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。     

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.     

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。     

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。     

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.     

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.     

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。     

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.     

EXPONENTIAL MAP ALGORITHM FOR STRESS UPDATES IN ANISOTROPIC MULTIPLICATIVE ELASTOPLASTICITY FOR SINGLE CRYSTALS

This paper presents a new stress update algorithm for large-strain rate-independent single-crystal plasticity. The theoretical frame is the well-established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts. A distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts, resulting in a very convenient representation of the Schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of Eulerian vectors. The key contribution of this paper is an algorithmic formulation of the exponential map exp: sl(3) → SL(3) for updating the special linear group SL(3) of unimodular plastic deformation maps. This update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration. The resulting fully implicit stress update algorithm treats the possibly redundant constraints of single-crystal plasticity by means of an active set search. It exploits intrinsically the simple representation of the Schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of Eulerian vectors updates. The performance of the proposed algorithm is demonstrated by means of a representative numerical example.     

薄膜X射线应力分析的实验方法

提出一种适用于薄膜材料X射线应力分析的试样三维定向模式,在X射线低掠入射的前提下允许按实验所需选择测量方向.高密勒指数晶面衍射和测量方向的合理选择有助于提高测量精度,也利于经典sin2ψ分析法实验线性关系的建立,从而简化了分析和计算程序.     

地震工程中动力方程求解的逐步积分方法

许多数值逐步积分方法在地震动力问题分析中得到了应用，但对于每一问题选用适当的逐步积分方法非常必要。本文介绍了地震工程中应用的一些时域数值逐步积分方法，分析与阐述了它们的基本特性（计算稳定性，精度，高频能耗性，幅值超越性），并在此基础上就合理地选用数值逐步积分方法问题给出了建议。     

精细时程积分中状态转换矩阵的自适应算法

本文提出了基于Ｐａｄｅ逼近理论的计算精细时程积分中的状态转换矩阵的算法。这种算法与基于Ｔａｙｌｏｒ级数展开的方法相比，有更高的精度，而且具有自适应功能。文中的数值实验结果印证了这一点。     

动应力参数选择原则满足的条件

本文根据交变应力下构件的强度计算理论,得出了在振动时效时,只有外加动应力使构件内应力循环特性r大于γ_(mk),构件内平均应力σ_m大于σ_(mk),动应力参数选择原则不能得到满足的结论。     

拉伸载荷下楔环连接壳体的应力解析方法

楔环连接结构为摩擦-接触多体组合连接结构,一个典型的楔环连接结构主要由两个连接壳体和一对楔环带构成。建立拉伸载荷下楔环连接结构的力学模型,将楔环连接壳体看成由弹性圆环、短圆柱形壳以及长圆柱形壳组成,基于板壳理论和力法推导壳体截面内力精确解求解方程。当环腔段壳体足够长时,讨论壳体截面内力的简化解,并通过精确解讨论简化解的使用条件。