Semi-analytical solution for drained expansion analysis of a hollow cylinder of critical state soils

The expansion of a thick-walled hollow cylinder in soil is of non-self-similar nature that the stress/deformation paths are not the same for different soil material points.As a result,this problem cannot be solved by the common self-similar-based similarity techniques.This paper proposes a novel,exact solution for rigorous drained expansion analysis of a hollow cylinder of critical state soils.Considering stress-dependent elastic moduli of soils,new analytical stress and displacement solutions for the nonself-similar problem are developed taking the small strain assumption in the elastic zone.In the plastic zone,the cavity expansion response is formulated into a set of first-order partial differential equations(PDEs)with the combination use of Eulerian and Lagrangian descriptions,and a novel solution algorithm is developed to efficiently solve this complex boundary value problem.The solution is presented in a general form and thus can be useful for a wide range of soils.With the new solution,the non-self-similar nature induced by the finite outer boundary is clearly demonstrated and highlighted,which is found to be greatly different to the behaviour of cavity expansion in infinite soil mass.The present solution may serve as a benchmark for verifying the performance of advanced numerical techniques with critical state soil models and be used to capture the finite boundary effect for pressuremeter tests in small-sized calibration chambers.

ASYMPTOTIC ERROR EXPANSIONS OF QUADRATIC SPLINE COLLOCATION SOLUTIONS FOR TWO-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the following problem:The quadratic spline collocation, with uniform mesh and the mid-knot points are taken as the collocation points for this problem is considered. With some assumptions, we have proved that the solution of the quadratic spline collocation for the nonlinear problem can be written as a series expansions in integer powers of the mesh-size parameter. This gives us a construction method for using Richardson’s extrapolation. When we have a set of approximate solution with different mesh-size parameter a solution with high accuracy can he obtained by Richardson’s extrapolation.

Toroidal Multipolar Expansion for Fast L-Mode Plasma Boundary Reconstruction in EAST

A new method for plasma boundary reconstruction, based on the toroidal multipolar expansion （TME） scheme, is applied successfully in EAST. TME applies a limited number of toroidal multipolar moments based on toroidal coordinates to treat a two-dimensional problem of axisymmetric plasma equilibrium. The plasma boundary reconstructed by TME is consistent with the results by using EFIT. The method is sufficiently reliable and fast for real time shape control.

THE ASYMPTOTIC EXPANSIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS

In this paper we study the singularly penurbed boundary value problem: where e is a positive small parameter In the conditions: we prove the existences, and uniformly valid asymptotic expansions of solutions for the given boundary value problems, and hence we improve the existing results.

Analytical solutions for finite cylindrical dynamic cavity expansion in compressible elastic-plastic materials

Analytical solutions for the dynamic cylindrical cavity expansion in a com-pressible elastic-plastic cylinder with a finite radius are developed by taking into account of the effect of lateral free boundary, which are different from the traditional cavity expan-sion models for targets with infinite dimensions. The finite cylindrical cavity expansion process begins with an elastic-plastic stage followed by a plastic stage. The elastic-plastic stage ends and the plastic stage starts when the plastic wave front reaches the lateral free boundary. Approximate solutions of radial stress on cavity wall are derived by using the Von-Mise yield criterion and Forrestal’s similarity transformation method. The effects of the lateral free boundary and finite radius on the radial stress on the cavity wall are discussed, and comparisons are also conducted with the finite cylindrical cavity expansion in incompressible elastic-plastic materials. Numerical results show that the lateral free boundary has significant influence on the cavity expansion process and the radial stress on the cavity wall of metal cylinder with a finite radius.

ON THE COEFFICIENTS OF DIFFERENTIATED EXPANSIONS AND DERIVATIVES OF CHEBYSHEV POLYNOMIALS OF THE THIRD AND FOURTH KINDS

Two new analytical formulae expressing explicitly the derivatives of Chebyshev polynomials of the third and fourth kinds of any degree and of any order in terms of Chebyshev polynomials of the third and fourth kinds themselves are proved. Two other explicit formulae which express the third and fourth kinds Chebyshev expansion coefficients of a general-order derivative of an infinitely differentiable function in terms of their original expansion coefficients are also given. Two new reduction formulae for summing some terminating hypergeometric functions of unit argument are deduced. As an application of how to use Chebyshev polynomials of the third and fourth kinds for solving high-order boundary value problems, two spectral Galerkin numerical solutions of a special linear twelfth-order boundary value problem are given.

Numerical Solution of the Coupled Viscous Burgers’ Equation Using Differential Quadrature Method Based on Fourier Expansion Basis

The differential quadrature method based on Fourier expansion basis is applied in this work to solve coupled viscous Burgers’ equation with appropriate initial and boundary conditions. In the first step for the given problem we have discretized the interval and replaced the differential equation by the Differential quadrature method based on Fourier expansion basis to obtain a system of ordinary differential equation (ODE) then we implement the numerical scheme by computer programing and perform numerical solution. Finally the validation of the present scheme is demonstrated by numerical example and compared with some existing numerical methods in literature. The method is analyzed for stability and convergence. It is found that the proposed numerical scheme produces a good result as compared to other researcher’s result and even generates a value at the nodes or mesh points that the results have not seen yet.

Multi-objective Transmission Expansion Planning Considering Life Cycle Cost

为克服目前全寿命周期成本（life cycle cost,LCC）技术的应用局限于设备运行或维护阶段的不足,针对输电网整体建立一个3维LCC层级模型,包括时间维度、元件维度和费用维度。费用维度进一步分解为设备级、系统级、外部环境成本。研究了以可靠性为中心的维护手段的应用对维护成本的影响,利用电量不足期望值计算故障成本。在此基础上,对风电等4种不确定因素进行建模,建立以LCC成本最小和切负荷量最小为多目标的输电网机会约束规划模型。采用正态边界交点算法联合改进小生境遗传算法,对模型有效求解。最后,分别对18节点系统和77节点系统进行算例分析。研究结果给出了帕累托解集及推荐的最优规划方案;此外,LCC费用分解图表明了各费用的比重和影响,有利于指导未来资产管理。

Implicit expansion rate of the Earth in global plate motions

Based on eight published plate motion models, we separately estimated the net area changes of tectonic plates and the area change of the solid Earth surface over geological time using the Euler vectors of plates with determined boundaries. Then, under the context of a currently expanding Earth, we inferred the change rate of the Earth’s mean radius from the estimated net area changes. The results show that the total increases and decreases in the areas of different plates cannot be compensated. Specifically, the area of the Northern Hemisphere decreases while that of the Southern Hemisphere increases, but the net area of the solid Earth surface slightly increases in th computing period(0.01 Ma). For the latest NNRMORVEL56 plate motion model, the area of the Southern Hemisphere increases by 7802 km2 while the area of the Northern Hemisphere decreases by 7711 km^2. This indicates a net area increase of 91 km2 in the solid Earth surface corresponding to an expansion rate of 0.06 mm/a for the Earths mean radius.This result coincides with the slow rate of expansion derived from geodetic measurements and geophysical modeling.

VECTOR WAVE FUNCTION EXPANSION FOR SOLVING ELECTROMAGNETIC SCATTERING BY BURIED OBJECTS

An analysis of solving the electromagnetic scattering by buried objects using vectorwave function expansion is presented.For expanding the boundary conditions both on the planarair-earth interface and on the spherical surface,the conversion relations between the cylindricaland spherical vector wave functions are derived.Hence the vector wave function expansion isconveniently applied to solve this complex boundary-value problem.For the excitation of the in-cident plane wave and the dipole above the earth,the scatterlng patterns of the buried conductingand dielectric spheres are presented and discussed.

Asymptotic Expansion of Temperature Close to a Singularity of a Plate

The thermal conduction in a thin laminated plate is considered here. The lateral surface of the plate is not regular. Consequently, the boundary of the middle plane admits a geometrical singularity. Close to the origin, the lateral edge forms an angle. We shall prove that the classical bidimensional problem associated with the thin plate problem is not valid. In this paper, using the boundary layer theory, we describe the local behavior of the plate, close to the perturbation.

乳腺癌放疗应用3D打印补偿膜的摆位误差及安全性影响

目的探讨乳腺癌根治术后放射治疗体表覆盖3D打印补偿膜后的摆位误差及安全性。方法收集滨州医学院附属医院2023年1—6月收治的29例乳腺癌放疗患者,治疗方式分为先后应用3D组织补偿膜两种方法。利用锥形束CT(CBCT)采集的图像分析三维方向上的摆位误差大小并计算计划靶区(PTV)的外放范围,以及急性放射性皮炎的发生率。结果X、Y、Z方向临床靶区(CTV)外扩至PTV边界分别为0.94、0.84、0.52 cm。X轴方向上身体质量指数(BMI)24 kg/m^(2)的摆位误差大于其余两组,差异有统计学意义(P<0.05);Z轴方向上≥28 kg/m^(2)的摆位误差24~28 kg/m^(2)组,差异有统计学意义(P<0.05);X轴方向上首次摆位误差显著小于分次间,差异有统计学意义(P<0.05)。先后应用补偿膜2级放射性皮炎发生率分别为3.45%、13.79%,差异有统计学意义(P<0.05)。结论对于BMI 24 kg/m^(2)的患者要关注X轴方向的摆位。为避免放射性皮炎的发生,尽量在治疗前15次添加补偿膜。

基于多项式混沌展开法的涡流无损检测高效元模型辅助探测概率的分析

探测概率对于量化涡流无损检测系统的检测能力非常重要。模型辅助探测概率的参数需要大量试验或仿真数据才可以确定,往往难以实现。应用基于退化核函数加速的边界元法的数值模型,提出使用基于普通最小二乘法的多项式混沌展开算法的元模型提升三维涡流无损检测问题探测概率的效率。通过有限截面线圈检测金属板面槽的算例,引入线圈位置和提离距离为不确定传播的参数,测试结果表明,该元模型预测的模型参数与基于退化核函数加速的边界元法物理模型计算的模型参数相对误差在1%以内,极大降低了所需的计算开销。

分散式速度反馈控制流激薄板声振响应的模态解及特性

采用模态展开法推导了湍流边界层和分散式速度反馈控制共同作用下薄板的响应和声辐射,给出了与分散式速度反馈控制增益系数、单元位置、数量和大小相关的模态阻尼的显示表达式。给定激励和参数的条件下,通过与元素法的计算结果进行对比,验证了模态展开法具有较高的计算效率和准确性。讨论了分散式速度反馈控制单元的布置方式和数量对模态阻尼的影响,以及反馈控制单元的布置方式对薄板动能、辐射声功率和模态平均辐射系数的影响。数值分析结果表明反馈控制单元的数量和布放位置对控制效果影响显著,反馈控制单元沿螺旋线布置能明显拓宽控制频带;两种反馈控制单元布置方式,在动能和辐射声功率控制较好的共振频率处,除第一阶模态外,模态平均声辐射效率随反馈增益的增大明显提高。

基于膨胀波效应的高超声速进气道肩部流动分离控制研究

为改善高超声速进气道唇口激波/附面层干扰诱导的肩部流动分离,从膨胀波及激波理论出发,推导出了膨胀波效应影响下的斜激波附面层干扰理论公式,获得了影响斜激波诱导分离的主要因素:膨胀角梯度、激波角及波前马赫数。在此基础上,开展了膨胀波效应影响下的流动分离控制研究,给出了膨胀波效应影响下斜激波诱导分离的判别及预测方法。结果表明:增大激波入射点处膨胀角梯度,可以显著减小甚至消除肩部流动分离;随着激波角增大,激波强度及逆压力梯度增加,分离区尺寸显著增大。而波前马赫数对分离区尺寸的影响不显著;在进口马赫数3.57~5.18,唇罩角度6°~10°范围内,当激波入射点处逆压比梯度小于250 m^(-1)时,斜激波诱导的流动分离消失,可为改善超声速/高超声速进气道内流道流动分离提供技术支撑。

不同地质超深基坑上下同步逆作法结构施工技术研究

上下同步逆作法在克服施工场地条件受限、有效缩短工程施工周期及环境保护方面,有着明显的优势。上下同步施工除应考虑场地的综合利用,为上下结构施工提供条件外,在实施过程中确保结构自身的安全性、围护体的可靠性更为重要。针对新作地下室外墙的逆作法施工工艺,总结了上部结构和核心筒的施工流程安排、不同地质上下同步施工分界层的选择、地下室水平和竖向构件的连接等关键技术,为类似工程的实施提供借鉴。

THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR ELLIPTIC EQUATIONS

In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansion in entire region is obtained.

SINGULARLY PERTURBED SEMI-LINEAR BOUNDARY VALUE PROBLEM WITH DISCONTINUOUS FUNCTION

A class of singularly perturbed semi-linear boundary value problems with discontinuous functions is examined in this article. Using the boundary layer function method, the asymptotic solution of such a problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is also proved. Numerical result is presented as an illustration to the theoretical result.

SINGULAR PERTURBATION OF BOUNDARY VALUE PROBLEM FOR QUASILINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS INVOLVING TWO SMALL PARAMETERS

The singularly perturbed boundary value problem for quasilinear third-order ordinary differential equation involving two small parameters has been considered. For the three cases epsilon/mu (2) --> 0(mu --> 0), mu (2)/epsilon --> 0(epsilon --> 0) and epsilon = mu (2), the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

Application of Boundary Collocation Method to Two-Dimensional Wave Propagation

Boundary Collocation Method （BCM） based on Eigenfunction Expansion Method （EEM）, a new numerical method for solving two-dimensional wave problems, is developed. To verify the method, wave problems on a series of beaches with different geometries are solved, and the errors of the method are analyzed. The calculation firmly confirms that the results will be more precise if we choose more rational points on the beach. The application of BCM, available for the problems with irregular domains and arbitrary boundary conditions, can effectively avoid complex calculation and programming. It can be widely used in ocean engineering.