A New Explicit Algorithm for Bi-Phasic Mixture Flow in MIM

Metal injection moulding (MIM) is a new technology to manufacture small intricate parts in large quantity. Numerical simulation plays an important role in its development. To predict the specific segregation effect in MIM injection, mixture theory is adopted to model the injection flow by a bi-phasic model. This model conducts to the solution of two-coupled Stokes equations. It is an extremely computational consuming solution in the scope of the traditional algorithms, which induce a serious challenge to cost-effectivity of the MIM simulation. Referred to some methods proposed by Lewis in mono-phasic simulation and the implicit algorithms in MIM simulation, a new explicit algorithm is proposed and realized to perform efficiently this type of bi-phasic flow. Numerically this algorithm is devised to perform the simulation in a fully uncoupled manner except for a global solution of the pressure field in each time step. The physical coupling is taken into account in a sequential pattern by fractional steps.

Nonlinear evaluations of unconditionally stable explicit algorithms

Two explicit integration algorithms with unconditional stability for linear elastic systems have been successfully developed for pseudodynamic testing. Their numerical properties in the solution of a linear elastic system have been well explored and their applications to the pseudodynamic testing of a nonlinear system have been shown to be feasible. However, their numerical properties in the solution of a nonlinear system are not apparent. Therefore, the performance of both algorithms for use in the solution of a nonlinear system has been analytically evaluated after introducing an instantaneous degree of nonlinearity. The two algorithms have roughly the same accuracy for a small value of the product of the natural frequency and step size. Meanwhile, the first algorithm is unconditionally stable when the instantaneous degree of nonlinearity is less than or equal to 1, and it becomes conditionally stable when it is greater than 1. The second algorithm is conditionally stable as the instantaneous degree of nonlinearity is less than 1/9, and becomes unstable when it is greater than 1. It can have unconditional stability for the range between 1/9 and 1. Based on these evaluations, it was concluded that the first algorithm is superior to the second one. Also, both algorithms were found to require commensurate computational efforts, which are much less than needed for the Newmark explicit method in general structural dynamic problems.

Stability of an explicit time-integration algorithm for hybrid tests, considering stiffness hardening behavior

An explicit unconditionally stable algorithm for hybrid tests,which is developed from the traditional HHT-α algorithm,is proposed.The unconditional stability is first proven by the spectral radius method for a linear system.If the value of α is selected within [-0.5,0],then the algorithm is shown to be unconditionally stable.Next,the root locus method for a discrete dynamic system is applied to analyze the stability of a nonlinear system.The results show that the proposed method is conditionally stable for dynamic systems with stiffness hardening.To improve the stability of the proposed method,the structure stiffness is then identified and updated.Both numerical and pseudo-dynamic tests on a structure with the collision effect prove that the stiffness updating method can effectively improve stability.

Explicit incremental-update algorithm for modeling crystal elasto-viscoplastic response in finite element simulation

Computational stability and efficiency are the key problems for numerical modeling of crystal plasticity, which will limit its development and application in finite element (FE) simulation evidently. Since implicit iterative algorithms are inefficient and have difficulty to determine initial values, an explicit incremental-update algorithm for the elasto-viscoplastic constitutive relation was developed in the intermediate frame by using the second Piola-Kirchoff (P-K) stress and Green stain. The increment of stress and slip resistance were solved by a calculation loop of linear equations sets. The reorientation of the crystal as well as the elastic strain can be obtained from a polar decomposition of the elastic deformation gradient. User material subroutine VUMAT was developed to combine crystal elasto-viscoplastic constitutive model with ABAQUS/Explicit. Numerical studies were performed on a cubic upset model with OFHC material (FCC crystal). The comparison of the numerical results with those obtained by implicit iterative algorithm and those from experiments demonstrates that the explicit algorithm is reliable. Furthermore, the effect rules of material anisotropy, rate sensitivity coefficient (RSC) and loading speeds on the deformation were studied. The numerical studies indicate that the explicit algorithm is suitable and efficient for large deformation analyses where anisotropy due to texture is important.

Study on Contact Algorithm of Dynamic Explicit FEM for Sheet Forming Simulation

Based on existing algorithms, a newly developed contact search algorithm is proposed. The new algorithm consists of global search, local searching, local tracking and penetration calculation processes. It requires no iteration steps. It can deal with not only general tool surfaces with vertical walls, but also tool surfaces meshed with elements having very poor aspect ratios. It is demonstrated that the FE code employing this new contact search algorithm becomes more reliable, efficient and accurate for sheet metal forming simulation than conventional ones.

Investigation into the Computational Costs of Using Genetic Algorithm and Simulated Annealing for the Optimization of Explicit Friction Factor Models

Research reports show that the accuracies of many explicit friction factor models, having different levels of accuracies and complexities, have been improved using genetic algorithm (GA), a global optimization approach. However, the computational cost associated with the use of GA has yet to be discussed. In this study, the parameters of sixteen explicit models for the estimation of friction factor in the turbulent flow regime were optimized using two popular global search methods namely genetic algorithm (GA) and simulated annealing (SA). Based on 1000 interval values of Reynolds number (Re) in the range of and 100 interval values of relative roughness () in the range of , corresponding friction factor (f) data were obtained by solving Colebrook-White equation using Microsoft Excel spreadsheet. These data were then used to modify the parameters of the selected explicit models. Although both GA and SA led to either moderate or significant improvements in the accuracies of the existing friction factor models, SA outperforms the GA. Moreover, the SA requires far less computational time than the GA to complete the corresponding optimization process. It can therefore be concluded that SA is a better global optimizer than GA in the process of finding an improved explicit friction factor model as an alternative to the implicit Colebrook-White equation in the turbulent flow regime.

一种具有可控数值阻尼的无条件稳定半显式积分算法

结构模型经过有限元方法空间离散化处理之后,可能引入虚假的高频分量,这部分高频分量会对结构的动力响应求解带来不利影响。为此,需要引入算法的数值阻尼有效地抑制这部分虚假的高频分量。使用半显式算法格式,通过匹配隐式ρ_(∞)-Bathe算法放大矩阵的特征方程系数,提出一种具有可控数值阻尼的无条件稳定半显式积分算法,记为NSE(New Semi-Explicit)-ρ_(∞)算法,新算法通过两个自由参数ρ_(∞)和γ控制算法的数值阻尼,并且无需对结构运动方程进行加权处理。对新算法的稳定性、精度、周期延长和振幅衰减等数值特性进行分析,结果表明,新算法对于线弹性体系和非线性刚度软化体系均为无条件稳定。通过具有代表性的数值算例,将新算法与两种具有可控数值阻尼的无条件稳定显式积分算法进行对比,证明新算法能够更加有效地抑制虚假高频分量。

Extensions of nonlinear error propagation analysis for explicit pseudodynamic testing

Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.

Comparison and assessment of time integration algorithms for nonlinear vibration systems

A corrected explicit method of double time steps(CEMDTS) was introduced to accurately simulate nonlinear vibration problems in engineering. The CEMDTS, the leapfrog central difference method, the Newmark method, the generalized-a method and the precise integration method were implemented in typical nonlinear examples for the purpose of comparison. Both conservative and non-conservative systems were examined. The results show that it isn't unconditionally stable for the precise integration method, the Newmark method and the generalized-a method in nonlinear systems. The stable interval of the three methods is less than that of the CEMDTS. When a small time step(?t≤T_(min)/20) is employed, the precise integration method is endowed with the highest accuracy while the CEMDTS possesses the smallest computation effort. However, the CEMDTS becomes the most accurate one when the time step is large(?t≥0.3T_(min)) or the system is strongly nonlinear. Therefore, the CEMDTS is more applicable to the nonlinear vibration systems.

On a New Algorithm for Numerical Simulation of Inner Hydroforming

Inner hydroforming is a new manufacturing technique. It presents a great importance for car manufacturing and other industries. To determine the forming process, numerical simulation will play a very important role. To overcome the difficulties of instability and non linearity, a new algorithm is proposed. The algorithm takes the advantages of dynamic transient solution and ensures its stability by a modified Runge Kutta scheme. Adaptive step size is applied with a practically inexpensive error estimation to achieve good efficiency. Numerical examples have shown an advantage in comparison with the currently used central difference algorithm.

A NEW EXPLICIT SIMULATION FOR MOULD FILLING WITH HIGH VISCOUS FEEDSTOCK

In the simulation of the metal injection moulding (MIM), the behaviours of feedstock are much di?erent from which of the polymer injection. It is a mixture of the metallic powder in high concentration and some plastic binder. The advance in simulation of the mould ?lling with such high viscous feedstock is featured by the development of a fully explicit vectorial algorithm. On the basis of previous explicit software realized by the authors, the new algorithm avoids the global solution for pressure ?elds and the use of MINI elements to improve its e?ciency. Except for the operations at element level, neither global solution nor the construction of global matrix is required in simulation. A special strategy is used to regulate the incompressibility condition in ?lled domain at each time step. In case of the MIM problems, this method provides a fast way to simulate the ?lling processes. The computational cost is about linearly proportional to the degree of freedom number. Moreover, this vectorial algorithm can be easily parallelized for high performance computation with multi-clusters. The comparison of numerical results with previous simulations on 3D cases proves the validity and e?ciency of new algorithm.

单步无条件稳定显式结构动力学算法

在结构动力学分析中,数值积分方法通常被用来高效和准确地求解复杂结构系统在动态负载下的响应。基于量纲分析的原理,提出一种求解结构动力学问题的单步无条件稳定显式算法。首先对所构造的关于位移和速度的函数关系式进行无量纲化处理,然后通过算法精度要求、无条件稳定条件和数值阻尼可控条件确定了其最终递推格式,并根据算法最终递推格式分析得出算法耗散与弥散特性、超调和自启动特性和多自由度系统计算步骤,最后通过数值算例验证了算法的收敛精度、可控数值阻尼和计算效率优势。研究结果表明:对于线性和非线性系统,该算法都兼具显式算法的非迭代特性和隐式算法的无条件稳定特性;该算法能实现真正意义上的自启动并且在速度和位移上均无超调;该算法的数值阻尼由单自由参数控制,数值耗散和弥散对系统低模态响应的影响可以忽略不计,与具有代表性的非迭代显式算法KR-α法相比,该算法在引入数值阻尼滤除虚假高频模态的同时更真实地保留了低阶振型的贡献,从而表现出更好的计算精度;该算法在求解非线性结构动力学问题时相较于常用隐式算法有着显著的计算效率优势,并略优于两求解器非迭代显式算法KR-α法。研究结果很有希望成为求解非线性结构动力学问题的最新且更加有效的显式算法。

基于NSGA-Ⅱ的复合材料防撞梁碰撞损伤多目标优化

为在设计时考虑低速碰撞损伤对碳纤维复合材料(CFRP)防撞梁力学性能的影响,发展了改进Hashin失效准则的VUSDFLD子程序来判定低速碰撞时CFRP防撞梁7个方向的损伤程度,采用壳单元模拟了复合材料的力学性能,建立了CFRP防撞梁低速碰撞有限元显式动力学模型。采用该方法对相同实验条件下的复合材料层合板低速冲击剩余强度进行了计算,并将计算结果与实验结果进行了对比,仿真结果与实验结果吻合较好。在此基础上,以复合材料防撞梁铺层厚度和铺层角度为设计变量,将复合材料防撞梁的质量和低速冲击时产生的损伤单元数作为优化目标,建立了CFRP防撞梁低速碰撞损伤动力学多目标优化模型,采用基于Pareto策略改进的NSGA-Ⅱ非支配排序遗传算法对其进行多目标优化求解。优化后,CFRP防撞梁质量由1.02 kg降为0.76 kg,减重率为25%;损伤单元数由30238个降为23206个,损伤降低率为23%。结果表明,所发展基于Hashin失效准则的VUSDFLD子程序和对CFRP防撞梁低速碰撞损伤多目标优化是行之有效的,为复合材料防撞梁结构的优化设计提供了参考。

三维地质建模技术与方法综述

三维地质建模是起源于工业领域计算机图形学引用到地学领域形成的三维数字化技术,地质体轮廓不规则性、特性的空间不均匀性、已知数据的稀疏性和认识过程的反复性决定了三维地质建模对图形几何算法和渲染技术的特殊要求,也决定了与其他领域三维技术如GIS和BIM之间存在的基础性差别。针对我国基础建设领域工程地质三维地质建模技术类型繁多、良莠不齐的现实,本文系统性地阐述了三维地质建模的基础理论与核心技术、建模方法、应用功能实现与展望:(1)三维地质建模以离散数学理论为基础,插值算法是其中最关键的核心技术,文中介绍和对比分析了离散光滑(DSI)和克里金两种插值方法,从原理和应用的角度论证了DSI具有更好的适应性;(2)显式和隐式建模方法是核心技术针对不同场景形成的三维地质建模的通用方法,在工程地质领域分别适合于勘探为主和物探为主的情形,文中结合应用案例阐述了各自的特点;(3)应用功能是显式和隐式建模方法针对不同特点的地质体的应用方式,其中的通用型功能针对地层和构造等所有地学领域都涉及的地质体,定制化功能则针对行业关心的特定地质体(如水电行业的深切河谷岸坡卸荷带)且以提高建模效率为主要目的。本文通过对三维地质建模技术的阶段性总结,为未来发展提供有价值的技术指引,并将为三维工程地质体结构的透明化表征提供重要的技术支撑。

基于因素空间理论的扫类连环多分类算法

为解决多分类问题,基于因素空间理论中因素显隐的思想,在扫类连环分类算法基础上,定义类别的合并,提出因素显隐的合并扫类连环分类方法,给出算法步骤,并用数值算例进行分析;定义类别的两两组合,提出因素显隐的两两扫类连环分类方法,给出算法步骤,并用数值算例进行分析。提出采用因素显隐的差额绝对值方法解决两个算法执行过程中出现的决策类别分不开的问题;对UCI数据集中3个实例与支持向量机作了算法对比分析,研究结果表明:提出的合并扫类连环分类方法、两两扫类连环分类方法实现了因素显隐,分类算法的精确度优于支持向量机。多分类学习的因素显隐研究结论拓展了因素空间的理论及应用研究。

显式算法中三维黏弹性人工边界应用及输水隧洞动力响应分析

为确保大型复杂三维有限元模型动力响应分析的稳定性及高效性,结合二维黏弹性边界理论及其在动力显式分析中稳定性的改善方法,提出了一种适用于ABAQUS/Explicit模块的三维黏弹性人工边界方法,并依托某输水隧洞与临近高铁隧道的立交工程,在设有三维黏弹性边界的基础上研究高速列车振动荷载对既有水工隧洞的振动影响特性。结果表明,采用动力显式分析时,稳定性改善后的黏弹性人工边界具有良好的吸能效果,满足远域地基的回弹性能;振动荷载对输水隧洞的动力影响随着作用距离的增大而减小,且各断面的动力响应极值均出现在底板中心。

基于OpenSees的饱和土场地中地下结构地震反应研究

应用OpenSees有限元计算程序,选取某地铁车站结构为主要分析对象,构建了饱和土-地下结构体系地震反应运算模型,并利用该模型进行系统的地震反应计算。将现场饱和土动力反应视为饱和两相介质近场波动问题,选取时域显式数值算法进行计算,同时考虑了土体的弹塑性。研究结果显示:(1)因选取弹塑性土体本构,土体-地下结构的位移反应时程和输入地震动的位移时程体现出了显著性差异。(2)对于两层三跨地下结构,在以剪切波形式输入的地震动作用下,顶板的峰值加速度和侧向位移最大,中板次之,底板最小,场地土体对地震波具有放大效应,顶层的层间位移大于底层。(3)在地震动作用下,地下结构不同区域应力时程的改变规律存在非常显著的差异。中柱底部与底板节点处的应力峰值最大。地震动输入结束时,结构存在残余应力。

双动自能式灭弧室静侧传动系统动力学仿真与优化

在高压断路器分闸与合闸过程中,静侧传动系统的强度直接影响产品的机械寿命,550 k V断路器与以往的产品相比,提高了电压等级,意味着更难满足机械寿命要求,因此需要更加准确地预测和提高静侧传动系统的结构强度以保证寿命要求。文中建立了双动自能式灭弧室静侧传动系统的柔性瞬态动力学模型,该模型基于Hypermesh进行前处理,并利用Ls-dyna进行了瞬态动力学仿真求解。在分析过程中运用了显示算法,充分考虑了网格类型、接触类型、间隙、碰撞冲击等因素的影响。应力仿真结果表明:不同速度工况下,分合闸操作过程中关键零部件存在高应力风险,文中以拉杆销为例,列出了其高应力分布图以及应力时域曲线,峰值应力达到了约380 MPa,存在优化的空间。同时还输出了零部件之间的接触力,速度曲线,以及系统能量等结果,这些仿真结果表明:接触力大小和方向以及速度变化均符合实际运动趋势,沙漏能始终未超过内能峰值的5%,接触未发生明显的滑移和穿透,这些结果确保了仿真分析的合理性。随后针对高应力区域进行了设计方案优化并和原方案进行了仿真对比。对比结果表明:各个风险点的峰值应力明显降低,横梁、导轨、小垫片上的风险点应力下降比例最高可达到50%,优化效果明显。对优化方案进行了疲劳寿命分析,寿命结果表明:关键零部件的应力风险点可以达到10 000次以上。最终进行了机械寿命实验,实验结果表明:优化方案能够满足万次机械寿命的实验要求且未发生过度磨损,验证了仿真结果以及优化设计的有效性。

Deformation mechanism of cold ring rolling in view of texture evolution predicted by a newly proposed polycrystal plasticity model

An explicit polycrystal plasticity model was proposed to investigate the deformation mechanism of cold ring rolling in view of texture evolution. The model was created by deducing a set of linear incremental controlling equations within the framework of crystal plasticity theory. It was directly solved by a linear algorithm within a two-level procedure so that its efficiency and stability were guaranteed. A subroutine VUMAT for ABAQUS/Explicit was developed to combine this model with the 3D FE model of cold ring rolling. Results indicate that the model is reliable in predictions of stress-strain response and texture evolution in the dynamic complicated forming process; the shear strain in RD of the ring is the critical deformation mode according to the sharp Goss component （{110}？100？） of deformed ring; texture and crystallographic structure of the ring blank do not affect texture type of the deformed ring;texture evolves rapidly at the later stage of rolling, which results in a dramatically increasing deformation of the ring.

基于灰狼优化算法的变截面点阵结构设计及性能优化

点阵结构因其比强度高、比刚度高,减振降噪性好和隔热吸能能力强等特点,已被广泛应用于航空航天和交通运输等领域主承力零部件设计.但现有的点阵结构设计大都基于等截面假设开展,严重制约了材料分布优化的寻优空间,无法满足质量敏感领域极致轻量化设计的迫切需求.而目前关于变截面点阵结构设计的研究大都基于实验的“试错式”经验调配模式,其相应的理论设计方法尚不完善.文章基于灰狼智能优化算法,提出了一种高效的变截面点阵结构设计方法.首先,基于水平集函数构建变截面点阵的显式几何描述模型,以实现变截面点阵几何形状的自由描述;其次,采用能量均匀化方法预测变截面点阵单胞的宏观等效力学属性,建立宏观点阵结构与变截面单胞构型间的内在联系;然后,以变截面点阵的几何描述参数为设计变量,材料用量为约束条件,最小化柔度为目标函数,构建变截面点阵优化数学模型,并采用灰狼优化算法实现上述模型的高效求解,得到性能优化的变截面点阵结构;最后,通过二维和三维数值算例和仿真分析共同验证了所提方法的正确性和有效性,并与相同条件下等截面点阵结构的承载能力进行了比较.结果表明:优化后变截面点阵结构的柔度相较于相同条件下的等截面点阵结构可降低30%以上,具有更优异的承载能力.研究结果丰富了变截面点阵结构设计理论,在高端装备极致轻量化设计领域具有重要应用前景.