流体力学中SPH算法张力不稳定性研究

将光滑粒子流体动力学(SPH)算法写成矩阵形式后,分别利用小量摄动和线性化来研究其张力不稳定性,并由前者得知SPH全离散格式误差扩散主要由常规误差扩散和误差相位扭曲构成,由后者得到了误差变化的线性关系和系统矩阵,且都可得到相同于Swegle的张力不稳定性充分条件。忽略连续性方程和本构方程的影响,得到系统矩阵的特征方程,并得到能近似表征张力不稳定性存在的矩阵。求解相邻三个粒子的系统的表征矩阵的特征值,发现它们因误差相位差异而存在鞍点、中心点、焦点三种情况。在波数K=π/?X下,得到了特征值满足误差稳定时初始光滑长度的合理取值;并指出了光滑长度更新与准不可压缩理论中人工声速选取与算法稳定性的关系。并通过该关系计算得到了Monaghan与Morris分别在利用准不可压缩理论模拟不可压缩流动时,为保证计算稳定而提出的密度变化率大小的经验值。     

拉伸正交各向异性有限宽板偏心圆孔的应力集中系数表达式

用近似解析方法推导出拉伸正交各向异性有限宽板偏心圆孔的应力集中系数的显式表达式,除了比较极端的情况外,该式的精度较好。误差估计基于与有限元分析结果的比较。当偏心度取为零,即变为有限宽板中心圆孔时,此简化情况下的应力集中系数表达式与文献值和有限元解吻合得很好。推导的方法虽然简单,但结果比较理想。利用所推导的表达式可以求解各向异性材料的应力集中系数问题。     

NORMALIZED SMOOTHING FUNCTIONS FOR SPH IMPACT COMPUTATIONS

This paper presents a normalized smoothing function (NSF) algorithm that can improve the accuracy of smooth particle hydrodynamics (SPH) impact computations. It is presented specifically for axisymmetric geometry, but the principles also apply to plane strain and three-dimensional geometry. The approach consists of adjusting the standard smoothing functions for every node (and every cycle) such that the normal strain rates are computed exactly for conditions of constant strain rates (linear velocity distributions). This, in turn, generally improves accuracy for non-uniform strain rates. This can significantly improve the accuracy for free boundaries, for non-uniform arrangements of SPH nodes, and for small smoothing distances. A new smoothing function is also introduced. The NSF algorithm is shown to provide improved accuracy for a series of cylinder impact examples that includes two different smoothing functions and two different smoothing distances.     

基于加速度泰勒展开的动力学方程显式积分方法

该文旨在提出兼顾适用性、可靠性与高效性的结构振动时域积分算法。基于加速度的泰勒展开式,引入截断系数考虑高阶项的影响,提出了具有4阶精度的加速度公式;通过积分并考虑典型时间步初始时刻系统动力平衡条件,建立了位移和速度的单步递推公式,运用终止时刻系统运动方程修正加速度。与多步积分法相比,单步积分法无需记录当前时间步以外时刻响应。稳定性分析表明,临界步长相比中心差分法增加40%。通过线性系统振动响应计算发现,当步长-系统固有周期（荷载周期）比达到0.2时,该文方法的振幅衰减率和周期延长率均小于5%;对于非线性系统,为降低算法阻尼和周期误差的影响,需控制步长周期比小于0.1。     

拉伸环向周期裂纹管的应力强度因子

利用裂纹非自发扩展的能量释放率,即G^*-积分理论分析求解了拉伸周期裂纹管应力强度因子问题,给出了周期裂纹管应力强度因子的系列解答.该解亦可作为开裂曲板应力强度因子的近似解.     

结构几何非线性分析中临界点的直接求解

结构非线性分析中解路径上的临界点是反映结构承载特性的重要参数。该文基于结构非线性解路径跟踪的弧长法提出一个以解路径弧长为参数,直接求解临界点的Newton法。该算法具有很好的求解精度,适用范围广,对于单重临界点和多重临界点问题均能有效解决。数值算例表明:该文方法准确、可靠、高效。     

域外奇点法分析薄板的弯曲和平面应力问题

本文首先给出了作者推导的两边简支无限长薄板弯曲问题和平面应力问题的基本解，然后运用域外奇点法及给出的基本解分析了一对边简支矩形薄板的弯曲和平面应力问题．计算结果表明，这种方法具有计算量少、精度高等优点。     

A thermo-visco-plastic damage model and SPH simulations of plugging failure

ABSTRACT

A thermo-visco-plasticity model, recently developed based on a microinertia driven dynamic flow rule, is exploited to account for damage due to fracture. This is accomplished by adjoining the equations for thermo-visco-plasticity, herein discretized through the smooth particle hydrodynamics (SPH), with a “pseudospring” based discrete damage model. In treating ductile fractures, this coupled material model accounts for the inertia associated with moving microstructural defects and time lags for the dissipative fluxes to attain the steady state. In this approach, while the microinertia-driven flow rule provides a vehicle to evolve plastic strain, pseudosprings are exploited to treat material damage and the resulting reduced force transfer. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic-strain/damage parameters, and thus the numerical implementation avoids a computationally intensive return mapping. We demonstrate the performance of the proposed model through SPH-based numerical simulations and also undertake a validation exercise against experimental observations from gas-gun penetration tests on an 8-mm thick Weldox 460 E steel plate.     

Normalized SPH with stress points

Smoothed particle hydrodynamics is extended to a normalized, staggered particle formulation with boundary conditions. A companion set of interpolation points is introduced that carry the stress, velocity gradient, and other derived field variables. The method is stable, linearly consistent, and has an explicit treatment of boundary conditions. Also, a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement. Test problems show that these improvements lead to increased accuracy and stability. Published in 2000 by John Wiley & Sons, Ltd.     

天然胶松弛曲线的一种拟合方法

采用单一的Maxwell模型确定被测材料的平均松弛时间,适当选择各运动单元的松弛时间,建立了五参数数学模型,各参数均用最小二乘法拟合。结果表明,均方根偏差均小于3％,松弛谱基本呈正态分布。     

注射成型中聚合物熔体应力分布的研究

对聚苯乙烯在注射成型过程中全展区的熔体进行了应力分布的研究计算结果与理论预测和实验值具有较好的一致性。     

A parameter to improve stability for a family of dissipative integration methods

There is a family of integration methods which has unconditional stability for linear elastic and stiffness softening-type systems; however, it becomes conditionally stable for stiffness hardening-type systems. Consequently, its applications are inconvenient or limited due to the conditional stability in stiffness hardening-type systems. This drawback can be overcome by introducing a free parameter into its formulation. The numerical properties of this family method are almost unaffected by this free parameter except that the stability property is improved. Thus, the method’s unconditional stability is successfully extended into stiffness hardening-type systems in addition to linear elastic and stiffness softening-type systems.     

TWO SIMPLE FAST INTEGRATION METHODS FOR LARGE-SCALE DYNAMIC PROBLEMS IN ENGINEERING

A new simple explicit two-step method and a new family of predictor–corrector integration algorithms are developed for use in the solution of numerical responses of dynamic problems. The proposed integration methods avoid solving simultaneous linear algebraic equations in each time step, which is valid for arbitrary damping matrix and diagonal mass matrix frequently encountered in practical engineering dynamic systems. Accordingly, computational speeds of the new methods applied to large system analysis can be far higher than those of other popular methods. Accuracy, stability and numerical dissipation are investigated. Linear and nonlinear examples for verification and applications of the new methods to large-scale dynamic problems in railway engineering are given. The proposed methods can be used as fast and economical calculation tools for solving large-scale nonlinear dynamic problems in engineering.     

纤维束张紧力缠绕复合材料飞轮的预应力简化分析

在纤维束缠绕时施加张紧力,使得固化成型后的飞轮内部形成一定的预加径向压应力,这是提高飞轮径向强度的有效方法之一。基于过盈配合的思想建立了计算张紧力缠绕导致的复合材料飞轮内部预应力和变形的简化模型和方法。通过算例分析发现:等张力缠绕产生的环向应力在半径方向上先减小后增大,径向压应力不断变小;变张力缠绕过程中,张紧力由小逐渐变大时,飞轮的径向压应力增大,径向强度提高;飞轮设计中仅仅依靠张紧力缠绕是不够的,还必须和固化成型后的厚壁筒之间的过盈套装一起来设计合理的径向预加压应力。     

On the equivalence of dynamic relaxation and the Newton‐Raphson method

Dynamic relaxation is an iterative method to solve nonlinear systems of equations, which is frequently used for form finding and analysis of structures that undergo large displacements. It is based on the solution of a fictitious dynamic problem where the vibrations of the structure are traced by means of a time integration scheme until a static equilibrium is reached. Fictitious values are used for the mass and damping parameters. Heuristic rules exist to determine these values in such a way that the time integration procedure converges rapidly without becoming unstable. Central to these heuristic rules is the assumption that the highest convergence rate is achieved when the ratio of the highest and lowest eigenfrequency of the structure is minimal. This short communication shows that all eigenfrequencies become identical when a fictitious mass matrix proportional to the stiffness matrix is used. If, in addition, specific values are used for the fictitious damping parameters and the time integration step, the dynamic relaxation method becomes completely equivalent to the Newton‐Raphson method. The Newton‐Raphson method can therefore be regarded as a specific form of dynamic relaxation. This insight may help to interpret and improve nonlinear solvers based on dynamic relaxation and/or the Newton‐Raphson method.     

A partitioned approach for the coupling of SPH and FE methods for transient nonlinear FSI problems with incompatible time‐steps

We propose a method to couple smoothed particle hydrodynamics and finite elements methods for nonlinear transient fluid–structure interaction simulations by adopting different time‐steps depending on the fluid or solid sub‐domains. These developments were motivated by the need to simulate highly non‐linear and sudden phenomena requiring the use of explicit time integrators on both sub‐domains (explicit Newmark for the solid and Runge–Kutta 2 for the fluid). However, due to critical time‐step required for the stability of the explicit time integrators in, it becomes important to be able to integrate each sub‐domain with a different time‐step while respecting the features that a previously developed mono time‐step coupling algorithm offered. For this matter, a dual‐Schur decomposition method originally proposed for structural dynamics was considered, allowing to couple time integrators of the Newmark family with different time‐steps with the use of Lagrange multipliers. Copyright © 2016 John Wiley & Sons, Ltd.     

An explicit time integration technique for dynamic analyses

A simple explicit solution technique for problems in structural dynamics, based on a Modified Trapezoidal rule Method (MTM) approximation of the governing ordinary differential equations, is developed. The resulting conditionally stable explicit method (MTM) can be easily implemented and is extremely simple to use. Particular attention is focused herein on the concept of numerical stability of the proposed method for a free-vibrational response of a linear undamped Single-Degree-Of-Freedom system (SDOF). To examine the effectiveness, strengths, and limitations of MTM, error analyses for the natural period, the displacement, the velocity and the associated phase angle for a free undamped simple mass–spring system are derived and compared with Modified Euler Method (MEM) and the well-known Newmark Beta Method (NBM). Numerical examples for a SDOF system and a Multi-Degree-Of-Freedom (MDOF) system are presented to illustrate the strengths and the limitations of the proposed method.     

非饱和土中温度引起水分迁移的光滑粒子法数值模拟

基于光滑粒子法(Smoothed particle hydrodynamics,SPH)的基本原理,尝试着对给出的非饱和土中水热耦合问题进行数值模拟。首先,采用基于SPH算法自行编制的程序对抛物型偏微分方程进行求解,并与解析解做出对比。计算结果表明,SPH算法用来数值模拟抛物型偏微分方程是可行的及有效的,这就为进一步采用SPH算法计算非饱和土在温度作用下的水分迁移问题提供了理论依据。然后,对非饱和土介质中热能传输以及水分迁移的规律进行了数值计算,其中重点计算了不同热扩散系数、温度诱致的水分扩散系数、等温条件下的水分扩散系数和热源条件下的体积含水率和温度分布的特点,并对其演化过程和机理进行分析,从而将SPH算法的应用范围作了扩展。     

半圆孔板承受拉伸和弯曲时的三维应力集中

根据Hellinger-Reissner原理建立了具有一个无外力圆柱表面三维8节点杂交应力元,元内假定应力场满足以柱坐标表示的三维平衡方程及无外力圆柱面上的外力边界条件,当元退化为二维时也满足协调方程。单元位移场选取与相邻元协调。用这种特殊杂交应力元,在相当粗的网格下即能准确地分析具有半圆孔厚(薄)板的三维(二维)应力集中。     

双股液体射流撞击雾化的SPH方法数值模拟

双股液体射流撞击雾化过程存在复杂的界面运动,传统网格法很难处理。运用SPH方法对双股液体射流撞击雾化问题进行三维数值模拟;根据实际的双股液体射流撞击雾化过程提出了合理的简化模型;弱可压缩状态方程中参考压强采用了新的计算公式;利用有限差分与SPH一阶导数相结合的方法处理粘性项中的二阶导数;对人工应力提出了新的参数值选择方案。将数值仿真结果与文献实验结果进行对比,二者比较吻合,表明SPH方法很适合解决射流撞击雾化等复杂的界面运动问题。