Independent continuous and mapping method of structural topology optimization based on the global stress approach

There are three difficulties in topology optimization of continuum structures. 1) The topology under multiple load case is more difficult to be optimized than under single load case, because the former becomes a multiple objective based on compliance objective functions. 2) With local constraints, such as an elemental stress limit, the topology is more difficult to be solved than with global constraints, such as the displacement or frequency limits, because the sensitivity analysis of the former has very expensive computation. 3) With the phenomenon of load illness, which is similar with stiffness illness in the structural analysis, it is not easy to get the reasonable final topological structure, because it is difficult to consider different influences between the loads with small forces and big forces, and some topology paths of transferring small forces may disappear during the iteration process. To overcome difficulties above, four measures are adopted. 1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises strength theory, all elements’ stress constraints are transformed into a structural energy constraint. 3) The phenomenon of load illness is divided to classify into three cases. 4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of load illness are solved in terms of different complementary approaches. Several numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of load illness can be solved well by the weighting method that takes the structural energy as a weighting coefficient.     

Independent continuous and mapping method of structural topology optimization based on global stress approach

There are three difficulties in topology optimization of continuum structures. 1) The topology under multiple load case is more difficult to be optimized than under single load case, because the former becomes a multiple objective based on compliance objective functions. 2) With local constraints, such as an elemental stress limit, the topology is more difficult to be solved than with global constraints, such as the displacement or frequency limits, because the sensitivity analysis of the former has very expensive computation. 3) With the phenomenon of load illness, which is similar with stiffness illness in the structural analysis, it is not easy to get the reasonable final topological structure, because it is difficult to consider different influences between the loads with small forces and big forces, and some topology paths of transferring small forces may disappear during the iteration process. To overcome difficulties above, four measures are adopted. 1) Topology optimization model is established by independent continuous mapping (ICM) method. 2) Based on the von Mises strength theory, all elements’ stress constraints are transformed into a structural energy constraint. 3) The phenomenon of load illness is divided to classify into three cases. 4) A strategy based on strain energy is proposed to adopt ICM method with stress globalization, and the problems of the above mentioned three cases of load illness are solved in terms of different complementary approaches. Several numerical examples show that the topology path of transferring forces can be obtained more easily by substituting global strain energy constraints for local stresses constraints, and the problem of load illness can be solved well by the weighting method that takes the structural energy as a weighting coefficient.     

某轻型载货车储气罐支架振动断裂分析与优化

为了有效解决某轻型载货车储气罐支架的断裂故障,首先基于建立的储气罐支架有限元模型进行振动特性分析,分析结果表明其前三阶固有频率接均处于发动机激励频率范围之外,不会产生共振。其次测试各种道路的时域载荷,测试结果表明其中角度搓板路的激励频率与储气罐支架第一阶固有频率相接近,从而引起共振,不满足振动特性要求。然后对其进行振动强度分析,分析结果表明其应力水平不达标,其最大应力点与开裂处一致。再对其进行振动疲劳寿命预测分析,分析结果表明其疲劳寿命也不达标,其危险点也与失效位置相同。再采用集成平台对储气罐支架的结构进行优化设计,优化之后其模态频率、振动强度和振动疲劳均符合性能要求,并且其重量也有所减轻,总体优化效果较佳。最后整车试验结果表明优化之后储气罐支架的振动大幅度降低,并且没有发生失效。     

机载SAR天线座连接支架的拓扑优化设计

拓扑优化方法在雷达天线座的减重设计中具有突出优势,特别适合于大型精密雷达和机载雷达天线座的结构优化设计。文中建立了连接支架的拓扑优化模型,以单元密度为设计变量,体积分数上限为约束条件,加权应变能最小化为优化目标,对机载SAR天线座连接支架进行了拓扑优化设计。考虑到结构美观和制造性,添加了对称平面约束和拔模约束。结果表明:拓扑优化结果符合仿生学原理,在减轻质量的同时,也提高了结构性能。     

典型安装架在随机振动下的优化设计

采用仿真和试验的方法对机载电子设备安装架在随机振动条件下的优化设计进行了研究。首先,采用静力等效思路将随机振动载荷转化为静载荷,对安装架在静载荷下进行拓扑优化。接着,基于拓扑优化结果进行了模型设计和动力学仿真分析,分析结果表明,在保证优化后质量不高于原设计模型的条件下,优化后安装架的强度和刚度都有显著提高。最后,通过随机振动试验验证了该优化设计的可行性。     

Power flow response based dynamic topology optimization of bi-material plate Structures

Work on dynamic topology optimization of engineering structures for vibration suppression has mainly addressed the maximization of eigenfrequencies and gaps between consecutive eigenfrequencies of free vibration, minimization of the dynamic compliance subject to forced vibration, and minimization of the structural frequency response. A dynamic topology optimization method of bi-material plate structures is presented based on power flow analysis. Topology optimization problems formulated directly with the design objective of minimizing the power flow response are dealt with. In comparison to the displacement or velocity response, the power flow response takes not only the amplitude of force and velocity into account, but also the phase relationship of the two vector quantities. The complex expression of power flow response is derived based on time-harmonic external mechanical loading and Rayleigh damping. The mathematical formulation of topology optimization is established based on power flow response and bi-material solid isotropic material with penalization(SIMP) model. Computational optimization procedure is developed by using adjoint design sensitivity analysis and the method of moving asymptotes(MMA). Several numerical examples are presented for bi-material plate structures with different loading frequencies, which verify the feasibility and effectiveness of this method. Additionally, optimum results between topological design of minimum power flow response and minimum dynamic compliance are compared, showing that the present method has strong adaptability for structural dynamic topology optimization problems. The proposed research provides a more accurate and effective approach for dynamic topology optimization of vibrating structures.     

MM52160龙门导轨磨床立柱的拓扑优化

对MM52160龙门导轨磨床的立柱部分进行结构拓扑优化.建立立柱三维模型,对其进行静力学分析和模态分析.在原有模型不改变质量的情况下进行简化模型,结果表明：简化模型比原模型的最大静态位移减小了2.42 μm,第一阶固有频率提高了2.85％.对篱化模型进行拓扑优化,查看材料分布.对优化后的结构进行动静态刚度分析,分析结果表明：优化后的结构对比原模型后最大静态位移减小了0.81 μm,第一阶固有频率提高了3.72％,质量减少了15％.通过结构拓扑优化,优化后的结构动静态刚度提高了,质量减少了.     

振动夹具的综合优化设计

夹具设计要求质量轻、刚度大。为了在这两者间取得平衡,文中综合使用拓扑优化和尺寸优化两种方法对夹具进行优化设计以实现设计目标。基于拓扑优化结果设计了夹具的拓扑优化模型。虽然相对于初始模型,该模型的第1阶固有频率降低了36.5%,但其质量降低了66.7%,表明拓扑优化效费比显著。以设计参数的合理设计范围作为约束条件,把使第1阶固有频率最大和夹具质量最轻作为优化目标来实施尺寸优化,得到夹具的详细设计模型。与拓扑优化模型相比,该模型的质量降低了3%,第1阶固有频率提升了6%。之后对振动夹具实施了随机振动试验。受试设备安装点的功率谱密度响应曲线的均方根值最大为输入谱均方根值的1.17倍,说明夹具具有良好的动力学传递特性,夹具的综合优化设计方法有效可行。     

一种测控天线支架的优化设计

在航天领域,星上载荷的质量直接影响整星的发射成本。为了降低星上天线的质量,文中以某卫星测控天线支架为研究对象,在满足天线电性能和力学性能的前提下,采用传统方法和拓扑优化分别对支架进行改进设计,然后利用有限元分析软件Workbench对天线进行仿真分析,得到模态响应曲线和正弦振动应力云图,并对比分析仿真结果,获得支架的最优结构设计方案。该支架通过拓扑优化设计并采用增材制造（3D打印）技术加工,不仅满足各项性能指标要求,而且其质量降低了20.3%,加工时间也缩短了近60%。     

基于模态控制的结构/控制一体化优化设计

先分析了结构主动控制的模态控制。从结构与控制器一体化优化设计的角度出发 ,提出了以结构的质量和控制能量最小化为优化目标、以基频和结构的动响应为约束的联合优化设计模型。并对该优化设计模型进行了一定的简化处理 ,采用改进的拓扑组方法进行结构的集成拓扑优化设计。数值算例的结果表明 ,结构 /控制一体化优化设计是可行且有效的。     

考虑载荷随机性的可行域调整的结构拓扑优化设计

考虑载荷大小和方向的不确定性,以结构柔顺度的期望和方差的加权和为目标函数,结构体积为约束函数,研究稳健结构拓扑优化方法。首先给出载荷大小和方向不确定情况下结构柔顺度期望和方差及其导数的显式近似式,而后改进可行域调整方案,提出具有收敛特征的稳健结构拓扑优化设计方法,探讨结构柔顺度期望和方差的权重因子以及随机量的方差对拓扑构型的影响。给出的算例表明,不论是确定载荷拓扑优化还是随机载荷拓扑优化,方法是可行和有效的,且可获得一系列清晰的拓扑构型和稳健的优化拓扑。     

基于拓扑优化的卧式旋压机床身加强肋布局优化设计方法

提出了基于拓扑优化的卧式旋压机床身加强肋布局优化设计方法。在确定设计空间及载荷后,采用带惩罚的变密度法(Solid Isotropic Microstructures with Penalization,SIMP)的结构拓扑优化技术,以多工况静力结构柔度和1阶自然频率为优化目标,建立了床身模结构拓扑优化模型,并在考虑工艺性的前提下,确定了床身板件焊接加强肋的最优布局。优化前、后的对比表明,优化后床身的静、动态性能均得到了显著提高,最大应力下降了13.39%,导轨刚度提高10.78%,1阶自然频率提高了9.28%。     

基于HyperMesh/OptiStruct的发动机支架结构拓扑优化设计

利用SolidWorks三维建模软件建立发动机支架的原始计算机辅助设计(computer aided design, CAD)模型,并将其CAD模型导入HyperMesh,生成三维模型,对发动机支架有限元模型的静态特性和动态特性进行分析,进而利用HyperMesh自带的OptiStruct优化模块中的变密度拓扑优化算法...     

电容式微加速度传感器微结构的拓扑优化

采用均匀化方法,以电容式微加速度传感器微结构的第一阶谐振频率为目标函数,以微结构的体积作为约束条件,建立了微结构的拓扑优化模型,对叉指式微加速度传感器微结构进行了拓扑优化设计,经计算获得满足体积约束并使第一阶谐振频率最大的微结构拓扑形式。计算结果表明该方法可以很好地解决微加速度传感器灵敏度和谐振频率这一对矛盾,在满足灵敏度的要求下提高微加速度传感器的测量范围上限,不失为一种先进的、有效的电容式微加速度传感器微结构的设计方法。     

基于各向正交惩罚材料密度法的汽车控制臂的优化设计

建立了以刚度最优值(最小柔顺性)为目标函数,体积约束作为约束条件,有限元单元的相对密度为设计变量的汽车控制臂结构拓扑优化模型,对多功能车上使用的A型控制臂结构在概念设计阶段进行了拓扑优化。优化过程中采用各向正交惩罚材料密度法(SIMP)理论建立数学模型,并应用优化准则算法求解数学模型,得到控制臂的概念设计优化模型,为结构详细设计阶段的形状优化和尺寸优化提供设计依据。从结构概念设计的结果知:优化设计过程较稳定、能有效满足概念设计的需要。     

基于拓扑优化的加工中心十字滑台结构设计

基于零件结构静态和动态性能及轻量化的总体设计目标,利用结构拓扑优化方法完成了立式加工中心十字滑台的结构设计,解决了零件结构静、动刚度不足问题及质量过重导致的机床加速性能不良等问题。首先,详细分析了十字滑台的工况。其次,针对同时满足十字滑台具有良好的静动态性能并减轻其质量的设计需求,采用结构的柔度最小和基频最大为目标函数以及体积比为约束的多目标、多工况的结构拓扑优化方法,进行了十字滑台的结构拓扑优化设计,获得了其结构构型。最后,分析并对比了十字滑台新结构和原有结构的刚度、固有频率、质量及机床加速性能,验证了新结构具有良好的性能。     

桁架结构动力学拓扑优化设计解的存在性探讨

首先证明了桁架结构在拓扑构形不变的情况下 ,优化的关键约束—频率的极值的存在。然后进一步从两个方面给出了桁架结构动力学拓扑优化解存在的基本理论 :无固频约束时 ,设计变量连续且不考虑上限约束 ,则优化问题总是有解 ;考虑固频约束时 ,频率约束是是否有解的关键约束 ,并且改变结构拓扑形状可以改变解的存在性。文中算例说明所提理论是正确、合理和有效的。     

Isogeometric topology optimization based on energy penalization for symmetric structure

We present an energy penalization method for isogeometric topology optimization using moving morphable components (ITO–MMC), propose an ITO–MMC with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an ITO–MMC with a symmetric constraint. The energy penalization method can solve the problems of numerical instability and convergence for the ITO–MMC and the ITO–MMC subjected to the structural symmetric constraint with asymmetric loads. Topology optimization problems of asymmetric, bilateral symmetric, and periodic symmetric structures are discussed to validate the effectiveness of the proposed energy penalization approach. Compared with the conventional ITO–MMC, the energy penalization method for the ITO–MMC can improve the convergence rate from 18.6% to 44.5% for the optimization of the asymmetric structure. For the ITO–MMC under a bilateral symmetric constraint, the proposed method can reduce the objective value by 5.6% and obtain a final optimized topology that has a clear boundary with decreased iterations. For the ITO–MMC under a periodic symmetric constraint, the proposed energy penalization method can dramatically reduce the number of iterations and obtain a speedup of more than 2.     

拓扑优化的数控车削中心床鞍轻量化设计

对数控车削中心床鞍的结构轻量化设计方法进行了研究。基于机床在切削作用下的典型工况,分析其载荷和边界条件;建立体积约束下的床鞍结构多工况静态性能和动态性能多目标拓扑优化数学模型,根据拓扑优化结果构建床鞍的优化概念模型;利用结构优化设计的思想对概念模型进行结构刚度设计,最终为企业提供了新的床鞍结构方案;在保证床鞍刚度和动态性能的前提下,床鞍的质量减少了14.33%,表明该设计方法能够有效实现结构轻量化设计。     

基于拓扑优化的某系留气球设备挂架优化设计

文中针对某型系留气球设备挂架尺寸大,承载重、自重和刚强度要求严苛等特点,开展了挂架结构的优化设计工作.基于拓扑优化技术对设备挂架的结构形式,特别是主要承力部件的布局进行了重新设计,并对新设计方案进行了有限元分析和静力加载试验.结果显示,新设计方案在结构刚强度和重量上都优于原设计方案,且各种指标均满足设计要求.