Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Buckling Optimization of Curved Grid Stiffeners through the Level Set Based Density Method

Stiffened structures have great potential for improvingmechanical performance,and the study of their stability is of great interest.In this paper,the optimization of the critical buckling load factor for curved grid stiffeners is solved by using the level set based density method,where the shape and cross section(including thickness and width)of the stiffeners can be optimized simultaneously.The grid stiffeners are a combination ofmany single stiffenerswhich are projected by the corresponding level set functions.The thickness and width of each stiffener are designed to be independent variables in the projection applied to each level set function.Besides,the path of each single stiffener is described by the zero iso-contour of the level set function.All the single stiffeners are combined together by using the p-norm method to obtain the stiffener grid.The proposed method is validated by several numerical examples to optimize the critical buckling load factor.

基于Level Set方法的40CrMnMoA合金钢的奥氏体晶粒长大模型

为准确描述40CrMnMoA合金钢的奥氏体晶粒长大行为,借助Gleeble-1500D型热模拟机对40CrMnMoA合金钢进行了保温试验,温度为900~1150℃,时间为10~2000 s。基于试验结果,通过非线性回归建立了40CrMnMoA合金钢Burke-Turnbull奥氏体晶粒长大模型,构建了基于Level Set方法的40CrMnMoA合金钢奥氏体晶粒长大的介观尺度有限元模型并进行计算。结果表明:保温温度与保温时间对40CrMnMoA合金钢的晶粒长大行为均具有较大的影响。40CrMnMoA合金钢的奥氏体平均晶粒直径随保温时间的延长呈抛物线增长。所建立的Burke-Turnbull晶粒长大动力学模型具有较高的精度,试验值与计算值相关系数(R)为0.9932。40CrMnMoA合金钢奥氏体再结晶晶粒长大激活能(Q_(m))为142845.37 J/mol。通过对比仿真计算与试验所得的晶粒组织,验证了本文所建有限元模型可有效地预测40CrMnMoA合金钢的奥氏体晶粒长大演变过程。

Topology Optimization for Steady-State Navier-Stokes Flow Based on Parameterized Level Set Based Method

In this paper,we consider solving the topology optimization for steady-state incompressibleNavier-Stokes problems via a new topology optimization method called parameterized level set method,which can maintain a relatively smooth level set function with a local optimality condition.The objective of topology optimization is to􀀀nd an optimal con􀀀guration of theuid and solid materials that minimizes power dissipation under a prescribeduid volume fraction constraint.An arti􀀀cial friction force is added to the Navier-Stokes equations to apply the no-slip boundary condition.Although a great deal of work has been carried out for topology optimization ofuidow in recent years,there are few researches on the topology optimization ofuidow with physical body forces.To simulate theuidow in reality,the constant body force(e.g.,gravity)is considered in this paper.Several 2D numerical examples are presented to discuss the relationships between the proposed method with Reynolds number and initial design,and demonstrate the feasibility and superiority of the proposed method in dealing with unstructuredmesh problems.Three 3D numerical examples demonstrate the proposedmethod is feasible in three-dimensional.

A Low Mach Number IMEX Flux Splitting for the Level Set Ghost Fluid Method

Considering droplet phenomena at low Mach numbers,large differences in the magnitude of the occurring characteristic waves are presented.As acoustic phenomena often play a minor role in such applications,classical explicit schemes which resolve these waves suffer from a very restrictive timestep restriction.In this work,a novel scheme based on a specific level set ghost fluid method and an implicit-explicit(IMEX)flux splitting is proposed to overcome this timestep restriction.A fully implicit narrow band around the sharp phase interface is combined with a splitting of the convective and acoustic phenomena away from the interface.In this part of the domain,the IMEX Runge-Kutta time discretization and the high order discontinuous Galerkin spectral element method are applied to achieve high accuracies in the bulk phases.It is shown that for low Mach numbers a significant gain in computational time can be achieved compared to a fully explicit method.Applica-tions to typical droplet dynamic phenomena validate the proposed method and illustrate its capabilities.

MULTI-PHASE ACTIVE CONTOUR MODEL FOR IMAGE SEGMENTATION BASED ON LEVEL SETS

A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.

PYRAMIDAL MULTIPHASE LEVEL SET FRAMEWORK FOR BRAIN TUMOR DETECTION USING GENERALIZED TECHNIQUE OF PAINTING BACKGROUND

The pyramidal multiphase level set framework （PMLSF） based on the technique of painting background （TPBG） and the Chan-Vese model can detect multiple objects on a given image. However, the boundaries of the sub-object obtained by PMLSF-TPBG are not variable since a specialcolor parameter is used in TPBG. To solve the problem, a new technique utilizing a varying parameter is proposed to ensure that PMLSF is effective for the detection of the desired boundaries of the sub-object. The interval of the variable color parameter is proved and the effects of the parameter are also discussed. Experimental results for the brain tumor detection show that different boundaries of the brain tumors can be detected with different color parameters. It is especially useful for clinical diagnoses.

Level set函数快速步进重构的隐式分区并行

为进一步提高共享内存架构下level set函数重构并行效率,本文提出一种隐式分区并行重构方法,该方法无需提前进行区域分解,只需预先分割交界面,便可实现快速步进并行重构,且区域分解也同步进行。根据圆球、Zalesak球和哑铃等值面快速步进并行重构结果表明:隐式分区算法的计算耗时小于显式分区算法;相同线程数量下隐式并行算法带来的加速比与显式算法接近,8线程下隐式分区并行算法的加速比达到4;隐式分区算法中节点重演次数少于显式分区算法节点回滚次数。

基于Level Set方法的医学图像分割

对图像分割进行了研究,这是医学图像处理中的关键问题之一.提出了一种结合Fast Marching算法和Watershed变换的医学图像分割方法.首先用非线性扩散滤波对原始图像进行平滑,然后利用Watershed算法对图像进行过度分割,最后用改进的Fast Marching方法对图像进行分割.除此之外,根据区域之间的统计特性的相似度重新定义了Fast Marching方法的速度函数.实验结果表明,该方法能够快速、准确地得到医学图像的分割结果.

Level Set方法及其在两相流数值模拟研究中的应用

本文介绍了一种崭新的捕捉两相流相界面的 Ｌｅｖｅｌ Ｓｅｔ方法，并应用该方法对两种互不相容流体间的平面界面波动现象进行了数值模拟，捕捉到了两相流界面波动过程中的一些复杂现象。计算结果与实验观测现象符合良好，表明这种方法是一种很有前途的两相流数值模拟方法，很值得进一步研究和推广。

界面追踪的Level Set和Particle Level Set方法

Level Set方法是20世纪90年代很流行的界面追踪技术,国外已有个别实例将此方法应用于不可压缩流体的计算。但其对界面具有抹圆的作用,造成梯度很大的界面失真。Particle Level Set方法可以弥补这一缺陷。本文首先介绍了这两种界面追踪的方法。然后采用五阶WENO格式离散空间导数,并采用三阶 TVD Runge Kutta方法离散时间导数,用计算机Fortran语言建立了界面追踪的模型。最后通过平移流场中的同心方框、旋转流场中的缺口圆和剪切流场中圆的三维界面的追踪算例,对两种方法进行了对比验证。同时,用剪切流场中圆的算例对比了 Particle Level Set和单纯拉哥朗日方法。结果表明,Particle Level Set对界面的描述更为精细,可以用于大梯度的界面追踪;Particle Level Set和单纯拉哥朗日方法的结果很接近。

用Level Set方法对水下两个气泡运动的数值模拟

利用Level Set方法,三维数值模拟了两个气泡的上升运动.通过改变气泡尺寸及位置,研究气泡对在上升过程中的尾迹流及其相互作用规律.数值模拟准确再现了气泡对的变形、吸引或排斥行为,气泡上升速度计算结果与经验关联式结果吻合;气泡周围的速度场揭示了两个气泡尾迹流的流体动力学作用;对于水平或垂直放置的气泡对,当下方气泡有大于50%的投影面积进入到上方气泡的尾流区时,两个气泡将发生聚并现象.

Level set方法在空化流动计算中的应用(英文)

文章将Level set方法应用于自然空化与通气空化流动计算中,通过耦合入相间的质量传输方程,建立了一个用于描述气、汽、液多相空化流动的数值模拟方法,分别对绕圆头回转体和Clark-Y型水翼的自然空化流动和绕圆盘的通气空化流动进行了数值模拟研究,并与实验结果进行了对比,研究结果表明:相较常用的多相流模型(mixture model),Lev-el set方法通过时间和空间上的压缩离散方案,减小了相间界面的扩散,准确地捕捉到了相间的界面,可以有效地运用于空化多相流动。

基于Level Set方法的人脸轮廓提取与跟踪

提出一种基于levelset方法的图像序列中人脸轮廓提取与跟踪算法 ,首先利用图像帧间差分快速检测出运动区域 ,并根据人脸图像的投影映射规则确定人脸所在的外接矩形 ,然后以此矩形作为初始曲线 ,采用一种改进的levelset模型精确提取出人脸轮廓 .由于图像序列中人脸是一直运动的 ,该文引入一阶线性Kalman滤波模型对人脸运动进行估计 ,从而较好地跟踪了运动中的人脸轮廓 .

基于Level set方法的微观水驱油模拟分析

通过引入Level set方法,构建两相界面运移数学表征方法,结合Navier-Stokes方程建立两相微观渗流数学模型,借助有限元方法进行求解,并利用微观玻璃刻蚀模型驱替实验验证数值模拟结果。结果表明,基于该渗流数学模型的数值模拟结果与实验结果的吻合度很高。利用Navier-Stokes方程并结合Level set方法实现了两相流体驱替的微观数值模拟,从而为研究微观两相渗流特征及驱油机理提供了一种新方法。在不等径并联喉道单元模型基础上,进行了不同驱替条件下的数值模拟计算,分析了发生孔隙尺度两相窜流的临界喉道直径比的变化特征,结果表明驱替压差及油水两相黏度比越大,越容易发生微观窜流,更易导致在较小喉道中形成微观残余油。本文研究结果为微观水驱油机理的进一步研究奠定了基础。

基于Level Set方法的曲线演化

Level Set方法是一种描述曲线以曲率相关的速度演化的有力工具,最近几年在医学图像处理、自然现象的模拟以及计算机视觉等领域得到了广泛的应用.其中,曲线演化后的平滑算法和轮廓跟踪方法是Level Set方法实际应用中的两个关键算法.给出了一种平滑Level Set距离函数的简单方法.该方法只采用内插值的方式,消除平面上的全部孤立点以及部分可能产生歧义的点,在允许存在部分冗余点的情况下,利用曲线轮廓跟踪算法,得到平面上所有曲线的轮廓.经过实验验证,该方法简单、高效,适应范围广.

充模过程的Level Set两相流模拟

采用Level Set两相流方法模拟了熔体充模过程,避免了处理复杂的边界以及用Ghost方法将熔体内的速度值外推到熔体外的情况。分别对型腔水平中面与垂直中面的充模过程进行了模拟。讨论了不同注射速度、不同注射口数量以及不同Reynolds数对充模过程的影响,得出了不同时刻各种情况下熔体界面的位置与充模过程刚结束时型腔内的压力分布,分析了熔体在型腔内运动的不同阶段的特点及形成不同阶段的原因。结果表明,在注射口宽度与型腔宽度相差不大的情况下,如果采用中低速充模,则整个充模运动过程以比较平稳的扩展性运动为主,充模较完全,熔体不发生破裂,制件效果较好。充模速度越大,熔体达到平稳流动的时间越短,充模过程越短。数值模拟结果与实验结果一致,同时表明Level Set两相流方法在求解拓扑性质发生较大变化问题时具有很大的优势。

求解不可压缩两相流的复合Level Set-VOF方法

目前,不可压缩两相流问题的数值求解方法主要有VOF方法和Level Set方法等.根据CLSVOF方法基本思想,通过将VOF和Level Set两种方法结合,实现了复合Level Set-VOF方法追踪不可压缩两相流相界面的模拟计算;对比分析了VOF、Level Set和复合Level Set-VOF方法计算经典两相流问题的结果.研究结果表明,复合Level Set-VOF方法继承了VOF方法精确构造相界面和Level Set方法精确计算表面张力的优点,能够有效削弱两相流求解过程中出现的虚假流动问题,因此可以更加精确地求解不可压缩两相流问题.

界面捕捉Level Set方法的(AMR)数值模拟

在流体力学方程的计算中采用高精度WENO格式,用AMR(adaptive mesh refinement)方法提高流场局部分辨率,在采用Level Set函数标定物质界面的计算中用GFM(ghost fluid method)方法进行界面处理,尝试将AMR技术与界面追踪技术相互融合并应用于数值模拟,对不同的模拟结果进行了比较.