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.     

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。     

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ESO的约束阻尼板拓扑优化设计研究

基于渐进结构拓扑优化方法（Evolution Structural Optimization，ESO），以阻尼材料用量为约束条件、模态损耗因子最大化为目标函数，研究了约束阻尼板结构的拓扑优化设计问题，推导了灵敏度分析公式，给出了阻尼结构拓扑优化设计方法，得到了在一定阻尼材料用量下约束阻尼板结构的模态损耗因子最大的拓扑构形。该方法对于阻尼结构的优化设计有一定的意义，具有较强的工程实用性。     

基于双向渐进结构优化法的柔性机构设计

基于双向渐进结构优化法提出一种面向柔性机构的拓扑优化设计策略。由于采用0/1离散拓扑设计变量和启发式变量更新机制,双向渐进结构优化法一般适用于结构刚度相关的凸优化设计问题。柔性机构以最大化驱动端的位移为设计目标,属于典型的非凸优化问题,难以直接应用该方法开展相应的设计。针对于此,通过定义一种由驱动位移和刚度特性（柔顺度）加权平均的优化目标函数,实现基于双向渐进结构优化法的柔性机构设计。该优化目标函数具有双重功效：（1）通过逐步（设计迭代步）衰减刚度特性的贡献,实现优化问题由刚度设计向驱动设计的动态演化,可应用双向渐进结构优化法开展机构的拓扑构型设计;（2）通过调节加权系数,实现对设计机构的驱动性能和刚度特性的灵活匹配调控,可有效抑制铰链的形成、防止应力集中引起的失效。典型算例的设计结果显示,提出的发展的演化式设计策略可实现稳健且高效的柔性机构设计。     

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。     

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.

     

Topology optimization of a PCB substrate considering mechanical constraints and heat conductivity

A material mixing method was suggested to obtain an optimal topology for a multiple material structure with multiple thermal criteria, based on Evolutionary Structural Optimization (ESO). To examine the validity of the method, it was applied to a printed circuit board (PCB) substrate. The overall efficiency of material usage in a PCB substrate was measured in terms of the combination of thermal stress and heat flux density by using a combination strategy with weighting factors. A Pareto optimal topology solution having multiple thermal criteria was obtained. The effects of weighting factors for multiple thermal criteria as well as mechanical boundary conditions on optimal topologies were investigated. It was found that as the weighting factor for heat flux density becomes larger, the sizes of holes at the center portion become larger in order to dissipate thermal energy much more efficiently. It was also found that as the magnitudes of the heat conduction are getting larger, a similar tendency of the optimal topologies is obtained to the above. The thermal stress on the clamped four sides is larger than that on the two sides clamped. It is verified that the suggested material mixing method works very well for topology optimization of a PCB substrate for various mechanical boundary conditions with multiple thermal criteria.     

基于应变能的双方向结构渐进优化方法

渐进结构优化法已发展成为工程设计中的一种重要方法,但由于其误删除单元的不可恢复性限制了它的广泛应用。文中基于在优化结构边界和孔洞周围附加人工材料的思路,并结合evdutionary structural optimization(ESO)方法和单元应变能分析,建立结构有限单元增、删的准则,给出一种基于应变能的结构拓扑双方向渐进优化算法。算例表明该方法是正确和有效的。     

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.

     

基于单元材料属性更改的结构渐进拓扑优化方法

提出了一种基于单元材料特性更改的结构渐进拓扑优化方法,通过定义设计区域内单元的存在状态为设计变量,以结构的材料用量为约束条件,实现了线弹性结构拓扑优化设计。该方法采用承载能力很弱的各向同性实体单元(弹性模量和密度均很小)代替结构实体单元,实现单元的拓扑变化,即单元的删除是将实体单元改变为弹性模量和密度很小的单元。单元删除取决于由灵敏度分析得到的每个单元对结构性能的贡献。同时结合了灵敏度再分配技术控制棋盘格式,使各单元对结构性能的贡献或影响因子实现平滑过渡。算例表明,本文的单元材料特性更改的结构渐近拓扑优化方法与灵敏度再分配棋盘格式控制技术相结合的方法,可以得到边界清晰、结构合理的拓扑优化构形。     

Topology optimization of compressor bracket

Topology optimization is very useful engineering technique especially at the concept design stage. It is common habit to design depending on the designer’s experience at the early stage of product development. Structural analysis methodology of compressor bracket was verified on the static and dynamic loading condition with 2 bracket samples for the topology optimization base model. Topology optimization is able to produce reliable and satisfactory results with the verified structural model. Base bracket model for the topology optimization was modeled considering the interference with the adjacent vehicle parts. Objective function was to minimize combined compliance and the constraint was the first natural frequency over 250 Hz. Multiple load cases such as normal mode calculation and gravity load conditions with 3-axis direction were also applied for the optimization, expecting an even stress distribution and vibration durability performance. Commercial structural optimization code such as optistruct of Altair Engineering was used for the structural topology optimization. Optimization was converged after 14 iterations with the satisfaction of natural frequency constraint. New bracket shape was produced with the CATIA based on the topology optimization result. The new bracket from topology optimization result was compared with the traditional concept model and topology optimization base model under 4 load cases. 14 % 1’st natural frequency of new bracket with only 4 % mass increment increased compared to the concept model. 31 % mass decreased compared to the base model without the increment of stress under gravity load cases. It was analyzed thata new bracket would not fail during a vibration durability test, and these results were verified with a fabricated real sample under the durability condition.     

Optimum shape design of rotating shaft by ESO method

Evolutionary structural optimization (ESO) method is based on a simple idea that the optimal structure can be produced by gradually removing the ineffectively used material from the design domain. ESO seems to have some attractive features in engineering aspects: simple and fast. In this paper, ESO is applied to optimize shaft shape for the rotating machinery by introducing variable size of finite elements in optimization procedure. The goal of this optimization is to reduce total shaft weight and resonance magnification factor (Q factor), and to yield the critical speeds as far from the operating speed as possible. The constraints include restrictions on critical speed, unbalance response and bending stresses. Sensitivity analysis of the system parameters is also investigated. The results show that new ESO method can be efficiently used to optimize the shape of rotor shaft system with frequency and dynamic constraints.     

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.     

多层渐进黑白拓扑优化设计方法

提出一种多层渐进黑白(0-1)拓扑优化设计方法。采用SIMP方法松弛设计变量,利用灵敏度过滤消除棋盘格。将拓扑图中无效的中间单元看成多余材料,在此基础上,采用体积比多层延拓方案,逐步逼近优化问题的目标体积比,同时,利用基于相对密度的单元渐进筛选方法,分层地去除设计域中的无效材料,保留其中的最有效材料,并逐层缩小拓扑优化模型的可利用材料域。通过这种方式,使0-1拓扑设计转化为具有连续设计变量的多层渐进拓扑优化过程,从而最终得到满足目标体积比的黑白拓扑。最后,以柔性最小化及柔顺机构拓扑设计问题为例,进行了算法验证,结果表明该算法能够实现较好的0-1收敛效果。     

基于Epsilon算法加速的导重法拓扑优化求解研究

针对拓扑优化模型求解过程中需要多次迭代才能得到满足一定精度要求的收敛结果的问题,提出了一种基于向量Epsilon算法加速迭代序列收敛的方法。在求解大型连续体结构拓扑优化过程中,依据导重法迭代格式首先迭代了k次,然后对所得到的迭代序列的后m项作Epsilon算法运算,将所得到新向量作为下次导重法迭代的初始值,以此类推直到满足收敛条件。通过两个算例验证了所提出方法的有效性。计算及研究结果表明,用Epsilon算法加速后的迭代格式求解拓扑优化问题能够减少迭代次数,具有更高求解效率。     

不确定性优化方法及应用

对不确定性优化方法进行研究并应用。建立悬臂梁结构优化模型和火箭发动机喷管型面优化模型,分别进行确定性优化与不确定性优化。优化过程中对悬臂梁结构采用蒙特卡洛仿真方法,对火箭发动机喷管型面进行了响应面近似。优化结果显示：不确定性优化确实得到了更加可行的设计结果。     

运用拓扑优化的结构损伤定位

以结构共振频率和结构某点的反共振频率为基础,对拓扑优化中的渐进结构优化法应用于结构损伤定位的可行性进行了研究。基于结构共振频率和反共振频率的灵敏度分析,建立了损伤定位的数学模型,提出了利用渐进结构优化法进行损伤定位的策略。针对单一和多处损伤结构,分别给出了损伤定位的数值算例,对不同的损伤结构予以讨论,并准确识别出了损伤位置。结果表明,在已经测得结构损伤前后共振频率和反共振频率的基础上,渐进结构优化法能够在整个结构区域内寻找损伤点,有较好的搜寻效果。     

液压挖掘机动臂内部筋板的拓扑优化设计

分析了液压挖掘机的典型工况及受力情况,并在铲斗挖掘工况下对其动臂进行了有限元计算。针对动臂内部筋板的布局,提出了一种箱型结构内部加强筋的布局优化方法,并基于渐进结构优化方法(ESO),对内部筋板的布局进行了拓扑优化,快速简便地确定了箱型结构内部加强筋的布局。对比优化前后有限元分析结果表明,此方法能够减小结构最大等效应力并减少高应力区。用试验验证了此方法的有效性和实用性。