Development of Cubic Bezier Curve and Curve-Plane Intersection Method for Parametric Submarine Hull Form Design to Optimize Hull Resistance Using CFD

Optimization analysis and computational fluid dynamics （CFDs） have been applied simultaneously, in which a parametric model plays an important role in finding the optimal solution. However, it is difficult to create a parametric model for a complex shape with irregular curves, such as a submarine hull form. In this study, the cubic Bezier curve and curve-plane intersection method are used to generate a solid model of a parametric submarine hull form taking three input parameters into account： nose radius, tail radius, and length-height hull ratio （L/H）. Application program interface （API） scripting is also used to write code in the ANSYS DesignModeler. The results show that the submarine shape can be generated with some variation of the input parameters. An example is given that shows how the proposed method can be applied successfully to a hull resistance optimization case. The parametric design of the middle submarine type was chosen to be modified. First, the original submarine model was analyzed, in advance, using CFD. Then, using the response surface graph, some candidate optimal designs with a minimum hull resistance coefficient were obtained. Further, the optimization method in goal-driven optimization （GDO） was implemented to find the submarine hull form with the minimum hull resistance coefficient （Ct）. The minimum C, was obtained. The calculated difference in （7, values between the initial submarine and the optimum submarine is around 0.26%, with the C, of the initial submarine and the optimum submarine being 0.001 508 26 and 0.001 504 29, respectively. The results show that the optimum submarine hull form shows a higher nose radius （rn） and higher L/H than those of the initial submarine shape, while the radius of the tail （r1） is smaller than that of the initial shape.

An efficient cubic trigonometric B-spline collocation scheme for the time-fractional telegraph equation

In this paper,a proficient numerical technique for the time-fractional telegraph equation(TFTE)is proposed.The chief aim of this paper is to utilize a relatively new type of B-spline called the cubic trigonometric B-spline for the proposed scheme.This technique is based on finite difference formulation for the Caputo time-fractional derivative and cubic trigonometric B-splines based technique for the derivatives in space.A stability analysis of the scheme is presented to confirm that the errors do not amplify.A convergence analysis is also presented.Computational experiments are carried out in addition to verify the theoretical analysis.Numerical results are contrasted with a few present techniques and it is concluded that the presented scheme is progressively right and more compelling.

Performance of global look-up table strategy in digital image correlation with cubic B-spline interpolation and bicubic interpolation

Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.

On the Parametric Modeling of Turbine Blade Section Curve

Geometric parameters of the turbine blade are classified according to their destined functions, and the mathematical definition of those parameters in the section curve is introduced in detail. Some parts of the section curve shape can be adjusted freely, offering more flexibility to designers.

Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation

This work is concerned with the application of a redefined set of extended uniform cubic B-spline(RECBS)functions for the numerical treatment of time-fractional Telegraph equation.The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid.Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure.The derivation of uniform convergence has also been presented.Some computational experiments are executed to verify the theoretical considerations.Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.

Parametric Selection and Continual Combination of Building Surface

A method to reparametrize G retional curve to obtain a C^1 curve is given. A practical G^1 continual connective between adjacent NURUS patches along common guadratic boundary curve is presented in this paper, and a specific algorithm for control points and weights of NURBS patches is discussed.

Estimation of the water–oil–gas relative permeability curve from immiscible WAG coreflood experiments using the cubic B-spline model

Immiscible water-alternating-gas（WAG） flooding is an EOR technique that has proven successful for water drive reservoirs due to its ability to improve displacement and sweep efficiency.Nevertheless,considering the complicated phase behavior and various multiphase flow characteristics,gas tends to break through early in production wells in heterogeneous formations because of overriding,fingering,and channeling,which may result in unfavorable recovery performance.On the basis of phase behavior studies,minimum miscibility pressure measurements,and immiscible WAG coreflood experiments,the cubic B-spline model（CBM） was employed to describe the three-phase relative permeability curve.Using the Levenberg-Marquardt algorithm to adjust the vector of unknown model parameters of the CBM sequentially,optimization of production performance including pressure drop,water cut,and the cumulative gas-oil ratio was performed.A novel numerical inversion method was established for estimation of the water-oil-gas relative permeability curve during the immiscible WAG process.Based on the quantitative characterization of major recovery mechanisms,the proposed method was validated by interpreting coreflood data of the immiscible WAG experiment.The proposed method is reliable and can meet engineering requirements.It provides a basic calculation theory for implicit estimation of oil-water-gas relative permeability curve.

Shape Control and Modification of Rational Cubic B-Spline Curves

This paper considers the construction of a rational cubic B-spline curve that willinterpolate a sequence of data points x'+ith specified tangent directions at those points. It is emphasisedthat the constraints are purely geometrical and that the pararnetric tangent magnitudes are notassigned as in many' curl'e manipulation methods. The knot vector is fixed and the unknowns are thecontrol points and x'eightsf in this respect the technique is fundamentally different from otherswhere knot insertion is allowed.First. the theoretical result3 for the uniform rational cubic B-spline are presented. Then. in theplanar case. the effect of changes to the tangent at a single point and the acceptable bounds for thechange are established so that all the weights and tangent magnitUdes remain positive. Finally, aninteractive procedure for controlling the shape of a planar rational cubic B-spline curve is presented.

Displacement Response Reconstruction of Slender Flexible Structures Based on Cubic Spline Fitting Method

How to reconstruct a dynamic displacement of slender flexible structures is the key technology to develop smart structures and structural health monitoring(SHM), which are beneficial for controlling the structural vibration and protecting the structural safety. In this paper, the displacement reconstruction method based on cubic spline fitting is put forward to reconstruct the dynamic displacement of slender flexible structures without the knowledge of modeshapes and applied loading. The obtained strains and displacements are compared with the results calculated by ABAQUS to check the method's validity. It can be found that the proposed method can accurately identify the strains and displacement of slender flexible structures undergoing linear vibrations, nonlinear vibrations, and parametric vibrations. Under the concentrated force, the strains of slender flexible structures will change suddenly along the axial direction. With locally densified measurement points, the present reconstruction method still works well for the strain concentration problem.

星载共口径多波束赋形反射面天线设计

为了满足星载通信中多任务并行需求,提出了一种由格里高利型反射面和三个馈源喇叭天线组成的共口径多波束反射面天线,该天线能够产生两个固定轮廓波束和一个点波束。天线设计是采用射线追踪法确定点波束馈源位置以建立天线基础结构,并通过Zernike多项式和Cubic B-splines函数共同对主、副反射面进行赋形优化来完成。为了验证该方法的有效性,对口径为1.1 m的天线进行仿真设计,结果表明两个赋形轮廓波束在Ku收、发频段边缘增益(EOC gain)分别为27.7、28.0、28.0、28.2 dBi,固定点波束在服务区EOC gain不低于34 dBi并且在0~6.5°范围内的扫描波束增益不低于35 dBi。

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation.Experimental results are presented to show the advantages of the proposed algorithms.

齿轮啮合过程中载荷、应力及磨损的计算机模拟

利用边界元的基本思想 ,将边界曲线离散成许多单元和结点 ,对这些离散点进行啮合和磨损分析 ,提出了用参数三次样条曲线来模拟磨损后的齿面 ,实现了对任意啮合点磨损量的计算。本文编制了一系列的软件 ,实现了用计算机进行齿轮啮合过程中载荷、应力及磨损的动态模拟 。

渐开线圆柱齿轮啮合过程中磨损的计算机仿真

利用边界元的基本思想,渐开线直齿圆柱齿轮可以简化到端面进行分析,从而将空间啮合问题转化为平面啮合问题.将边界曲线离散成许多单元和结点,对这些离散点进行啮合和磨损分析,提出了用参数三次样条曲线来模拟磨损后的齿面,实现了对任意啮合点磨损量的计算.编制了一系列的软件,实现了用计算机对齿轮啮合过程中的载荷、应力及磨损进行动态模拟。

基于离散点截形螺旋面加工原理研究

提出了基于离散点的圆柱螺旋面成形刀具计算方法,分别建立了已知螺旋面工件截形离散点数据计算成形刀具廓型的数学模型及已知刀具截形离散点数据计算由其加工的螺旋面工件的数学模型。利用累积三次参数样条法计算螺旋面工件截形及成形刀具廓型各离散点的倾斜角。分析了成形刀具的计算误差,对成形刀具数据型值点以累积三次参数样条进行插值,用双圆弧样条拟合的方法进行光顺处理。实例证明,两模型是正确性的、可行的,能够满足离散点条件下螺旋面高效率、高精度的加工要求。

一组基于三角函数的类三次参数曲线

给出了一组基于函数空间{1,sin,cos,sin2}的类三次三角参数曲线,称之为QCT-曲线,主要包括QCT-Ferguson曲线、QCT-Bézier曲线及均匀QCT-B样条曲线。讨论了QCT-曲线的性质、应用及相互之间的关系。事实表明,QCT-曲线不仅具有三次多项式曲线的诸多性质,而且在一定条件下可相互转化。另外,QCT-曲线无需有理形式即可精确地表示圆、椭圆、抛物线等二次曲线弧。

基于非线性输出频响函数的NES动力学参数设计

基于非线性输出频率响应函数(Nonlinear Output Frequency Response Function,NOFRF),对引入了被动非线性消振器(Nonlinear Energy Sink,NES)的单自由度振动系统进行了分析,从频域分析的角度评价NES的振动抑制效果,对其进行动力学参数设计。首先,建立了引入NES的振动系统非线性动力学模型。然后,通过数值仿真,对单自由度系统进行了非线性输出频率响应函数分析和输出频率响应分析,从频域分析的角度解释了在原振动系统中引入NES对原系统固有频率几乎没有影响的原因。最后,通过分析NES各参数对振动抑制效果的影响,对NES进行了动力学参数设计。本文得出的分析结果对于工程领域中NES的设计具有非常重要的指导意义。

确定土体前期固结压力的非参数化拟合模型

土体前期固结压力是判断土体固结状态的一个重要指标。对不同固结状态的土,其沉降计算公式不同,准确确定土体前期固结压力非常重要。在采用常规参数化模型进行e-lgp曲线拟合求解最大曲率点不完善的基础上,提出了非参数化模型——3次平滑样条曲线进行拟合的方法,计算表明:该模型对试验数据适应性好,拟合精度高。基于卡萨格兰德确定前期固结压力的方法,通过MATLAB语言编制了相应的计算程序PCP Calculation,程序界面友好,可准确绘制图形,计算结果令人满意。

基于CAD/CAM技术的机器人连续轨迹规划

在复杂零件造型及弧焊中,提出了基于CAD/CAM技术的机器人连续轨迹规划算法。该算法利用CAM中的造型及铣加工功能模块获得待加工工件表面信息,然后综合考虑机器人系统加工精度和加工速度的要求,采用累加弦长的三次参数B样条算法,调整和优化工艺参数,并将CNC轨迹转化成机器人运动轨迹。实验证明,该算法所生成的连续轨迹运动精度更高,运行更平稳,可满足面向复杂轮廓的现代高速高精度的机械加工要求。

基于计算机辅助测量的隧道断面测量新方法

介绍了如何将三次参数样条插值法运用到铁路隧道断面轮廓曲线拟合的过程,及如何计算出轮廓曲线的数学表达式,并利用所求方程,对隧道断面面积进行计算,实现了其与标准隧道断面的比较,计算出了实际断面的超、欠挖面积和体积。在算法基础上,设计开发出一个应用系统———计算机辅助隧道断面测量系统,通过实验验证了该方法的正确性。这一方法的应用,将断面量测与洞室位移监测相结合,实现了隧道断面测量的数字化,改进了传统隧道断面的验收工作,降低了其外业难度,提高了测量精度。

三次参数曲线的区间扩展

为了在传统三次参数曲线中引入形状参数,通过将三次Ferguson曲线、三次Bézier曲线、三次均匀B样条曲线等传统三次参数曲线的定义区间由固定区间[0,1]扩展为动态区间[0,α],构造了3种带参数α的三次参数曲线,分别称之为三次α-Ferguson曲线、三次α-Bézier曲线以及三次均匀α-B样条曲线.所构造的α-曲线是原三次参数曲线的同次扩展,不仅方程结构简单,继承了原曲线的性质,而且可通过修改参数α的值实现对曲线形状的调整,是一种简单有效的形状可调参数曲线构造方法.