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.     

利用双向渐进结构优化法对结构固有振型的优化

利用双向渐进结构优化法研究结构的固有振型优化问题，双向渐进结构优化法(bi—directional evolutionary struetural optimization，简称BESO)是一种拓扑优化方法，它基于这样一个简单的优化程序：从结构中一步步地删去对结构目标性能低效或无效的材料，同时增加对结构目标性能高效的材料，从而使材料布局趋于优化。文中分别采用近似重分析思路的方法和基于变分法推导的公式计算单元特征向量灵敏度，并简单阐述BESO法对结构固有振型(特征向量)进行拓扑优化的一般过程。数值算例表明，用该方法对结构固有振型的优化是行之有效的，且用变分法计算特征向量灵敏度进行优化较之近似重分析法效率更高。     

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.     

Topology optimization based on the harmony search method

A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclusions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

     

Efficient,high-resolution topology optimization method based on convolutional neural networks

Topology optimization is a pioneer design method that can provide various candidates with high mechanical properties. However, high resolution is desired for optimum structures, but it normally leads to a computationally intractable puzzle, especially for the solid isotropic material with penalization (SIMP) method. In this study, an efficient, high-resolution topology optimization method is developed based on the super-resolution convolutional neural network (SRCNN) technique in the framework of SIMP. SRCNN involves four processes, namely, refinement, path extraction and representation, nonlinear mapping, and image reconstruction. High computational efficiency is achieved with a pooling strategy that can balance the number of finite element analyses and the output mesh in the optimization process. A combined treatment method that uses 2D SRCNN is built as another speed-up strategy to reduce the high computational cost and memory requirements for 3D topology optimization problems. Typical examples show that the high-resolution topology optimization method using SRCNN demonstrates excellent applicability and high efficiency when used for 2D and 3D problems with arbitrary boundary conditions, any design domain shape, and varied load.     

基于应力的双向渐进结构拓扑优化设计

双向渐进结构优化法（BESO）是近年来兴起的一种解决各类结构优化问题的数值方法,其原理是通过同时删除和增补单元,使剩下的结构逐渐趋于优化。提出了基于应力约束的渐进结构优化方法,与其它优化方法相比,该方法原理简单,计算效率高,工程应用方便,并通过算例证明该方法的有效性和可行性。     

双向渐进结构拓扑优化设计研究

双向渐进结构优化法（BESO）是近年来兴起的一种懈决各类结构优化问题的数值方法。其原理是通过同时删除和增补单元,使剩下的结构逐渐趋于优化。文章提出了基于应力约束的渐进结构优化方法,与其它优化方法相比,该方法原理简单,计算效率高,工程应用方便,并通过算例证明该方法的有效性和可行性。     

Topology optimization for lightweight cellular material and structure simultaneously by combining SIMP with BESO

This paper presents a hybrid algorithm for topology optimization of lightweight cellular materials and structures simultaneously by combining solid isotropic material with penalization (SIMP) and bi-directional evolutionary structural optimization (BESO). Microstructure of the lightweight cellular material is assumed unique in the structure to make the proposed method feasible. A new sensitivity analysis formula with respect to the discrete variable is derived by a principal submatrix stiffness matrix, by which the material can be effectively removed from or added to cellular. Moreover, the validity of the proposed method is then demonstrated through two numerical examples (a simple supported beam and a cantilever beam), which can be easily applied in a variety of practical situations.

     

基于功能截面分解的大型横梁拓扑优化

针对复杂载荷工况下横梁等大型三维结构件拓扑优化结果可读性差、无法对结构优化提供有效指导的问题,提出基于功能截面分解的拓扑优化方法。基于力的分解与等效原理,将三维实体分解为三个平面内的二维功能截面,根据各功能截面的受力方式确定其抗弯或抗扭属性;在此基础上,分别对两个主要承载的功能截面进行二维拓扑优化分析,并综合二维功能截面分析结果完成三维实体的整体拓扑优化,实现了将三维实体拓扑优化问题转化为二维功能截面的拓扑优化问题。以CXK5463车铣加工中心横梁为例,对结构拓扑优化效果进行了验证,仿真实验结果表明,功能截面分解方法可以得到清晰的应力传递路径,在保证横梁静动态特性基本稳定的基础上,横梁减重12.67%,优化效果较为明显。提出的方法可为大型、重型复杂结构件的拓扑优化研究提供借鉴与参考。     

Layout optimization of box girder with RBF-NNM-APSO algorithm

The layout optimization problem of complex box girder structure is solved with a new method RBF-NNM-APSO formed with the digital neural network model (NNM) of radial basis function (RBF) and adaptive particle swarm optimization (APSO) algorithm in this paper. The optimized surrogate model is proposed and applied to the configuration optimization of heavy-duty box girder of casting crane for improving the mechanical properties of the optimized object and expediting proceedings. First, the parametric command flow finite element numerical model of box girder is established. The RBF neural network is trained by constructing a mixed orthogonal experimental table of parameters, and the relationship between the design variables and the maximum stress and deformation is established. Subsequently, the trained RBF neural network design scheme is optimized by APSO algorithm. Finally, on the premise of not increasing the total mass, a new layout form of box girder is obtained.

     

基于工况风险评估的叉车门架多工况拓扑优化

以某3T型内燃叉车的标准门架为例,实现了典型工况下门架系统的整体非线性有限元分析;基于工况数据（工作时长、结构应力及形变位移）,提出了工况风险评估方法及工况风险指标（RI）的概念;依据工况风险指标,提出了一种分配多工况拓扑优化权重系数的方法;采用折中规划法,以多工况下门架加权柔度最小为目标函数对门架结构进行拓扑优化;根据优化结果对门架结构进行改进设计,并进行了有限元分析。研究结果表明：风险评估法较传统平均分配法能得到更优的目标值;与原门架结构相比,新门架结构在3种典型工况下的最大应力分别减小10.05%、10.25%和1.58%,最大位移分别减小13.17%、12.93%和8.28%,质量减小7 kg。     

带锯机架整体的筋板结构设计与优化

为减小木工带锯机床整体振动,提高加工精度,降低整体质量,对筋板结构建立系统振动数学模型,根据运动微分方程对筋板结构单元进行动态性能和载荷分析,得出最适合该机床的筋板结构类型,并采用三维建模软件对机床机架进行参数化建模。根据实际工况,采用ANSYS对机架整体进行有限元静力学分析。基于静力学仿真结果,采用拓扑优化方法对机架进行轻量化设计,并对机架尺寸提出修改和优化方案。研究结果表明,井字形筋板结构和T字形筋板结构为该机架的最优筋板结构单元,且满足刚度和强度要求;通过轻量化设计使机床整体质量下降16.9%,实现轻量化目标。     

Complex wavelet enhanced shape from shading transform for estimating surface roughness of milled mechanical components

The metal surface topology contains abundant information related to the health states of the cutting tool as well as the cutting operation. In this paper, we attempt to adopt 2D digital images of the machined metal surface, acquired via non-contact photo-imaging techniques, as the monitoring media. A Wallis filter based dodging algorithm is applied to cure the uneven contrast phenomenon caused by imperfect lighting illumination. 3D digital models were derived and retrieved from the digital image using a wavelet enhanced Shape from shading (SFS) transform. The minimization based SFS is presented to retrieve the 3D digital surface from the milled workpiece. The dual tree complex wavelet transform is adopted to enhance SFS such that the interfering noise can be suppressed. In the end, quantitative surface roughness indicators are utilized to estimate the surface roughness numerically. A milling cutting experiment of aero-material of aluminum alloy 7075 was carried out to verify the effectiveness of the proposed approach. The comparison results demonstrate that the proposed approach was capable of retrieving 3D surfaces of high precision. With the approach, the digital image emerges as a promising vehicle for machining condition monitoring of CNC machines.

     

车身结构NVH特性多目标拓扑优化研究

建立了某车身地板结构动力学有限元模型,通过分析自由模态固有频率和多点激励下频率响应,验证了车身地板数值分析模型的有效性。以地板结构各激励点最大振动速度的平方和最小化作为目标函数,建立了多目标拓扑优化模型。通过解读优化结果,提出了地板结构改进方案。改进后的车身地板结构各阶自由模态固有频率增加达10%以上,各激励点速度响应大大降低,NVH特性明显提高。研究表明,减小振动速度的多目标拓扑优化设计是一种改善车身NVH特性的有效方法。     

Topology optimization with displacement-based nonconforming finite elements for incompressible materials

This investigation is concerned with the topology optimization using displacement-based nonconforming finite elements for problems involving incompressible materials. Although the topology optimization with mixed displacement-pressure elements was performed, a displacement-based approach can be an efficient alternative because it interpolates displacement only. After demonstrating the Poisson locking-free characteristics of the employed nonconforming finite elements by a simple patch test, the developed method is applied to solve the design problems of mounts involving incompressible solid or fluid. The numerical performance of the nonconforming elements in topology optimization was examined also with existing incompressible problems. This paper was recommended for publication in revised form by Associate Editor Tae Hee Lee Gang-Won Jang received his M.S. degree in 2000, and Ph.D. degree in 2004, both from the School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea. He is currently an Assistant Professor at the School of Mechanical and Automotive Engineering, Kunsan National University, Jeonbuk, Korea. His current interest concerns topology optimization of multiphysics problems and thin-walled beam analysis. Yoon Young Kim received his B.S. and M.S degrees from Seoul National University, Seoul, Korea, and the Ph.D. degree from Stanford University, Palo Alto, CA, in 1989. He has been on the faculty of the School of Mechanical and Aerospace Engineering, Seoul National University, since 1991. He is also the Director of the National Creative Research Initiatives Center for Multiscale Design. His main research field is the optimal design of multiphysics systems, mechanisms, and transducers. He has served as an editor of several Korean and international journals, and as an organizing committee member of several international conferences.     

基于锥束CT图像的数字样品建模方法研究

提出了一种同时包含物体内部材料分布和表面几何信息的数字样品概念,研究并实现了基于锥束CT图像的数字样品建模方法。在材料建模方面,根据材料识别提出了一种计算材料相分布的方法;在几何建模方面,针对锥束CT图像的特点,提出并实现了一种局部结构重构和整体拓扑重构相结合的三维物体表面重构新方法。实验表明,该研究为三维物体内部结构和表面信息的测量重构提供了一种可行的新建模方法和实现技术。     

基于耐撞性拓扑优化的汽车关键安全件设计

将耐撞性拓扑优化方法应用到车辆实际开发过程中,阐述了基于LS-DYNA显式有限元算法的耐撞性拓扑优化方法,并给出其迭代求解的数学模型。结合该方法,对某车辆的门槛梁进行40%偏置碰撞和侧面碰撞的并行拓扑优化,根据优化结果的材料分布情况进行了工程诠释。在整车碰撞有限元模型中对工程诠释结果进行了验证,结果表明：耐撞性拓扑优化方法行之有效,且拓扑优化结果使得车辆的碰撞性能有一定的提高。     

考虑3D打印工艺约束的液压流道拓扑优化设计

为了解决传统液压阀块体积笨重、制造工艺繁琐且效率损失大的问题,使用3D打印和流体拓扑优化相结合的方法对液压流道进行优化设计。以入口和出口处压差最小为目标,通过流体拓扑优化对常见的液压阀体T形通道进行优化,得到更加符合流体特性的流道,并设计了可以无支撑进行3D打印的圆角正方形截面形状,进行了3D打印试验,优化后的流道3D打印成形效果较好。利用Fluent进行流体仿真,结果显示,当入口流速在2~5 m/s时,优化后的流道有效避免了气穴的形成,最大压力减小了40%以上,入口和出口处压差减小了28%以上,湍流改善了85%以上,流体性能得到显著提升。     

A new topology optimization scheme for nonlinear structures

A new topology optimization algorithm based on artificial bee colony algorithm (ABCA) was developed and applied to geometrically nonlinear structures. A finite element method and the Newton-Raphson technique were adopted for the nonlinear topology optimization. The distribution of material is expressed by the density of each element and a filter scheme was implemented to prevent a checkerboard pattern in the optimized layouts. In the application of ABCA for long structures or structures with small volume constraints, optimized topologies may be obtained differently for the same problem at each trial. The calculation speed is also very slow since topology optimization based on the roulette-wheel method requires many finite element analyses. To improve the calculation speed and stability of ABCA, a rank-based method was used. By optimizing several examples, it was verified that the developed topology scheme based on ABCA is very effective and applicable in geometrically nonlinear topology optimization problems.