Abstract ：

著名的英国物理学家麦克斯韦(James Clerk Maxwell，1831—1879)在力学上也具有多种开创性的贡献，其中的桁架结构布局优化研究，属于至今方兴未艾的研究热点——结构拓扑优化的范畴，而麦克斯韦早在100多年前就首次提出来了。由于时间久远，麦克斯韦对桁架这类离散结构布局优化的贡献时间，国内相当多的一些涉及研究结构优化的专著、教科书和期刊的文章中，各自将其列为1864年、1870年、1872年和1890年等等，真是莫衷一是，不一而足。多数人，包括笔者，未曾想这个时间点会有这么多的说法，乃至以讹传讹，浑不知晓。当我们产生一念，想了解麦克斯韦在什么年纪做出这么重大的发现时，令我们瞠目结舌的是，1890年是他去世11年之后了！于是查文献，发现国外记录麦克斯韦对离散结构布局优化贡献的时间也很不一致，比如Michell，Rozvany和Makoto Ohsaki分别认为该时间是1890年、1872年和1894年，于是产生了力学史中棘手的一桩公案。通过多方查阅麦克斯韦的原文和出处，分析判断，认为1872年是合理的，厘清这桩公案对力学史和方法论的研究必定有所裨益。

Keyword ：

贡献时间 力学史与方法论 离散结构布局优化 麦克斯韦

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Abstract ：

为提高机床关键基础大件立柱的综合性能,通过振动噪声测试分析系统,开展不同方向上某机床立柱的敲击测试实验,以得到其全部模态.在实验结果分析基础上,利用Abaqus软件进行面向筋板布局的立柱多目标拓扑优化分析.根据分析结果,修整并重构新的立柱筋板布局.优化前后立柱有限元分析对比显示,其质量减轻10.09%,最大变形量减少5%,固有频率亦有一定程度提升.优化结果表明所进行的工作,既减轻了立柱整体质量,节省了立柱工程用料,又在一定程度上提升了其动静态性能.

Keyword ：

拓扑优化 筋板布局 多目标优化 数控机床 机床立柱 轻量化设计

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Abstract ：

横梁是龙门导轨磨床的重要部件,动静态刚度直接影响机床性能.为在保证其性能前提下实现轻量化设计,提出一种结合拓扑结构优化的横梁轻量化设计方法.基于变密度法和优化设计理论,通过拓扑优化与尺寸优化方法对机床横梁进行结构轻量化设计.首先,介绍高精度龙门导轨磨床及优化设计理论,并基于变密度法优化横梁拓扑建模;其次,采用有限元分析方法对横梁进行静态及动态分析,并进行拓扑结构优化;最后,对比横梁优化前及优化后的性能.结果表明,横梁在优化后总变形和最大应力分别为0.015 848 mm和 3.702 3 MPa,较优化前的 0.017 778 mm和 3.927 9 MPa分别下降了 10.86%和 5.74%,横梁最终质量为9 849.7 kg,比优化前横梁减轻了425.3 kg,实现了横梁的轻量化.

Keyword ：

拓扑优化 轻量化设计 龙门导轨磨床 变密度法 横梁

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Abstract ：

本发明提供一种基坑内支撑布置方式的拓扑优化方法，包括以下步骤：步骤1、在ABAQ US有限元软件建立待优化的基坑内支撑初始结构模型；步骤2、定义设计区域和设计变量；步骤3、定义目标函数和约束条件；步骤4、输入载荷数值，设定约束条件进行迭代优化；步骤5、满足优化判别条件结束优化，不满足优化判别条件回到步骤4继续优化，直到满足优化判别条件结束优化。本发明利用ABAQUS有限元软件引入渐进结构优化算法对基坑内支撑的最优排布方式进行探究，在连续体拓扑优化中通过优化材料的分布和形状，使得应变能最小化，结构优化算法会在设计域内进行迭代搜索，通过调整材料的位置和形状，逐步寻找最优解。最终得到具有最小的应变能最优的基坑内支撑布置方式。

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Abstract ：

To improve the comprehensive performance of the key basic part column of the machine tool, the vibration and noise test and analysis system was used to conduct impact testing experiments on a certain machine tool column in different directions to obtain precise modal parameters. Based on the analysis of the experimental results, Abaqus software was utilized to perform the multi-objective topology optimization analysis of the columns for rib layout. Based on the analysis results, the new plate layout of the column was modified and reconstructed. The finite element analysis comparison of the columns before and after optimization shows that the mass is reduced by 10.09%, the maximum deformation decreases by 5%, and the natural frequency is also improved to a certain extent. The optimization results indicate that the engineering material used in the column is saved and the dynamic and static performance is improved. © 2025 Beijing University of Technology. All rights reserved.

Keyword ：

lightweight design CNC machine tool machine tool column rib layout multi-objective optimization topology optimization

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Abstract ：

To enhance the efficiency of topology optimization and reduce the number of gray units, power function, composite exponential function and rational fraction function are introduced as filtering functions based on independent continuous mapping (ICM) method, and a topology optimization model with minimum weight as the objective and displacement as the constraint is fomulated. Numerical examples were employed to investigate the effects of three kinds of filter functions and the parameter ratio of element weight and element stiffness filter functions on the efficiency of topology optimization and gray units were studied. Numerical examples show that the rational fraction function can effectively reduce the number of intermediate gray units, improve the convergence speed and reduce the weight of the structure. For the power function, when the parameter ratio of element weight and element stiffness filter function is 1∶ 7, the effect is optimal. For the composite exponential function, when the parameter ratio of element weight and element stiffness filter function is 1. 3 ∶ 0. 1, the effect is optimal. For the rational fraction filter function, when the parameter ratio of element quality and element stiffness filter function is 3∶ 63, the effect is optimal. © 2025 Beijing University of Technology. All rights reserved.

Keyword ：

displacement constraint gray-scale element filter function topology optimization independent continuous mapping (ICM) method optimal efficiency

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Abstract ：

This paper presents a deep learning-based topology optimization method for the joint design of material layout and fiber orientation in continuous fiber-reinforced composite structure (CFRCS). The proposed method mainly includes three steps: (1) a ResUNet-involved generative and adversarial network (ResUNet-GAN) is developed to establish the end-to-end mapping from structural design parameters to fiber-reinforced composite optimized structure, and a fiber orientation chromatogram is presented to represent continuous fiber angles; (2) to avoid the local optimum problem, the independent continuous mapping method (ICM method) considering the improved principal stress orientation interpolated continuous fiber angle optimization (PSO-CFAO) strategy is utilized to construct CFRCS topology optimization dataset; (3) the well-trained ResUNet-GAN is deployed to design the optimal structural material distribution together with the corresponding continuous fiber orientations. Numerical simulations for benchmark structure verify that the proposed method greatly improves the design efficiency of CFRCS along with high design accuracy. Furthermore, the CFRCS topology configuration designed by ResUNet-GAN is fabricated by additive manufacturing. Compression experiments of the specimens show that both the stiffness structure and peak load of the CFRCS topology configuration designed by the proposed method have significantly enhanced. The proposed deep learning-based topology optimization method will provide great flexibility in CFRCS for engineering applications. © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2024.

Keyword ：

Fiber-reinforced composite structure Generative and adversarial networks Additive manufacturing Topology optimization

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Abstract ：

本文把ICM方法中的过滤函数和变密度方法中的惩罚函数统称为映射函数，研究了该函数的选取问题，探讨了其选取对于结构拓扑优化优化迭代收敛效率的影响.为此，本文提出了高效率收敛的映射函数构造途径，写出了5类常见的具体映射函数形式，提出同高效率收敛映射函数MFHEC(Mapping function with highly efficient convergence)相配套的优化模型和寻优解法，先是自行比较了同类映射函数的过滤函数和准过滤函数寻优中收敛的快慢，然后相互比较了不同形式映射函数的快滤函数寻优收敛的快慢.以ICM方法求解位移约束下结构体积极小的拓扑优化问题为例，通过数值计算比较，印证了MFHEC函数的高效率收敛性.结果表明：同类函数比较中，快滤函数的收敛速度更快；5种不同类型映射函数比较中，幂函数形式的过滤函数收敛速度更快.最后需要强调的是：本文研究的映射函数的结论，包括ICM方法的过滤函数和变密度方法中的惩罚函数，二者都是同样适用的.

Keyword ：

求解效率 映射函数 ICM方法 结构拓扑优化

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为了使得拓扑优化在优化过程中得到的最终结果不再具有锯齿状边界,本文基于自适应网格方法,提出了一种可移动变形边界方法,主要通过ICM方法建立以重量最小为目标、位移为约束的优化模型,采用三角形网格作为基础网格,并使用数值算例对该方法进行验证,并与没有使用该方法得到的拓扑构型进行对比。数值结果表明:提出的可移动变形边界方法在改善锯齿状边界问题具有很好的效果。

Keyword ：

可移动变形边界方法 拓扑优化 位移约束

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随着现代通信的不断进步和微电子产业的迅速发展,电子产品小型化和高密度化逐渐成为主流趋势,有源相控阵天线的收发组件,作为雷达重要组成部分和高温组件,其散热性能为目前雷达散热中研究的重点。本文以有源相控阵天线中以低温共烧陶瓷材料(LTCC)作为基板的收发组件散热为研究对象,通过在收发组件上方添加液冷散热的方式进行辅助散热,改善收发组件散热问题。通过COMSOL Multiphysics软件使用二维密度拓扑优化的方式,以压降与平均温度为优化目标获取流道几何模型、温度与流体特性结果,并于传统直通型流进行对比。结果表明拓扑优化后热源位置温度有较好的改善。

Keyword ：

LTCC T/R组件 拓扑优化 微流道

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