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结构拓扑优化ICM法中高效率收敛映射函数MFHEC的选取

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固体力学学报 2024年第2期45卷 253-265页

作者：隋允康彭细荣北京工业大学材料与制造学部北京100022 湖南城市学院土木工程学院益阳413000

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... 详细信息

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.

关键词：结构拓扑优化映射函数求解效率 ICM方法

Independent continuous mapping for topological optimization of frame structures

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Acta Mechanica Sinica 2006年第6期22卷 611-619页

作者： yunkang sui Jiazheng Du Yingqiao Guo Department of Mechanics Beijing University of Technology Beijing 100022 China Lab. GMMS University of Reims Champagne-Ardenne BP1039 51687 Reims France

Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.

关键词： Frame structures Topological optimization ICM method Filter functions Element elimination

Lightweight Topology Optimization with Buckling and Frequency Constraints Using the Independent Continuous Mapping Method

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Acta Mechanica Solida Sinica 2019年第3期32卷 310-325页

作者： Hongling Ye yunkang sui Weiwei Wang College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology Beijing 100124 China

This research focuses on the lightweight topology optimization method for structures under the premise of meeting the requirements of stability and vibration characteristics. A new topology optimization model with the constraints of natural frequencies and critical buckling loads and the objective of minimizing the structural volume is established and solved based on the independent continuous mapping method. The eigenvalue equations and composite exponential filter functions are applied to convert the optimization formulation into a continuous, solvable mathematical programming model. In the process of topology optimization, suitable initial values of the filter functions are chosen to avoid local modes, and the dynamic frequency gap constraints are added in the optimal model to prevent mode switches. Furthermore, for the optimal structures with grey elements obtained by the continuous optimization model, the bisection-inverse iteration is applied to search the optimal discrete structures. Finally, a detailed scheme is given for the buckling and frequency topology optimization problem. Numerical examples illustrate that the modelling method of minimizing the economic index with given performance requirements is practical and feasible for multi-performance topology optimization problems.

关键词： Topology optimization Lightweight Buckling constraints Frequency constraints ICM method

Topology optimization of continuum structures considering damage based on independent continuous mapping method

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Acta Mechanica Sinica 2019年第2期35卷 433-444页

作者： Jiazheng Du Yunhang Guo Zuming Chen yunkang sui College of Mechanical Engineering and Applied Electronics Technology Beijing University of Technology Beijing 100124 China

A continuum topology optimization usually produces results similar to a skeleton structure. In addition, the material utilization in the optimized structure is greatly improved compared with the original structure. On the other hand, the redundancy of the structure is greatly reduced due to the removed material. A partial local failure in the optimized structure makes it more difficult for the entire structure to meet the strength/stiffness requirements. By using the independent continuous mapping (ICM) method, with minimal weight as the objective and both stress and displacement as the respective constraints, the continuum topology optimization models can be employed, which also consider damage. A dual-sequence quadratic programming (DSQP) algorithm is used to solve the topology optimization models. Numerical examples confirm the effectiveness and feasibility of the models. The results indicate that both a good load-path and weight reduction can be obtained. In addition, compared with the structure obtained using conventional topology optimization, redundancy is improved greatly, and the strength/stiffness requirements for the structure can be satisfied for each damage scenario. Furthermore, the results indicate that the strength/stiffness of the structure, after topology optimization, is slightly sensitive for local damage.

关键词： Damage Redundancy Topology optimization ICM method

Fatigue Topology Optimization Design Based on Distortion Energy Theory and Independent Continuous Mapping Method

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Computer Modeling in Engineering & Sciences 2021年第7期128卷 297-314页

作者： Hongling Ye Zonghan Li Nan Wei Pengfei Su yunkang sui Faculty of Materials and Manufacturing Beijing University of TechnologyBeijing100124China

Fatigue failure is a common failure mode under the action of cyclic loads in engineering applications,which often occurs with no obvious signal.The maximum structural stress is far below the allowable stress when the structures are damaged.Aiming at the lightweight structure,fatigue topology optimization design is investigated to avoid the occurrence of fatigue failure in the structural conceptual design beforehand.Firstly,the fatigue life is expressed by topology variables and the fatigue life filter function.The continuum fatigue optimization model is established with the independent continuous mapping(ICM)method.Secondly,fatigue life constraints are transformed to distortion energy constraints explicitly by taking advantage of the distortion energy theory.Thirdly,the optimization formulation is solved by the dual sequence quadratic programming(DSQP).And the design scheme of lightweight structure considering the fatigue characteristics is obtained.Finally,numerical examples illustrate the practicality and effectiveness of the fatigue optimization method.This method further expands the theoretical application of the ICM method and provides a novel approach for the fatigue optimization problem.

关键词： Fatigue optimization distortion energy theory S-N curve independent continuous mapping method

The ICM method with objective function transformed by variable discrete condition for continuum structure

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Acta Mechanica Sinica 2006年第1期22卷 68-75页

作者： yunkang sui Xirong Peng Numerical Simulation Center for Engineering The College of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijing 100022

ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

关键词： Structural topological optimization ICM method Checkerboard patterns Mesh dependence Thedeleting rate

化可分离凸规划为对偶规划显式模型的普适解法研究比较

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力学学报 2023年第10期55卷 2417-2426页

作者：彭细荣隋允康湖南城市学院土木工程学院湖南益阳413000 北京工业大学材料与制造学部北京100022

文章旨在提升对偶规划显式模型(dual programming-explicit model,DP-EM)的建模和求解的境界.DPEM模型从一类变量可分离凸规划的特点出发,突破了对偶目标二阶采用近似的定势,推导得出显式的对偶目标函数;应用于ICM方法求解连续体结构拓... 详细信息

文章旨在提升对偶规划显式模型(dual programming-explicit model,DP-EM)的建模和求解的境界.DPEM模型从一类变量可分离凸规划的特点出发,突破了对偶目标二阶采用近似的定势,推导得出显式的对偶目标函数;应用于ICM方法求解连续体结构拓扑优化问题时,其求解效率比对偶序列二次规划方法(DSQP)和可移动渐近线方法(MMA)求解效率更高.文章进一步把常见的一类显式模型抽象为普适的可分离凸规划列式,在需要满足的一些条件下,转换为DP-EM模型,并且提出4种处理方法:(1)对偶变量迭代逼近法;(2)指数函数形式的解法;(3)幂函数形式的解法;(4)基于变换的精确解法.为了进行数值验证,做了广泛的计算,限于篇幅,文章列出了5个具有代表性的算例,除了算例1属于纯数学问题,其余4个算例皆基于ICM方法,分别对于位移、应力、疲劳等约束和破损−安全的连续体结构拓扑优化问题,基于所提出的方法进行建模和求解,都显示了所提出方法的普适性及更高的求解效率.工作的意义在于:(1)深度方面,加深了结构优化对偶解法的研究;(2)广度方面,对数学规划对偶理论的发展做出了新的贡献.

关键词：结构拓扑优化映射函数求解效率 ICM方法

CHARACTERISTICS OF STRENGTH CONTROL OF ADAPTIVE STRUCTURE WITH ELECTROMECHANICAL COUPLING

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Acta Mechanica Solida Sinica 2002年第1期15卷 49-61页

作者： sui yunkang Shao jianyi College of Electromechanical Engineering Beijing Polytechnic UniversityBeijing 100022China Department of Engineering Mechanics Dalian University of TechnologyDalian 116023China

Based on the programming method, an electromechanical coupling adaptive statically indeterminate truss structure is controlled for increasing its load capacity. Several main parameters during the process of design of the adaptive structure are selected for a study of its characteristic during the control stage. The curves of each parameter for the effect of control results are plotted and corresponding conclusions are drawn. Thus, the theoretical basis is presented for optimal design, manufacture and control of the adaptive structure.

关键词： adaptive structure strength control characteristic research electromechanical coupling selection of parameters

结构安全观念的进化直至破损-安全的结构拓扑优化

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应用力学学报 2023年第6期40卷 1239-1248页

作者：隋允康彭细荣北京工业大学工程数值模拟中心北京100124 湖南城市学院土木工程学院益阳413000

确保结构安全是力学在工程应用中永远关心的问题,为此,综述了结构安全观念的进化过程,将其划分为5个阶段:其一、从材料的永驻安全到材料的常驻安全,这是观念的滥觞;其二,从材料的尽驻安全到构件的尽驻安全,这是观念的渐变;其三,从构件... 详细信息

确保结构安全是力学在工程应用中永远关心的问题,为此,综述了结构安全观念的进化过程,将其划分为5个阶段:其一、从材料的永驻安全到材料的常驻安全,这是观念的滥觞;其二,从材料的尽驻安全到构件的尽驻安全,这是观念的渐变;其三,从构件的尽驻安全到结构的破损-安全,这是观念的飞跃;其四,基于破损-安全的结构截面与形状优化,这是观念的叠加;其五,基于破损-安全的结构拓扑优化,这是观念的昇华。由于第五阶段是学者们在当前最关注的研究之一,对此着墨颇多,且举出了有代表性的理论和算例。接着,又在观念的启迪和观念本质上,进行了两方面的展开:其一,从基于破损-安全的结构分析和结构优化,讨论了观念的启迪,启迪1是,遵循破损-安全设计原则而不放弃安全-经济设计原则,启迪2是,沿袭超静定结构的感性设计经验上升到理性生成冗余区域的阶段;其二,从结构在役破损-安全的时间与空间剖析,讨论了观念的本质,并且给出了清晰的列表。

关键词：结构分析和优化结构安全观念发展历程基于破损-安全的结构拓扑优化