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.     

Optimization of a structure with contact conditions using equivalent loads

Engineering structures consist of various components, and the components interact with each other through contact. Engineers tend to consider the interaction in analysis and design. Interactions of the components have nonlinearity because of the friction force and boundary conditions. Nonlinear analysis has been developed to accommodate the contact condition. However, structural optimization using nonlinear analysis is fairly expensive, and sensitivity information is difficult to calculate. Therefore, an efficient optimization method using nonlinear analysis is needed to consider the contact condition in design. Nonlinear Response Optimization using Equivalent Loads (NROEL) has been proposed for nonlinear response structural optimization. The method was originally developed for optimization problems considering geometric/material nonlinearities. The method is modified to consider the contact nonlinearity in this research. Equivalent loads are defined as the loads for linear analysis, which generate the same response field as that of nonlinear analysis. A nonlinear response optimization problem is converted to linear response optimization with equivalent loads. The modified NROEL is verified through three examples with contact conditions. Three structural examples using the finite element method are demonstrated. They are shape optimization with stress constraints, size optimization with stress/displacement constraints and topology optimization. Reasonable results are obtained in the optimization process.     

多工况应力约束下连续体结构拓扑优化设计

建立多工况应力约束条件下连续体结构拓扑优化的数学模型，给出求解方法。采用包络法处理大量的应力约束，用改进的满应力法进行求解，方法简单、实用。提出的分层优化技术能使最优结构更为清晰。分层优化方法的基本思想是按载荷大小分为几个层次，后面层次的拓扑优化以前面层次得到的最优拓扑为基础，通过逐层优化，最终得到最优结构。分层优化时主要考虑属于本层载荷的影响，避免大小载荷混在一起，最优拓扑模糊不清的问题。为解决各层优化单元厚度相关太大，易造成结构刚度矩阵奇异的问题，提出对相应参数的调整方法。算例表明该方法是有效的。     

基于新分簇路由算法的温室监控网络节能研究

针对设施农业发展需求,根据温室结构特性,从能量高效与节点可信度方面出发,提出了一种新的3层无线传感器网络分簇路由算法。该算法分别在簇头节点的选择、簇区的形成和簇间路由通信方式上进行了改进,在簇的形成过程中同时考虑了节点的能量与位置信息,提出了新的簇头选择权值参数,并在选出的第1层簇头节点的基础上,进行阈值划分,均衡了网络的能耗与通信负载。仿真与实际应用结果表明,该算法在节点的能量消耗、网络通信流量等方面优于传统分簇路由协议,应用于温室监控项目中时,新的组网协议体积小,节省能量,均衡了各监控传感器节点的能耗负担,获得较好的拓扑结构,延长了1.5倍网络生命周期。     

多工况稳态热传导下的连续体拓扑优化

针对多工况拓扑优化问题,提出了多工况加权单约束拓扑优化模型。基于独立联系映射法,实现了多工况稳态热传导下的连续体拓扑优化设计。根据拓扑优化模型,分析了多工况拓扑优化“病态载荷”现象产生的原因,提出了初始结构总热能判定依据,通过对载荷工况系数的适当调整来消除“病态载荷”现象。通过数值算例,对不同优化模型下的拓扑优化结果进行分析比较。结果表明,独立连续映射法和多工况加权单约束模型在处理多工况稳态热传导拓扑优化问题中具有可行性和有效性。     

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。     

含自重载荷的功能梯度材料结构时域动力学拓扑优化设计

提出了一种含自重载荷的功能梯度材料(FGM)结构时域动力学拓扑优化设计方法。在固体各向同性材料惩罚(SIMP)框架下,提出了一种针对FGM-SIMP的结构自重载荷分布策略。以FGM结构动柔度最小为优化目标、以结构体积为约束,建立了动力学结构优化列式。基于伴随法,在时域内进行了灵敏度推导,并用移动渐近线方法进行求解。通过二维和三维典型数值算例系统研究了含自重载荷下FGM结构的拓扑优化设计问题,并深入探讨了自重载荷和材料梯度分布方向对结构优化结果的影响,发现自重载荷和材料梯度分布方向对FGM结构的优化构型和动刚度具有很大影响。最后,以均一材料(FGM的特例)为例,通过数值仿真和实验测试方法验证了所提方法的有效性,并证实了所提方法可有效提高结构的固有频率和结构动刚度。     

稳态热传导下的连续体结构拓扑优化

在稳态热传导连续体拓扑优化中,提出单元总热能、节点温度、区域内节点温度平方和三类不同性能指标,推导三类指标的伴随法敏度分析公式。基于独立连续映射法建立以三类指标为约束的体积最小化模型,应用过滤技术克服拓扑优化的数值不稳定性问题,实现了稳态热传导下的连续体拓扑优化设计。通过数值算例对优化结果进行讨论,其结果验证了方法和模型的可行性和有效性。     

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.     

Continuous measurement of interaction forces between wheel and rail

Oscillatory wheel load fluctuation of considerable amplitude is always observed in railway cars traveling at high speed. This paper describes a continuous method for measuring the derailment coefficient and the forces between the wheel and rail. The acceleration measured on the axle box indicates that the frequency of this fluctuation can be as high as 70 Hz. Continuous measurement of wheel load using conventional methods is not possible due to this high frequency phenomenon. We have developed a new method for continuous measurement of these forces and the derailment coefficient using two pairs of strain gauge bridges with output phases shifted by 90°, and summing their outputs with a weighting function. This method works for measuring the forces between wheel and rail at high frequencies.     

Buckling of columns: Allowance for axial shortening

This paper investigates the effect of axial shortening on (i) the elastic buckling of columns with a continuous elastic restraint, (ii) the elastic buckling of rotating columns and (iii) the free vibration of columns under a static axial load. These column problems can be solved in a unified approach because the resulting energy functional is similar. The field differential equation is derived by minimizing the energy functional with respect to the lateral displacement function via calculus of variations. The buckling load or fundamental frequency may be obtained by analytically solving the two-point boundary-value problem. It was found that the boundary conditions and the restraint parameter or angular velocity parameter affect the influence of axial shortening on the buckling load. In vibrating columns, tensile forces enhance the effect of axial stretching on the fundamental frequency.     

2MW风力发电机轮毂优化设计

优化设计是一种为了让自己的设计材料最省、支出最小的一种技术。通常,在设计中,会有许多的设计方案以供选择,如何从众多的方案中选择一个最好的方案,就需要有较好的设计方法。优化设计的方法有很多,而拓扑优化又称结构布局优化,是一种根据优化目标、载荷及约束而寻求结构材料最佳分配的优化方法。针对2MW风力发电机轮毂进行了拓扑优化,对比分析了优化前后轮毂的质量、及联合工况下的应力和变形,结果表明,联合工况下的应力及变形减小,动态应力最大值减小,动态强度提高;并在三维软件中重建模型,验证优化后模型进行工程实践的可行性。     

基于最大应力约束的柔顺机构拓扑优化设计

采用拓扑优化方法获得柔顺机构构型容易出现类铰链结构,导致应力集中、疲劳可靠性差。为了抑制类铰链结构,提出了一种基于最大应力约束的柔顺机构拓扑优化设计方法。采用改进的固体各向同性材料惩罚模型（Solid isotropic material with penalization,SIMP）,以柔顺机构的互应变能最大化作为目标函数,采用P范数方法对所有单元的局部应力凝聚化成一个全局化应力约束,利用自适应约束缩放法使得P范数应力更加接近最大应力,以机构的最大应力和体积作为约束,建立柔顺机构最大应力约束拓扑优化模型,采用全局收敛移动渐近线算法求解柔顺机构最大应力约束拓扑优化问题。结果表明,采用P范数方法进行柔顺机构最大应力约束拓扑优化设计,能够有效抑制类铰链结构。随着应力约束极限值减少,获得机构构型由集中式柔顺机构逐渐转变为分布式柔顺机构,应力分布更加均匀,但机构的互应变能逐渐减小。     

复杂环境下登船液压电梯导轨受力特性分析

为保证登船电梯在偏载、动载与风载等复杂环境下的安全稳定性,同时得到导轨受力随风速变化的关系,建立了液压缸、导轨有限元模型和两者之间的受力平衡方程。通过运用有限元方法,得到液压缸和导轨的挠度变形,从而求出导轨受力大小。通过对瓯江明珠号登船电梯导轨受力分析为例,计算出导轨在不同风速下的受力大小,为登船电梯导轨的设计选型提供理论参考。     

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.     

柔性剪切蒙皮支撑结构的拓扑优化

为了求解关于柔性剪切蒙皮支撑结构的多目标拓扑优化问题,提出了一种带有多重约束处理能力的位矩阵表示的非支配排序遗传算法。采用位矩阵作为遗传算法的染色体并引入基于矩阵操作的遗传算子,利用Ansys有限元分析获得结构质量、面内剪切性能和面外承载能力等目标。利用Matlab处理结构连通性和面内应变等约束并实现了基于矩阵的优化算法,获得了一系列可行的柔性剪切蒙皮支撑结构,在实际应用中可以根据需要选择合适的结构。从研究结果可以看出,该算法可以给多目标二维结构拓扑优化问题提供可行有效的解。     

Motion/posture modeling and simulation verification of physically handicapped in manufacturing system design

Non-obstacle design is critical to tailor physically handicapped workers in manufacturing system. Simultaneous consideration of variability in physically disabled users, machines and environment of the manufacturing system is extremely complex and generally requires modeling of physically handicapped interaction with the system. Most current modeling either concentrates on the task results or functional disability. The integration of physical constraints with task constraints is far more complex because of functional disability and its extended influence on adjacent body parts. A framework is proposed to integrate the two constraints and thus model the specific behavior of the physical handicapped in virtual environment generated by product specifications. Within the framework a simplified model of physical disabled body is constructed, and body motion is generated based on 3 levels of constraints(effecter constraints, kinematics constraints and physical constraints). The kinematics and dynamic calculations are made and optimized based on the weighting manipulated by the kinematics constraints and dynamic constraints. With object transferring task as example, the model is validated in Jack 6.0. Modelled task motion elements except for squatting and overreaching well matched with captured motion elements. The proposed modeling method can model the complex behavior of the physically handicapped by integrating both task and physical disability constraints.     

星载微波探测仪探测头部结构设计及验证

按照某星载微波探测仪探测头部的收拢包络、质量、基频和力学环境适应性等设计要求,针对探测头部结构设计的难点,提出了一种探测头部结构设计方案。通过采用“∏”字型折叠设计、集成化设计、轻量化设计和短而直接的传力路径设计等关键设计方法,解决了探测头部小型化、轻量化和高刚度的技术难点。经过力学仿真分析和地面试验,验证了探测头部结构设计的正确性和合理性。该探测头部的结构设计思路及验证方法可为后续星载微波探测载荷的结构设计提供参考。     

结合专家群体评估法的渐进结构优化算法

结构拓扑优化作为现在迅速发展的结构化设计的一个分支,已得到广泛应用。基于渐进结构优化(ESO)方法,结合灰色理论中的专家群体评估法,得到一种新的处理多目标优化的方法。首先使用线性加权法对一平面简支梁进行优化分析得到三组拓扑结构。然后运用该新方法对同一算例进行优化得到三组拓扑结构。并将最终拓扑结构进行对比。     

密封条结构参数优化设计方法

为了对轿车车门密封条结构参数进行优化设计，采用遗传算法和神经网络相结合的策略，首先利用神经网络建立密封条结构设计参数与压缩负荷、应力等的非线性全局映射关系，获得求解结构优化问题所需的目标函数，然后用遗传算法进行优胜劣汰的寻优搜索运算，求出最优解。优化结果表明，椭圆形结构在壁厚为1．5mm、高度为20mm时，压缩负荷和应力能达到目标函数要求。压缩负荷和应力的优化结果与理论计算值的误差分别为7．4％、9％，因此，利用神经网络和遗传算法进行结构参数优化的方法是可行的。