMATICA, the direct reduction method,vas extended and applied in 2 + 1-dimensional variable coefficient generalized Kadomtsev-Petviashvili equation( VCGRPE). As a result, several kinds of similarity reductions for VCGKPE are obtained which contain Painleve I, Painleve II and Painleve ni reductions.

Uphillshift decision strategy of an AMT off-road vehicle based on generalized road resistance coefficient

In order to improve the shift decision strategy for an off-road vehicle with automated manual transmission（AMT）,the generalized road resistance coefficient is defined based on the longitudinal dynamics analysis.Vehicle mass and generalized road resistance coefficient are estimated using the recursive least square（RLS）method with multiple forgetting factors.The improved shift schedule is designed based on the generalized road resistance coefficient under uphill road condition.The simulation and real vehicle test verify the effectiveness of improved shift strategy and the improvement of vehicle dynamic performance.

Direct Reduction and Exact Solutions for Generalized Variable Coefficients 2D KdV Equation under Some Integrability Conditions

在同类的平衡(HB ) 之中基于关上的连接方法和 ClarksonKruskal (CK ) 方法，我们学习概括可变系数 2D KdV 方程的类似减小。同时，这在在可变系数之间的一些 integrability 条件下面导致在平常的微分方程形式的直接减小，这被显示出。二个不同盒子被讨论了，为那些平常的微分方程的解决方案的搜索产出在在可变系数之间的一些限制下面的许多准确旅行和在夸张、三角法的函数形式的 solitonic 波浪解决方案。

ASSESSMENT OF LOCAL INFLUENCE FOR GENERALIZED CORRELATION COEFFICIENTS

In this paper, we study local influence analysis for Zhang's generalized correlation coefficients and Hotelling's generalized correlation coefficient by using approach. of local influence analysis suggested by Shi (1991), i.e., generalized influence function (GIF) and generalized Cook distance (GCD). An example is given to illustrate our results.

A Generalized Variable-Coefficient Algebraic Method Exactly Solving （3＋1）-Dimensional Kadomtsev-Petviashvilli Equation

A generalized variable-coefficient algebraic method is applied to construct several new families of exact solutions of physical interestfor (3+1)-dimensional Kadomtsev-Petviashvilli (KP) equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.

Exact Solutions of Generalized Burgers-Fisher Equation with Variable Coefficients

The generalized Riccati equation vational expansion method is extended in this paper. Several exact solutions for the generalized Burgers-Fisher equation with variable coefficients are obtained by this method, and some of which are derived for the first time. It is concluded from the results that this approach is simple and efficient even in solving partial differential equations with variable coefficients.

Stochastic back analysis of permeability coefficient using generalized Bayesian method

Owing to the fact that the conventional deterministic back analysis of the permeability coefficient cannot reflect the uncertainties of parameters, including the hydraulic head at the boundary, the permeability coefficient and measured hydraulic head, a stochastic back analysis taking consideration of uncertainties of parameters was performed using the generalized Bayesian method. Based on the stochastic finite element method （SFEM） for a seepage field, the variable metric algorithm and the generalized Bayesian method, formulas for stochastic back analysis of the permeability coefficient were derived. A case study of seepage analysis of a sluice foundation was performed to illustrate the proposed method. The results indicate that, with the generalized Bayesian method that considers the uncertainties of measured hydraulic head, the permeability coefficient and the hydraulic head at the boundary, both the mean and standard deviation of the permeability coefficient can be obtained and the standard deviation is less than that obtained by the conventional Bayesian method. Therefore, the present method is valid and applicable.

Similarity Solutions for Generalized Variable Coefficients Zakharov-Kuznetsov Equation under Some Integrability Conditions

在这份报纸，对称方法被带了在上到概括可变系数 ZakharovKuznetsov 方程。无穷小的对称和最佳的系统被推出，从这个最佳的系统，七基本的域是坚定的，并且为在最佳的系统的每向量域，系数的可被考虑的表格被发现，这也导致我们在二个变量把给定的方程转变成部分微分方程。在使用一些引用转变以后，提及的部分微分方程最后归结为平常的微分方程。为那些方程的答案的搜索在大多数情况中产出许多准确答案。

Wronskian and Grammian Solutions for Generalized (n + 1)-Dimensional KP Equation with Variable Coefficients

The generalized (n + 1)-dimensional KP equation with variable coefficients is investigated in this paper. The bilinear form of the equation has been obtained by the Hirota direct method. In addition, with the help of Wronskian technique and the Pfaffian properties, Wronskian and Grammian solutions have been generated.

The Use of Yanai’s Generalized Coefficient of Determination to Reduce the Number of Variables in DEA Models

This paper proposes a new method to reduce the dimensionality of input and output spaces in DEA models. The method is based on Yanai’s Generalized Coefficient of Determination and on the concept of pseudo-rank of a matrix. In addition, the paper suggests a rule to determine the cardinality of the subset of selected variables in a way to gain the maximal discretionary power and to suffer a minimal informational loss.

Generalized Likelihood Ratio Tests for Varying-Coefficient Models with Censored Data

In this paper, we extend the generalized likelihood ratio test to the varying-coefficient models with censored data. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows a distribution, with the scale constant and the number of degree of freedom being independent of nuisance parameters or functions, which is called the wilks phenomenon. Both simulated and real data examples are given to illustrate the performance of the testing approach.

Extended Symmetry of Generalized Variable-Coefficient Kadomtsev-Petviashvili Equation

In this paper, the extended symmetry of generalized variable-coefficient Kadomtsev-Petviashvili (vcKP)equation is investigated by the extended symmetry group method with symbolic computation. Then on the basis of theextended symmetry, we can establish relation among some different kinds of vcKP equations. Thus the exact solutionsof these veKP equations can be constructed via the simple vcKP equations or constant-coefficient KP equations.

Exact Solutions to the Generalized Dispersive Long Wave Equation with Variable Coefficients

By using the homogeneous balance principle(HBP),we derive a B■cklund trans- formation(BT)to the generalized dispersive long wave equation with variable coefficients. Based on the BT,we give many kinds of the exact solutions of the equatioh,such as,single solitary solutions,multi-soliton solutions and generalized exact solutions.

EXACT SOLUTIONS FOR GENERAL VARIABLE-COEFFICIENT KdV EQUATION

By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

A General Calculating Method of Rotor’s Torsional Stiffness Based on Stiffness Influence Coefficient

In order to develop a general calculating rotor’s torsional stiffness based on stiffness influence coefficient for different rotor assembling, the calculation method of the torsional stiffness influence coefficient of equal thickness disc is researched in this paper at first. Then the torsional stiffness influence coefficient λ of equal thickness disc is fit to a binary curved face and a calculation equation is obtained based on a large quantity of calculating data, which lays the foundation for research on a general calculating method of rotor torsional stiffness. Thirdly a simplified calculation method for equivalent stiffness diameter of stepped equal thickness disc and cone disc in the steam turbine generators is suggested. Finally a general calculating program for calculating rotor’s torsional vibration features is developed, and the torsional vibration features of a verity of steam turbine rotors are calculated for verification. The calculating results show that stiffness influence coefficient λ of equal-thickness disc depends on parameters of B and H, as well as the stiffness influence coefficient λ;and discs with complex structure can be simplified to equal-thickness discs with little error by using the method suggested in this paper;error can be controlled within 1% when equivalent diameter of stiffness is calculated by this method.