导重法求解单工况的拓扑优化问题

在拓扑优化中,因为设计变量多并且目标函数和约束函数都是设计变量的隐函数,求解难度较大,所以寻找更快更好的求解方法一直都是拓扑优化问题的研究重点。为此,将导重法引入到拓扑优化的求解中,介绍质量约束下求结构最优性能问题和性能约束下求结构最小质量问题的导重法迭代准则,采用密度惩罚(Solid isotropic material with penalization,SIMP)方法建立单工况下求最小柔度和最小质量这两类拓扑优化问题的优化模型,推导出用导重法求解这两类问题的迭代公式并计算了相应的算例,与ANSYS中采用的优化准则法(Optimality criteria,OC)和序列凸规划法(Sequential convex programming,SCP)进行对比分析。通过计算和对比分析显示出用导重法求解拓扑优化问题具有迭代公式简单、适用范围广、收敛速度快、求解效果好的优点。导重法为拓扑优化问题的求解提供了一条新的途径。     

基于RAMP插值模型结合导重法求解拓扑优化问题

在连续体拓扑优化领域中,寻求更好的建模方法和更快的求解算法一直是研究人员的研究重点。为此,针对拓扑优化设计方法中的变密度法进行深入分析。研究和比较各向同性惩罚微结构法(Solid isotropic microstructure with penalization,SIMP)和材料属性有理近似模型(Rational approximation of material properties,RAMP)的优缺点后,建立基于RAMP法的优化模型,并结合导重法求解算法,用于结构拓扑优化领域。详细推导单、多工况的最小柔度拓扑优化的迭代公式,给出导重法各变量的物理定义,并分别对单工况和多工况两个典型算例进行拓扑优化计算。算例结果令人满意,同时表明RAMP插值模型结合导重法求解结构拓扑优化问题具有设计变量少、迭代次数少、收敛速度快、优化效率高的特点,验证了其可行性和高效性。     

惯性载荷下飞行模拟器大臂结构的拓扑优化

采用导重法对惯性载荷下、以转动惯量为约束的拓扑优化问题进行求解。导重法经过改进,可以得到固定载荷下以整体柔顺度为目标、以转动惯量为约束的拓扑优化迭代公式。考虑到迭代计算时惯性载荷本身随各向同性固体微结构惩罚模型(Solid isotropic micro-structures with penalization,SIMP)中的伪密度的变化,进一步推导重力作用下的单工况拓扑优化迭代公式和重力-离心力同时作用下的多工况拓扑优化迭代公式,并通过相应算例证明其可行性和有效性。将得到的迭代算法应用于飞行模拟器大臂的优化设计中,并将由此得到的拓扑形貌与商业化优化软件Optistruct中得到的结果进行比较。对比显示:该算法比传统的序列线性规划法(Sequential linear programming,SLP)或移动渐近线法(Method of moving asymptotes,MMA)的优化效果更佳,且二者的迭代效率差别不大。导重法为惯性载荷作用下以总体柔度为目标、以转动惯量为约束的拓扑优化问题提供新的有效的解决思路。     

基于Lanczos法的模态重分析法在拓扑优化中的应用

在拓扑优化中,经常要求对结构进行修改,快速准确地计算修改后结构的低阶特征值对于提高整个结构优化的效率非常重要。将基于Lanczos算法的模态重分析法应用于拓扑优化过程中,利用初始结构模态分析结果,结合Lanczos算法和投影技术,采用缩减基方法求解修改结构的固有频率和振型, 则该方法同时具备了Lanczos向量快速收敛的优点和基于全局近似的缩减基向量的高精度。刚架算例验证了该重分析法的高精度。固支方形板和车架结构优化结果表明,该方法在保证求解精度的同时能够在一定程度上提高优化迭代速度。     

结构最优设计的一种自动高效迭代算法

论述结构优化数学规划法与准则法迭代求解的计算效率 ,讨论准则法遇到的两类困难与解决途径 ,介绍一种高效结构优化理性准则法———导重法所使用的步长因子法及其在自动迭代计算中存在的问题 ,提出一种求解结构优化准则方程组的自动高效迭代算法———类埃特金法 ,大量算例表明 ,该算法具有优化效率高 ,无需人为干预 ,适用范围广的优点。     

基于导重法的结构类周期性布局优化方法研究

受外形尺寸限制,一些结构的优化区域无法划分为均匀一致的有限元网格。由此产生的单元体积依赖性,常规周期性拓扑优化无法求解。提出一种基于导重法的结构类周期性布局优化方法。以最小柔度为目标函数,结构质量为约束条件,构建结构类周期性布局优化的数学模型。利用导重法推导出结构类周期性布局优化的迭代准则,解释其物理意义并给出其优化流程。以单元应变能密度为基础,提出一种改进的过滤方案以解决结构类周期性布局优化中单元体积依赖性问题。利用所提出的方法,对循环对称结构、二维汽车轮毂结构和梯形结构进行结构类周期性布局优化研究。研究结果表明,子域数目不同时均可以得到具有类周期性布局的最优拓扑形式。通过性能指标和相对应变能两个指标来评价三个算例的最优拓扑形式,验证了利用导重法求解结构类周期性布局优化的可行性和有效性。     

具有逼近0/1离散特性的拓扑优化迭代算法

利用连续性优化迭代算法求解具有逼近0/1离散特性的拓扑优化模型时,普遍存在向0/1两端极化效果差的问题,在拓扑结构上表现为边界灰度单元,为此,提出了一种具有逼近0/1离散特性的优化迭代算法——极化优化准则法(Polarized Optimality Criterion Method,POCM)。该算法与SIMP插值模型相结合,在算法更新迭代模型中,构建了具有向两端逼近特性的极化算子,从优化算法本质上使最优解逼近0/1离散特性,有效抑制了拓扑边界上的灰度单元,得到了具有清晰边界的最优拓扑构型,且提高了优化求解效率。经典数值算例表明所提方法的正确性和有效性。     

无网格法结构拓扑优化模型的GPU并行加速求解及应用

基于无网格法的连续体结构拓扑优化,具有计算精度高、可消除传统拓扑优化中的数值不稳定性等优势,然而无网格法结构拓扑优化模型的求解存在计算耗时长的问题。为此引入GPU(Graphic processing unit,GPU)并行加速技术,开展无网格法结构拓扑优化模型的GPU并行加速求解及应用研究,以缩短拓扑优化模型的求解耗时。基于交叉节点对思想构建了拓扑迭代中刚度矩阵的GPU并行组装流程,结合CUDA(Compute unified device architecture,CUDA)库函数与预处理共轭梯度法实现了离散方程的GPU并行加速计算,且通过提前计算并存储形函数及其导数值以避免重复计算,建立了无网格法拓扑优化模型的GPU并行加速求解算法。通过二维悬臂梁算例验证了算法的正确性,完成了二维曲形支架、三维支撑平台以及多工况固支梁的拓扑优化设计,并分析了GPU并行算法的加速性能。算例结果表明所提GPU并行加速算法的计算结果正确,且极大地提高了无网格法拓扑优化模型的求解效率。     

导重准则法在前车架结构优化设计中的应用

提出了一种实用高效的机械结构优化设计方法——导重准则法,该方法既能充分利用结构分析软件AN-SYS有限元建模、分析求解与结果输出方便的优势,又能发挥导重法优化效果好、收敛快的优越性,一般只需约5~7次优化迭代计算,即可得到十分显著的优化效果,大大提高了设计效率与设计质量.其优越性与实用性在某轮式装载机前车架的优化设计实践中得到充分验证.     

一种实用的机械结构优化设计方法

提出一种实用的机械结构优化设计方法-ANSYS与导重准则结合法，该方法既能利用结构分析商用软件ANSYS有限元建模，分析求解与结果输出方便的优势，又能发挥结构优化理性准则法。导重法优化效果好，收敛快的优越性，一般只需约5～7次优化迭代计算，即可得到十分重要的优化效果。大大提高了设计效率坦与设计质量。其优越性与实用性在某双模轮胎硫化机的优化设计实践中得到充分验证。     

基于改进优化准则法的自由阻尼结构动力学拓扑优化

针对自由阻尼结构拓扑优化问题,采用模态应变能的有限元求解方法,以单元相对密度值为拓扑设计变量,以材料用量和频率改变量为约束条件,构建以多模态损耗因子加权和为目标函数的拓扑优化模型,推导了目标函数对于设计变量灵敏度的表达式。考虑到常规优化准则法用于结构动力学寻优时,目标函数存在非凸性,迭代过程中出现负值设计变量,使得优化结果不收敛或陷入局部优化,故在一般优化准则法的基础上对拓扑优化模型进行数学意义上的迭代改进。改进优化准则法解决了设计变量出现非正及迭代发散等问题,保证了全体拓扑变量参与迭代过程。通过ANSYS编程对自由阻尼板进行了仿真,并引入MAC因子来控制结构的振型跃阶,结果显示:改进算法在控制阻尼材料体积为优化前体积60%时,各阶目标函数和拓扑构型在数次迭代后趋于稳定,单元中间密度值区域相对较少,自由阻尼结构获得了有效的减振。     

典型三维机械结构拓扑优化设计

为了提高拥有数万个单元以上的三维机械结构拓扑优化的计算效率, 基于渐进结构优化方法, 并结合结构位移计算的迭代方法, 建立一套三维机械结构拓扑优化的求解策略和算法.然后, 构建分别用于结构分析和结构优化迭代的两套数据流和它们间的映射方法, 研究和开发三维机械结构拓扑优化设计软件.完成几个典型和复杂的三维机械结构的仿真优化设计.设计结果表明,发展的方法和软件是正确和有效的, 且具有广泛的工程应用前景.     

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.     

Bi-directional evolutionary 3D topology optimization with a deep neural network

The FEM-based topology optimization repeats usually finite element analyses many times to converge to the stopping criteria. If the near-optimal topology data are available in advance at the beginning of an optimization process, the iterative computation could be greatly reduced. In an effort to obtain swiftly optimum topology solutions, the deep learning and neural networks with a special segmentation scheme of digital images are combined with the BESO (bi-directional evolutionary structural optimization) topology method in this study. The pre-trained digital images of 3200 optimum topologies construct the design domain for the main topology optimization. Additionally, a new post-processor is developed in order to reconstruct the relative locations among finite elements in the raw outputs generated by the neural network. The proposed method has been demonstrated to be efficient in lowering the iterations with several 2D and 3D optimization examples. The iteration counts can be reduced 63% for a 2D example and by 72.5% for a 3D one, compared to BESO results alone.

     

基于人工材料密度的新型拓扑优化理论和算法研究

对基于人工材料密度的拓扑优化理论作了深入分析;推导出了一种基于人工材料密度的拓扑优化准则算法,将该算法应用于拓扑优化的计算中,并给出了基于人工材料密度的拓扑优化迭代分析流程;提出了一种卷积因子方法,用于消除拓扑优化计算结果中易出现的棋盘格式和多孔材料现象;通过数值计算验证了理论和算法的有效性;分析讨论了不同优化参数对拓扑优化计算结果的影响。     

An improved element removal method for evolutionary structural optimization

The purpose of this study was to develop a new element removal method for ESO (Evolutionary Structural Optimization), which is one of the topology optimization methods, ESO starts with the maximum allowable design space and the optimal topology emerges by a process of removal of lowly stressed elements. The element removal ratio of ESO is fixed throughout topology optimization at 1 or 2%. BESO (bidirectional ESO) starts with either the least number of elements connecting the loads to the supports, or an initial design domain that fits within the maximum allowable domain, and the optimal topology evolves by adding or subtracting elements. But the convergence rate of BESO is also very slow. In this paper, a new element removal method for ESO was developed for improvement of the convergence rate. Then it was applied to the same problems as those in papers published previously. From the results, it was verified that the convergence rate was significantly improved compared with ESO as well as BESO.     

传热结构自适应拓扑优化准则法研究

合理的散热通道分布是提高小空间大热流密度传热结构散热性能最有效的手段。针对现有传热结构拓扑优化设计结果形态过于复杂,存在棋盘格、灰度单元等数值不稳定现象,提出一种基于基结构的散热通道分布的自适应拓扑优化方法。研究了适用于传热结构拓扑优化问题的基结构构建技术,建立满足库恩-塔克（Kuhn-Tucker,KKT）最优准则条件的迭代公式;以散热弱度最小为优化目标,以杆单元截面积为设计变量,对典型的二维和三维设计问题进行散热通道分布设计,并将设计结果与COMSOL软件优化结果进行对比。研究结果表明,提出的传热结构自适应拓扑优化方法产生的散热通道形态简单清晰,能满足散热性能,且优化过程收敛速度快,克服了现有优化方法产生的数值不稳定问题。     

A study on ranked bidirectional evolutionary structural optimization (R-BESO) method for fully stressed structure design based on displacement sensitivity

Evolutionary Structural Optimization (ESO) method is well known as one of several topology optimization methods and has been applied to a lot of optimization problems. While ESO method evolves the given model into an optimum by subtracting several elements, in AESO method elements are added in a previous step of the evolutionary procedure. And in BESO (Bidirectional ESO) method, some elements are either generated or eliminated from a previous model of evolutionary procedure. In this paper, Ranked Bidirectional Evolutionary Structural Optimization (R-BESO) method is introduced as one of the topology optimization methods using an evolutionary algorithm and is applied to several optimization problems. The method can get optimum topologies of the structures throughout fewer iterations comparing with previous several methods based on ESO. R-BESO method is similar to BESO method except that elements are generated near a candidate element according to the rank calculated by sensitivity analyses. The displacement sensitivity analysis was adopted by the nodal displacements of a candidate element in order to determine a rank on the free edges for two dimensional model or the free surfaces for three dimensional model. In this paper, R-BESO method is proposed as another useful design tool like the previous ESO and BESO method for the two bar frame problem, the Michell type structure problem and the three dimension short cantilever beam problem, which had been used to verify reasonability of ESO method family. For the three dimensions short cantilever beam problem an optimized topology could be obtained with much fewer iterations with respect to the results of other ESO methods.