摘要：Stiffened plates or shells are widely used in engineering structures as primary or secondary load-bearing *** to design the layout and sizes of the stiffeners is of great significance for structural *** this work,a new topology optimization method for simultaneously optimizing the layout and cross-section topology of the stiffeners is developed to solve this *** stilfeners and base plates are modeled by the beam and shell elements,respectively,significantly reducing the computational *** Giavotto beam theory,instead of the widely employed Euler or Timoshenko beam theory,is applied to model the stiffeners for considering the warping deformation in evaluating the section stiffness of the beam.A multi-scale topology optimization model is established by simultaneously optimizing the layout of the beam and the topology of the *** design space is significantly expanded by optimizing these two types of design *** numerical examples are applied to illustrate the validity and effectiveness of the proposed *** results show that the proposed two-scale optimization approach can generate better designs than the single-scale method.

摘要：Phononic materials with specific band-gap characteristics at desired frequency ranges are in great demand for vibration and noise isolation, elastic wave filters, and acoustic devices. The attenuation coefficient curve depicts both the frequency range of band gap and the attenuation of elastic wave, where the frequency ranges corresponding to the none-zero attenuation coefficients are band gaps. Therefore, the band-gap characteristics can be achieved through maximizing the attenuation coefficient at the corresponding frequency or within the corresponding frequency range. Because the attenuation coefficient curve is not smooth in the frequency domain, the gradient-based optimization methods cannot be directly used in the design optimization of phononic band-gap materials to achieve the maximum attenuation within the desired frequency range. To overcome this difficulty, the objective of maximizing the attenuation coefficient is transformed into maximizing its Cosine, and in this way, the objective function is smoothed and becomes differentiable. Based on this objective function, a novel gradient-based optimization approach is proposed to open the band gap at a prescribed frequency range and to further maximize the attenuation efficiency of the elastic wave at a specific frequency or within a prescribed frequency range. Numerical results demonstrate the effectiveness of the proposed gradient-based optimization method for enhancing the wave attenuation properties.

摘要：The metallic antenna design problem can be treated as a problem to find the optimal distribution of conductive material in a certain domain. Although this problem is well suited for topology optimization method, the volumetric distribution of conductive material based on 3D finite element method (FEM) has been known to cause numerical bottlenecks such as the skin depth issue, meshed 'air regions' and other numerical problems. In this paper a topology optimization method based on the method of moments (MoM) for configuration design of planar metallic antenna was proposed. The candidate structure of the planar metallic antenna was approximately considered as a resistance sheet with position-dependent impedance. In this way, the electromagnetic property of the antenna can be analyzed easily by using the MoM to solve the radiation problem of the resistance sheet in a finite domain. The topology of the antenna was depicted with the distribution of the impedance related to the design parameters or relative densities. The conductive material (metal) was assumed to have zero impedance, whereas the non-conductive material was simulated as a material with a finite but large enough impedance. The interpolation function of the impedance between conductive material and non-conductive material was taken as a tangential function. The design of planar metallic antenna was optimized for maximizing the efficiency at the target frequency. The results illustrated the effectiveness of the method.

摘要：Topology optimization is a powerful design approach that is used to determine the optimal topology in order to obtain the desired functional performance. It has been widely used to improve structural performance in engineering fields such as in the aerospace and automobile industries. However, some gaps still exist between topology optimization and engineering application, which significantly hinder the applica- tion of topology optimization. One of these gaps is how to interpret topology results, especially those obtained using the density framework, into parametric computer-aided design （CAD） models that are ready for subsequent shape optimization and manufacturing. In this paper, a new method for interpreting topology optimization results into stereolithography （STL） models and parametric CAD models is pro- posed. First, we extract the skeleton of the topology optimization result in order to ensure shape preser- vation and use a filtering method to ensure characteristics preservation. After this process, the distribution of the nodes in the boundary of the topology optimization result is denser, which will benefit the subsequent curve fitting. Using the curvature and the derivative of curvature of the uniform B-spline curve, an adaptive B-spline fitting method is proposed in order to obtain a parametric CAD model with the fewest control points meeting the requirement of the fitting error. A case study is presented to pro- vide a detailed description of the proposed method, and two more examples are shown to demonstrate the validity and versatility of the proposed method.

摘要：Additive manufacturing （AM） technologies, such as selective laser sintering （SLS） and fused deposition modeling （FDM）, have become the powerful tools for direct manufacturing of complex parts. This breakthrough in manufacturing technology makes the fabrication of new geometrical features and multiple materials possible. Past researches on designs and design methods often focused on how to obtain desired functional performance of the structures or parts, specific manufacturing capabilities as well as manufacturing constraints of AM were neglected. However, the inherent constraints in AM processes should be taken into account in design process. In this paper, the enclosed voids, one type of manufacturing constraints of AM, are investigated. In mathematics, enclosed voids restriction expressed as the solid structure is simply- connected. We propose an equivalent description of simply-connected constraint for avoiding enclosed voids in structures, named as virtual temperature method （VTM）. In this method, suppose that the voids in structure are filled with a virtual heating material with high heat conductivity and solid areas are filled with another virtual material with low heat conductivity. Once the enclosed voids exist in structure, the maximum temperature value of structure will be very high. Based upon this method, the simplyconnected constraint is equivalent to maximum temperature constraint. And this method can be easily used to formulate the simply-connected constraint in topology optimization. The effectiveness of this description method is illustrated by several examples. Based upon topology optimization, an example of 3D cantilever beam is used to illustrate the trade-off between manufacturability and functionality. Moreover, the three optimized structures are fabricated by FDM technology to indicate further the necessity of considering the simply-connected constraint in design phase for AM.

摘要：随着压电柔顺机构在航空航天及精密加工等高频振动环境中的广泛应用,亟需发展大行程、高频响压电柔顺机构的拓扑优化方法.现有的拓扑优化方法侧重于提高柔顺机构的输出行程,而忽略了其动态特性.文章提出一种考虑基频约束的压电柔顺机构拓扑优化方法.首先,为了更准确地描述压电驱动器与柔顺机构间的相互作用,将压电驱动器直接耦合进柔顺机构的优化分析模型中,建立了压电柔顺机构机-电耦合优化分析模型.其次,以输出位移为目标函数,基于变密度法,建立了考虑结构基频约束的压电柔顺机构拓扑优化方法.采用p-norm凝聚函数来近似结构基频,避免了迭代过程中特征值重复和模态切换所引起的不可导问题,并利用伴随法和链式求导法推导了目标函数和基频约束对设计变量的灵敏度.最后,通过数值算例验证了所提优化方法的有效性,讨论了基频约束对优化结果的影响.数值算例结果表明,所提方法迭代过程快速,收敛性好,能够在满足基频约束的前提下,实现输出行程最大化的设计.与仅考虑柔顺机构输出位移的优化结果相比,采用本文提出的方法所得优化构型的材料分布明显不同,且随着基频约束的增大,优化构型的基频相应变大,而输出位移变小.

摘要：结构和材料方向的并行拓扑优化是过去几十年来的一个热门话题.然而,如何避免此类问题掉入局部最优相当具有挑战性。为了解决这个问题,我们在以前的工作中提出了一种将离散材料优化方法和连续纤维取向优化方法相结合的方法,称之为离散-连续参数化(DCP),该方法同时继承了离散方法的全局搜索能力和连续方法的全设计空间然而,DCP方法需要太多设计变量,导致了巨大的计算负担.因此,我们在本工作中提出了一种改进的DCP方法,以减少设计变量的数量,同时又不牺牲优化问题的凸性。在该方法中,我们提出了一种扩展的多材料插值方法,该方法能够大大减少设计变量的数量。然后,我们将所提出的插值方法集成到DCP方法中,最终建立了结构拓扑和纤维取向协同优化的改进DCP方法.几个基准优化实例表明,该方法可以在能大大降低陷入局部最优的风险的同时,使用更少的设计变量.

摘要：变体飞机根据不同飞行状态改变机翼形状以获得最佳的气动效能,从而提高在多工况下执行多目标任务的能力.表面结构的柔性蒙皮设计是实现变体结构的关键,需要设计具有足够协同变形能力的同时,还能够承受表面的气动载荷、保持光滑气动外形性能的柔性蒙皮结构.针对这一需要,论文提出一种基于Ω形蜂窝的夹芯式大变形柔性蒙皮结构(Ω形柔性蒙皮).利用参数优化技术以最小化构型变形方向的刚度为目标确定Ω构型的拓扑结构;推导出Ω形蜂窝柔性蒙皮结构的面内等效弹性性能预测公式,并通过数值仿真分析了该结构的面内变形性能力和面外承载能力.通过与蛇形蜂窝和正余弦蜂窝两种夹芯式柔性蒙皮结构的面内变形能力的对比分析,验证了该柔性蒙皮的良好性能.结果表明,所提出的Ω形柔性蒙皮结构具有良好的面内可恢复的大变形能力和面外承载能力.

摘要：We present a design method for calculating and optimizing sound absorption coefficient of multi-layered porous fibrous metals （PFM） in the low frequency range. PFM is simplified as an equivalent idealized sheet with all metallic fibers aligned in one direction and distributed in periodic hexagonal patterns. We use a phenomenological model in the literature to investigate the effects of pore geometrical parameters （fiber diameter and gap） on sound absorption performance. The sound absorption coefficient of multi- layered PFMs is calculated using impedance translation theorem, To demonstrate the validity of the present model, we compare the predicted results with the experimental data. With the average sound absorption （low frequency range） as the objective function and the fiber gaps as the design variables, an optimization method for multi-layered fibrous metals is proposed. A new fibrous layout with given porosity of multi-layered fibrous metals is suggested to achieve optimal low frequency sound absorption. The sound absorption coefficient of the optimal multi-layered fibrous metal is higher than the single- layered fibrous metal, and a significant effect of the fibrous material on sound absorption is found due to the surface Dorosity of the multi-layered fibrous.

摘要：The purpose of this paper is to investigate the application of topology description function （TDF） in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the ＇Hamilton-Jacobi-type＇ equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson＇s ratio, the other with negative Poisson＇s ratio. The examples show the method based on TDF is effective for material design.