基于交叉过滤的刚架结构拓扑优化

针对目前离散体拓扑优化在大型刚架结构中的广泛应用以及此类方法对制造工艺的忽视,该文给出了交叉准确的数学描述,提出了交叉因子的概念,通过Heavisid函数建立了由截面积设计变量到交叉因子的连续函数。依此在优化模型中加入交叉过滤约束,利用基结构法建立了拓扑优化模型。最后将该方法应用到天线辐射梁的设计中,结果显示该方法能有效地消除不需要的单元交叉。     

一种变频率约束限的结构拓扑优化方法

针对仅频率约束和重量最小的结构拓扑优化问题,基于ICM(独立、连续、映射)方法和渐进结构优化方法的思路,提出了一种变频率约束限的结构拓扑优化方法.在优化迭代循环的每一轮子循环迭代求解开始时,为了控制拓扑设计变量的变化量,依据结构频率和其约束限,形成和引进了新的频率约束限.另外,建立了单元删除阈值和几轮迭代循环的单元删除策略.为了确保优化迭代中结构非奇异和方法具有增添单元的功能,在结构孔洞和边界周围引入了一层人工材料单元.结合拉格朗日乘子法,形成了一种新的连续体结构的拓扑优化方法.给出的算例表明该方法没有目标函数的振荡现象,且验证了该方法的正确性和有效性.     

基于变频率区间约束的结构材料优化设计

针对频率约束的结构材料优化问题,基于结构拓扑优化思想,提出变频率区间约束的结构材料优化方法。借鉴均匀化及ICM(独立、连续、映射)方法,以微观单元拓扑变量倒数为设计变量,导出宏观单元等效质量矩阵及导数,进而获得频率一阶近似展开式。结合变频率区间约束思想,获得以结构质量为目标函数、频率为约束条件的连续体微结构拓扑优化近似模型;采用对偶方法求解。通过算例验证该方法的有效性及可行性,表明考虑质量矩阵变化影响所得优化结果更合理。     

位移约束刚架拓扑优化的非线性有无复合体方法

为了提高基于物理模型的结构拓扑优化的寻优效率, 该文提出了非线性有无复合体, 以刚架结构在位移约束下的拓扑优化为例, 进行了结构重量目标函数极小化的数学模型建立和程序实现。与线性有无复合体不同, 非线性有无复合体是无限多个无穷小的“有单元”和“无单元”各自长度的非线性组合。由于每个梁单元“有”单元长度和“无”单元长度之和的不变性, 其拓扑变量可以用“有”单元的总长度予以表达。推导了结构重量、位移约束同结构拓扑变量的显式函数, 建立了优化模型。使用线性规划算法求解了相应的优化模型, 算例表明, 该文方法的寻优效率得到了提高。同作为数学变换的ICM(独立、连续和映射)方法比较, 该文提出的作为物理模型的方法, 二者在解决结构拓扑优化上具有异曲同工之效:后者的“有”单元长度的非线性关系替代了前者的单元重量、位移约束中的过滤函数。数学变换方法与物理模型方法的异同点更是耐人寻味。 方法     

连续体结构的变密度拓扑优化方法研究

为了实现使连续体结构的体积约束和柔顺度最小的拓扑优化及解决采用经典变密度法引起的结构优化结果存在如灰度单元、棋盘格等数值不稳定问题，提出了一种新的拓扑优化方法。首先，采用改进的固体各向同性材料惩罚法作为材料插值方案，建立结构拓扑优化模型；其次，通过引入基于高斯权重函数的敏度过滤法和设计新灰度单元抑制算子来解决数值不稳定问题；最后，借助优化准则法求解优化模型。通过算例分析可知：新策略可以改进拓扑优化方法；新的拓扑优化方法具有收敛速度较快、能更好地获取柔顺度小且拓扑构型好的优化结构和抑制灰度单元产生等优势。研究结果为其他连续体结构的拓扑优化研究提供了新思路。     

基于动响应约束的结构材料优化设计

针对于随机荷载作用下动响应为约束的结构材料优化问题,基于结构拓扑优化思想,提出了一种变动响应约束的结构材料优化方法。采用分式有理式和幂函数识别结构材料单元特性参数,以微观单元拓扑变量倒数为设计变量,导出了频率及振型对微观单元设计变量的一阶导数,进而得到了随机荷载作用下结构均方响应的一阶近似展开式。结合变约束限的思想,建立了以结构质量作为目标函数,均方响应作为约束条件的连续体微结构拓扑优化近似模型,并采用对偶方法进行求解。对典型结构进行了考虑单个和多个动响应约束的结构材料优化设计,优化所得结果验证了该方法的有效性和可行性。     

屈曲与应力约束下连续体结构的拓扑优化

基于ICM(独立、连续、映射)方法建立了以结构重量最小为目标,以屈曲临界力、应力同时为约束的连续体拓扑优化模型:采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开;借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明:该方法可以有效地解决屈曲与应力约束共同作用的连续体拓扑优化问题,能够得到合理的拓扑结构,并有较高的计算效率。     

基于多分辨率-多边形单元建模策略的多材料结构动刚度拓扑优化方法

利用多边形有限单元的高精度求解优势,融合多分辨率拓扑优化方法,实现粗糙位移网格条件下的高分辨率构型设计,由此提出多材料结构动刚度问题的拓扑优化方法。将多边形单元(位移场求解单元)劈分为精细的小单元,构造设计变量与密度变量的重叠网格,形成多分辨率-多边形单元的优化建模策略;以平均动柔度最小化为目标和多材料的体积占比为约束,建立多材料结构的动力学拓扑优化模型,通过HHT-α方法求解结构动响应,采用伴随变量法推导目标函数和约束的灵敏度表达式,利用基于敏度分离技术的ZPR设计变量更新方案构建多区域体积约束问题的优化迭代格式;通过典型数值算例分析优化方法的可行性和动态载荷作用时间对优化结果的影响机制。     

考虑结构稳定性的变密度拓扑优化方法

将稳定性问题引入传统变密度法中,可实现包含稳定性约束的平面模型结构拓扑优化。以单元相对密度为设计变量,结构柔度最小为目标函数,结构体积和失稳载荷因子为约束条件建立优化问题数学模型,提出了一种考虑结构稳定性的变密度拓扑优化方法。通过分析结构柔度、体积、失稳载荷因子对设计变量的灵敏度,并基于拉格朗日乘子法和Kuhn-Tucker条件,推导了优化问题的迭代准则。同时,利用基于约束条件的泰勒展开式求解优化准则中的拉格朗日乘子。通过推导平面四节点四边形单元几何刚度矩阵的显式表达式,得到了优化准则中的几何应变能。最后,通过算例对提出的方法进行了验证,并与不考虑稳定性的传统变密度拓扑优化方法进行对比,结果表明该方法能显著提高拓扑优化结果的稳定性。研究结果对细长受压结构的优化设计有重要指导意义,对结构的稳定性设计有一定参考价值。     

三杆类桁架材料模型多工况最小柔度优化

研究了多工况结构柔度最小化方法。提出了3杆类桁架连续体材料模型。推导了该材料的刚度矩阵及其导数。通过优化杆件分布场得到优化的类桁架连续体。克服了目前普遍采用单元的"有"和"无"表示结构拓扑的轮廓粗糙、锯齿状边界问题。结点位置的杆件密度和方向作为设计变量,杆件在单元内的密度和方向通过结点位置的数值插值得到,并且在单元内连续变化。由于没有抑制中间密度,完全不存在数值不稳定问题。类桁架连续体由于与杆系结构有明确的对应关系,可以合理地转化杆系结构。选择杆件分布场中的部分杆件可以形成杆系结构。如果再进一步作尺寸和形状优化就可以得到最终的拓扑优化结构。     

自由阻尼层结构阻尼材料配置优化的拓扑敏度法

提出阻尼胞单元和阻尼拓扑敏度等概念，建立了基于阻尼拓扑敏度综合评价的阻尼材料拓扑优化准则，并用于自由阻尼层结构振动控制中阻尼材料的配置优化。建立待控结构阻尼材料布局的拓扑基结构，计算各单元的阻尼拓扑敏度。再建立考虑重量目标及结构频响峰值约束的阻尼材料配置拓扑优化模型。根据所提出的阻尼材料拓扑优化准则，求解上述配置优化问题，确定阈值和各单元拓扑值。并用若干典型结构算例，验证所提出方法的正确性，讨论了阻尼材料布局拓扑基结构的规模与优化效率的关系。     

Truss topology optimization with static and dynamic constraints using modified subpopulation teaching–learning-based optimization

In this study, an improved version of the teaching–learning-based optimization (TLBO) algorithm is proposed for truss topology optimization (TTO), with static and dynamic constraints on planar and space trusses. The basic TLBO algorithm is improved to enhance its exploration and exploitation abilities by considering various factors such as the number of teachers, adaptive teaching, tutorial learning and self-motivated learning. The TTO problems are considered with multiple load conditions and subjected to constraints for natural frequencies, element stresses, nodal displacements, Euler buckling criteria and kinematic stability conditions. TTO is achieved with the removal of superfluous elements and nodes from the ground structure, and results in a mass saving. In this method, difficulties arise owing to singular solution and unnecessary analysis; therefore, the finite element model is reformed to resolve these issues. A single-stage optimization approach is used, in which size and topology optimization are considered simultaneously. The results obtained are compared with the best solutions obtained by the algorithm. The results reveal that the modified subpopulation teaching–learning-based optimization (MS-TLBO) algorithm is more effective than other state-of-the-art algorithms.     

A GA‐based technique for layout optimization of truss with stress and displacement constraints

Various developments of increasing complexity involved in layout optimization are discussed. The use of conventional GA in layout optimization is briefly mentioned with emphasis on its limitations and conditions imposed in finding the optimal design. The proposed new technique is applied to the benchmark example of Michell's truss for verification. The approach has also been applied to new examples of bridge truss and crane truss problems in order to demonstrate the generality and robustness for topology optimization. The approach is extended to include dual stress‐displacements constraints since many practical problems involve these two constraints simultaneously. Two‐bar and 10‐bar trusses are solved as examples for layout optimization with both stress and displacement constraints with satisfactory results. The effect of mutation on the final topology is also discussed. The major drawbacks of the ground structure approach are overcome in this proposed new method. The optimal designs obtained demonstrate the ability, robustness and generality of using the proposed new technique in layout optimization problems. Copyright © 2001 John Wiley & Sons, Ltd.     

Integrated layout design of multi‐component system

A new integrated layout optimization method is proposed here for the design of multi‐component systems. By introducing movable components into the design domain, the components layout and the supporting structural topology are optimized simultaneously. The developed design procedure mainly consists of three parts: (i) Introduction of non‐overlap constraints between components. The finite circle method (FCM) is used to avoid the components overlaps and also overlaps between components and the design domain boundaries. (ii) Layout optimization of the components and supporting structure. Locations and orientations of the components are assumed as geometrical design variables for the optimal placement while topology design variables of the supporting structure are defined by the density points. Meanwhile, embedded meshing techniques are developed to take into account the finite element mesh change caused by the component movements. (iii) Consistent material interpolation scheme between element stiffness and inertial load. The commonly used solid isotropic material with penalization model is improved to avoid the singularity of localized deformation in the presence of design dependent loading when the element stiffness and the involved inertial load are weakened by the element material removal. Finally, to validate the proposed design procedure, a variety of multi‐component system layout design problems are tested and solved on account of inertia loads and gravity center position constraint. Solutions are compared with traditional topology designs without component. Copyright © 2008 John Wiley & Sons, Ltd.     

A robust dual algorithm for topology design of structures in discrete variables

Dual optimization algorithms for the topology optimization of continuum structures in discrete variables are gaining popularity in recent times since, in topology design problems, the number of constraints is small in comparison to the number of design variables. Good topologies can be obtained for the minimum compliance design problem when the perimeter constraint is imposed in addition to the volume constraint. However, when the perimeter constraint is relaxed, the dual algorithm tends to give bad results, even with the use of higher‐order finite element models as we demonstrate in this work. Since, a priori, one does not know what a good value of the perimeter to be specified is, it is essential to have an algorithm which generates good topologies even in the absence of the perimeter constraint. We show how the dual algorithm can be made more robust so that it yields good designs consistently in the absence of the perimeter constraint. In particular, we show that the problem of checkerboarding which is frequently observed with the use of lower‐order finite elements is eliminated. Copyright © 2001 John Wiley & Sons, Ltd.     

A novel reliability-based topology optimization framework for the concurrent design of solid and truss-like material structures with unknown-but-bounded uncertainties

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples.     

考虑位移要求的大型三维连续体结构拓扑优化数值技术研究

大型复杂三维结构拓扑优化设计既具有理论意义,又具有重要的应用价值。基于等效转换的非奇异的结构优化模型,研究结构位移要求的最小结构重量设计问题。首先,介绍了位移约束的三维结构优化准则和公式。而后,为了提高拥有数万个单元以上的三维结构的计算效率,结合结构位移计算的迭代方法,在分析用于结构特性参数计算模型的基础上,建立了一套三维结构拓扑优化的求解策略和算法。最后,给出了几个典型和复杂的三维结构的拓扑优化设计算例。算例表明求解策略和算法是正确和有效的,且具有广泛的工程应用前景。     

桁架结构智能布局优化设计

结构的布局优化由于涉及尺寸、形状和拓扑三个层次的综合设计而成为优化问题中的难点,结合桁架结构提出了一个基于多个初始基结构的布局优化方法。以智能生成的、型式多样合理的基结构代替传统模型中的单一基结构,然后从不同基结构下的拓扑优化结果中找出最优设计。在克服传统基结构法有可能限制求解空间而丢失最优解这一局限性的同时,将形状和拓扑优化设计有效分离,降低了求解的难度,并且结合拓扑变化法,实现了桁架结构从选型生成、分析计算到优化设计的一体化智能设计过程。算例表明:利用该文提出的方法进行桁架结构的最优布局设计是可靠有效的。