A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.

Inverse problem of elastica of a variable-arc-length beam subjected to a concentrated load

An inverse problem of elastica of a variable-arclength beam subjected to a concentrated load is investigated. The beam is fixed at one end, and can slide freely over a hinge support at the other end. The inverse problem is to determine the value of the load when the deflection of the action point of the load is given. Based on the elasitca equations and the elliptic integrals, a set of nonlinear equations for the inverse problem are derived, and an analytical solution by means of iterations and Quasi-Newton method is presented. From the results, the relationship between the loads and deflections of the loading point is obtained.

IMPROVEMENTS ON THE ARC-LENGTH-TYPE METHOD

Arc-length-type and energy-type methods are two main strategies used in structural nonlinear tracing analysis, but the former is widely used due to the explicitness and clarity in conception, as well as the convenience and reliability in calculation. It is very important to trace the complete load-deflection path in order to know comprehensively the characteristics of structures subjected to loads. Unfortunately, the nonlinear analysis techniques are only workable for tracing the limit-point-type equilibrium path. For the bifurcation-point-type path, most of them cannot secure a satisfactory result. In this paper, main arc-length-type methods are reviewed and compared, and the possible reasons of failures in tracing analysis are briefly discussed. Some improvements are proposed, a displacement perturbation method and a force perturbation method are presented for tracing the bifurcation-point-type paths. Finally, two examples are analyzed to verify the ideas, and some conclusions are drawn with respect to the arc-length-type methods.

AN IMPROVED ARC-LENGTH METHOD AND APPLICATION IN THE POST-BUCKLING ANALYSIS FOR COMPOSITE STRUCTURES

Based on the conventional arc-length method, an improved arc-length method with high-efficiency is proposed. The weighted modifications with respect to the variation of structural stiffness and extra-interpolation modification by using the information of known equilibrium points are introduced to improve the incremental arc-length. An approximate expansion method for the accumulated and expected arc-length is used to ensure the convergence at given load levels in large range of applications. Numerical results show that the improved arc-length method has well adaptability and higher efficiency in the post-buckling analysis of plates and shells structures for tracing whole load-deflection path and obtaining the convergence values at any specified load levels.

Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave

A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity.By introducing the arc-length parameter,the pseudo arc-length method(PALM)smoothens the discontinuous solution in the arc-length space.This in turn weakens the singularity of the equation.To avoid constructing a high-order scheme directly in the deformed physical space,the entire calculation process is conducted in a uniform orthogonal arc-length space.Furthermore,to ensure the stability of the equation,the time step is reduced by limiting the moving speed of the mesh.Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves,it maintains a high computational efficiency.The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution.

What Projective Angle Makes the Arc-Length of the Trajectory in a Resistive Media Maximum? A Reverse Engineering Approach

We consider the motion of a massive point-like projectile thrown with initial velocity with respect to horizontal in a two-dimensional vertical plane under the influence of gravity in a viscose media. Two different velocity-dependent resistive media models are considered—linear and quadratic. With an objective to utilizing a Computer Algebra System (CAS), specifically Mathematica [1] numerically we solve the corresponding equations of motions. For a set of compatible parameters characterizing viscose forces graphically we display comparing the trajectories explicitly showing the impact of the models. Utilizing the model-dependent trajectory equations numerically we evaluate their associated arc-lengths. What distinguishes our approach vs. the existing body of work is the notion of the “reverse engineering”. Meaning, utilizing our numeric data we establish their corresponding analytic counter parts. Ultimately, utilizing both outputs numerically and analytically we determine the matching initial projectile angles maximizing their respective arc-lengths.

Stability analysis of slope in strain-softening soils using local arc-length solution scheme

Soils with strain-softening behavior — manifesting as a reduction of strength with increasing plastic strain — are commonly found in the natural environment. For slopes in these soils,a progressive failure mechanism can occur due to a reduction of strength with increasing strain. Finite element method based numerical approaches have been widely performed for simulating such failure mechanism,owning to their ability for tracing the formation and development of the localized shear strain. However,the reliability of the currently used approaches are often affected by poor convergence or significant mesh-dependency,and their applicability is limited by the use of complicated soil models. This paper aims to overcome these limitations by developing a finite element approach using a local arc-length controlled iterative algorithm as the solution strategy. In the proposed finite element approach,the soils are simulated with an elastoplastic constitutive model in conjunction with the Mohr-Coulomb yield function. The strain-softening behavior is represented by a piece-wise linearrelationship between the Mohr-Coulomb strength parameters and the deviatoric plastic strain. To assess the reliability of the proposed finite element approach,comparisons of the numerical solutions obtained by different finite element methods and meshes with various qualities are presented. Moreover,a landslide triggered by excavation in a real expressway construction project is analyzed by the presented finite element approach to demonstrate its applicability for practical engineering problems.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

C^2 CONTINUOUS NEARLY ARC-LENGTH PARAMETERIZED CURVE

An efficient method for C2 nearly arc-length parameterized curve is presented.An idea of approximation for the arc-length function of parametric curve which interpolates CAD data points is discussed.The parameterization is implemented by using parameter transformation.Finally,two numerical examples are given.

脉冲放电破岩等离子体通道长度预测方法

针对高压脉冲放电破岩电弧等离子体通道长度难以预测的问题,构建了高压脉冲放电破岩综合试验平台,测量了花岗岩-自来水组合介质下电弧等离子体通道发展特性及典型电流、电压参数,提取了不同电极间距和脉冲放电次数下岩石表面形成的破碎区域。基于能量平衡方程建立了岩石中电弧等离子体通道的阻抗模型,采用迭代优化算法获取阻抗模型参数的近似最优解,模型计算结果与试验结果的相对误差小于7%。基于优化参数,利用实测电流电压数据预测了等离子体通道的长度。模型预测的等离子体通道长度与实测值的绝对误差均处于毫米量级,且两者的相对误差小于10%,为高压脉冲放电破岩系统电源-电极负载的匹配设计提供了理论支撑。

共旋梁单元几何非线性分析的子结构方法

采用有限元方法分析结构的非线性行为必须进行多次迭代求解,因此在保证非线性计算精度的同时提高其计算效率是关键。该文以内含2个平面梁单元的子结构为例,建立一种平面梁结构基于共旋法与子结构的几何非线性分析方法。共旋法具有将刚体位移从结构的大位移中扣除而得到准确的小变形的特点,子结构法则能将内部节点的自由度凝聚到边界节点从而大大减少结构非线性平衡方程组的阶数,该文将两者结合并利用有较好的通过荷载和位移极限点功能的修正弧长法编制了计算程序,对荷载-位移曲线具有“位移跳跃”或“荷载跌落”显著特征的数个算例进行分析,与已有文献的结果对比验证了方法及程序的正确性。

基于杆系离散元理论的结构屈曲显式弧长法研究

基于杆系离散元理论,提出了一种显式弧长法用于结构弹性屈曲全过程分析。建立了新型接触单元-铰固接触单元的本构模型,分别采用离散元法和结构力学方法对铰固接触单元在已知端部位移工况下进行受力分析,并通过端部内力相等建立方程,推导了接触刚度系数;采用动力阻尼技术简化了颗粒运动方程的求解过程,然后引入总位移约束弧长法,详细阐述了与离散元法相结合的求解策略和实施过程,并给出了相关分析参数的计算公式;通过算例验证了该方法的准确性和适用性。在追踪结构屈曲平衡路径时,该方法无需组集刚度矩阵、不涉及矩阵奇异等不收敛问题,且参数少、稳定性好,与传统有限元弧长法相比更具优越性,为结构分析提供了新的算法工具。

海洋纤维增强柔性管压溃失效特性研究及参数敏感性分析

以一种黏结型的纤维增强柔性管作为研究对象,基于ABAQUS建立纤维增强柔性管的实体单元模型。根据二维Hashin失效判据判断柔性管失效情况,充分考虑管道内外护套层塑性及纤维增强层复合材料渐进失效,建立纤维增强柔性管的压溃数值模型。将特征值法与弧长法相结合,计算得到了较为精准的纤维增强柔性管临界压溃压力及对应的外压—椭圆度曲线;并对影响柔性管临界压溃压力的几个敏感性参数如椭圆度、纤维缠绕角度、直线度进行分析。研究结果表明椭圆度和直线度偏差的增大及纤维缠绕角度的降低均会使柔性管的临界压溃压力下降,该结果对纤维增强柔性管的设计与使用均具有一定的参考意义。

Erratum to "Uniform Coverage of Fibres over Open-contoured Freeform Structure Based on Arc-length Parameter" [Chinese Journal of Aeronautics 21(2008)571-577]

It is regretted that the author corrections requested at the proof stage were not made accurately. There are some incorrect typings in two equations which will lead to inaccurate results if readers perform calculations directly

船用高强钢GMAW-P脉冲焊接参数对电弧弧长的影响研究

对690 MPa级船用结构钢GMAW-P脉冲焊接过程电弧行为进行研究,分析了脉冲参数对电弧长度的影响。一脉一滴所在的弧长区间为3~6 mm,一脉多滴所在的弧长区间为5~8 mm,一脉一滴到一脉多滴的过渡区为5~6 mm,短路过渡弧长小于2 mm。脉冲时间上升,弧长增长;脉冲电流上升,弧长呈先上升后下降趋势;脉冲频率增大,弧长变长;基值电流升高,弧长减小。

基于模态分析的矿热炉自焙电极测长方法研究

随着现代技术的发展,以往利用人工测量矿热炉电极长度的方法逐渐被多样化的计算机技术、传感器技术等所替代。提出了一种模态分析方法:将矿热炉自焙电极简化为一维简支梁,用力锤锤击矿热炉炉壁产生激励输入信号,由矿热炉电极筒壁传导到底层石墨电极,经过反射接收信号;利用多维振动建立多自由度运动方程,求解得到电极振动参数,再代入求解电极长度。利用模态分析法将自焙电极长度测量转化为电极筒长度测量,极大地降低了电极测长难度,同时避免了资源的过多损耗。该研究对提高矿热炉工业生产效率、减少资源损耗及环境污染具有促进作用。

一类弧长与弦长成比例的曲线的构造

从河流的弯曲现象出发,分别在平面直角坐标系与极坐标系下构造了一类弧段上任一点到起点的弧长与弦长成π倍的理想曲线,探讨了该类曲线的存在性与唯一性.最后,将所得结论推广至空间中弧长与弦长成k倍的情形.

复数高斯投影若干数学性质分析

为进一步研究基于复变函数表示的高斯投影解析公式及相关理论和定理,在高斯投影复变函数表示的基础上,给出高斯投影正解复数平行圈半径、长度比和子午线收敛角的新公式。其次推导出高斯投影和墨卡托投影、高斯投影和等角球平面投影的变换关系。最后对复数高斯投影的数学本质进行了分析,进一步丰富了高斯投影的复变函数理论。

子午线弧长正反解表达式3种形式的解析

为了分析不同表达式在计算效率方面的影响,给出了子午线弧长的3种表达形式,将其展开系数改写为第三扁率n的表达形式,并对不同形式的子午线弧长的截断误差进行计算分析,选取合适的项数,给出展开式的实用公式。结果表明,基于n表示的子午线弧长,其系数在分数形式上看起来位数更少,形式更简单,更便于推广使用;当正解精度为毫米时,展开式只需保留前4项即可满足精度,当反解精度为0.0001″时,展开式只需保留前4项即可满足精度;对于3种表达形式,二倍角形式计算效率最高,因此建议在子午线弧长正反解过程中采用二倍角形式。

基于高参数均匀性的叶片曲面光顺造型方法

为进一步优化叶片的曲面模型质量,提出一种基于高参数均匀性的叶片曲面光顺建模方法。首先根据叶片的曲率特征,将单层数据点分成叶盆、叶背、前缘和后缘4个部分,通过叶片前缘和后缘的曲线拟合,获得拟合圆圆心,并以此生成叶片中弧线的诱导曲线。进而通过改进的牛顿迭代法获得一系列叶片截面轮廓线内切圆圆心,从而获得中弧线,对中弧线进行光顺处理以及弧长参数化,并利用中弧线-厚度分布的方式,结合过渡曲线生成光顺的截面轮廓线,保证过渡处曲率连续。最后,通过放样及融合优化算法快速自动地生成光顺的叶片曲面模型。利用该方法对某型号发动机叶片数据点进行曲面造型与加工验证,结果表明,优化后的曲面模型具有良好的光顺性,避免了由于模型不光顺导致的刀轨波动问题。