Topology optimization of continuum structures with bi-modulus materials

Since the elasticity of bi-modulus materials is stress dependent, it is difficult to apply most conventional topology optimization methods to such bi-modulus structures owing to great computational expense. Therefore, this study employs the material-replacement method to improve the computational efficiency for topology optimization of bi-modulus structures. In this method, first, the bi-modulus material is replaced by two isotropic materials which have the same tensile or compressive modulus. Secondly, the isotropic materials for finite elements are determined by the local stress/strain states. The local elemental stiffness can be modified according to the current modulus and stress state of the element. Thirdly, the relative densities of elements, acting as the design variables, are updated using the optimality criterion method. Finally, the distributions of elemental densities and moduli are obtained for further applications. Several typical numerical examples are used to demonstrate the effectiveness of the proposed method.     

Topology optimization for compliant mechanisms,using evolutionary-hybrid algorithms and application to the design of auxetic materials

Designing micro-structures that lead to materials with negative Poisson’s ratio, the so-called auxetics, is studied here with techniques of topology optimization for compliant mechanisms. Compliant mechanisms are monolithic structures that are able to deliver two or more different motions depending on the applied loading. Single and multi-objective topology optimization problems for the design of compliant mechanisms are formulated. This formulation together with simple homogenization thoughts links the behavior of the flexible microstructure with the overall, homogenized continuum and, in particular, the negative Poisson’s ratio effect (auxetic material). Due to the local minima that arise, iterative local search methods are not very effective. On the other hand genuine global optimization algorithms may become too expensive, due to the large number of design variables. A hybrid method based on global optimization algorithms such as Particle Swarm Optimization (PSO) and Differential Evolution (DE), using an iterative local search method as an evaluation tool is proposed and tested. The iterative local method is based on discretization of the design space with truss elements.     

宏观结构性能约束下的材料微结构拓扑优化

为了设计周期性多孔钢或钢/铝复合材料优化微结构,基于独立连续映射法,建立了以结构总质量最小化为目标,节点位移为约束的拓扑优化模型。假设宏观结构由多孔材料或复合材料组成,其等效特性采用均匀化理论计算得到。定义了微观材料拓扑变量,节点位移约束采用一阶泰勒展开近似。各种材料设计要求作为约束条件纳入到优化模型中。推导了节点位移和总质量的敏度表达式。采用基于求解偏微分的过滤方法消除了数值不稳定性。在二维数值算例中获得了各种满足设计要求的优化材料微结构。结果表明:提出的方法在材料微结构拓扑优化设计中具有可行性和有效性。      

Topology optimization of functionally graded cellular materials

Design of functionally graded material (FGM), in which the mechanical property varies along one direction, is the focus of this study. It is assumed that the microstructure of the FGM is composed of a series of base cells in the variation direction and self-repeated in other directions. Bi-directional evolutionary structural optimization technique in the form of inverse homogenization is used for the design of the FGM for specified variation in bulk or shear modulus. Instead of designing a series of base cells simultaneously, the base cells are optimized progressively by considering three base cells at each stage. Thus, the proper connections between adjacent base cells can be achieved with high computational efficiency. Numerical examples demonstrate the effectiveness of the proposed method for designing microstructures of 2D and 3D FGMs with specified variation in bulk or shear modulus. The proposed algorithm can also be easily extended to design FGMs with other functional properties.     

Topology optimization design of flextensional actuators

Flextensional actuators can be defined as a piezoceramic (or a stack of piezoceramics) connected to a flexible mechanical structure that converts and amplifies the output displacement of the piezoceramic. Essentially, the actuator performance depends on the distribution of stiffness and flexibility in the coupling structure and, therefore, on the coupling structure topology. In this work, we propose a general method for designing flextensional actuators with large output displacement (or generative force) by applying the topology optimization method. The goal is to design a flexible structure coupled to the piezoceramic that maximizes the output displacement (or force) in some specified direction. Static and low frequency applications are considered. To illustrate the implementation of the method, 2-D topologies of flextensional actuators are presented because of the lower computational cost; however, the method can be extended to 3-D topologies. By designing other types of coupling structures connected to the piezoceramic, new designs of flextensional actuators that produce output displacements or forces in different directions can be obtained, as shown. This method can be extended for designing flextensional hydrophones and sonars.     

Topology optimization in micromechanical resonator design

A?topology optimization problem in micromechanical resonator design is addressed in this paper. The design goal is to control the first several eigen-frequencies of a micromechanical resonator using topology optimization. The design variable is the distribution of mass in a constrained domain which we model via (1)?the Simple Isotropic Material with Penalization Model and (2)?the Peak Function Model. The overall optimization problem is solved using the Method of Moving Asymptotes and a Genetic Algorithm combined with a local gradient method. A?numerical example is presented to highlight the features of the methods in more detail. The advantages and disadvantages of each method are discussed.     

Topology optimization with multiple materials via moving morphable component (MMC) method

With the fast development of additive manufacturing technology, topology optimization involving multiple materials has received ever increasing attention. Traditionally, this kind of optimization problem is solved within the implicit solution framework by using the Solid Isotropic Material with Penalization or level set method. This treatment, however, will inevitably lead to a large number of design variables especially when many types of materials are involved and 3‐dimensional (3D) problems are considered. This is because for each type of material, a corresponding density field/level function defined on the entire design domain must be introduced to describe its distribution. In the present paper, a novel approach for topology optimization with multiple materials is established based on the Moving Morphable Component framework. With use of this approach, topology optimization problems with multiple materials can be solved with much less numbers of design variables and degrees of freedom. Numerical examples provided demonstrate the effectiveness of the proposed approach.     

Looking for design in materials design

Despite great advances in computation, materials design is still science fiction. The construction of structure-property relations on the quantum scale will turn computational empiricism into true design.     

拓扑与形状优化用于有效的产品设计

 介绍了基于有限元法(FEM)的计算机辅助结构优化方法． 拓扑优化有助于设计新零件的形状，形状优化则通过表面几何形状的局部调整改善零件的刚度或使用寿命．     

Topology design for composite components of minimum weight

This work presents a new philosophy for optimisation of composite structures in relation to lightweight design. It is based on Michell optimum lay-out theory, which uses orthogonal mesh structures disposed in the direction of principal stress trajectories, associated with an absolutely uniform distribution of stress in the fibres. The fibres in the composite component micro structure are disposed orthogonally like the minimum weight Michell structures, with voids filled with resin. This is the same mechanical principle which governs the optimisation of natural composites such as bones, horn, trees etc. Based on this natural rule, a procedure to find the optimum topology for the design of optimum composite mechanical components has been developed. A CAD-CAE software system based on finite element analysis using ABAQUS produces interactively on a screen the structure of optimum topology where the optimum fibre arrangement will be made.     

负泊松比微结构拓扑优化设计

在构建负泊松比结构拓扑优化模型时,直接用负泊松比的数学表达式构造目标函数,将使得目标函数高度非线性,迭代过程敏度分析困难。采用线性拟合法,构建了具有线性特征的负泊松比微结构拓扑优化目标函数,基于能量法和均匀化方法,结合拓扑优化理论,构建了一种可以快速准确求解负泊松比的拓扑优化设计模型,求解该模型得到了一种优化的拓扑构型及相应的负泊松比值。根据优化求解得到的结构模型,参考国家标准GB/T 22315-2008《金属材料弹性模量和泊松比试验方法》,利用有限元软件对其泊松比进行仿真计算,然后采用激光加工方式制造试样,并测试其泊松比,经过与优化模型求解得到的泊松比值对比分析,验证了所构建优化模型的正确性。本文方法既避免了以负泊松比表达式为优化函数时会出现的高度非线性问题,也降低了求解的复杂程度,为负泊松比微结构的设计提供了一种参考方法。     

基于多目标进化算法的压电换能器优化设计

为了解决单目标优化无法满足实际工程应用需求的问题,通过对一个约束性多目标优化问题的分析,以最大振幅和最小输入电压做为优化目标,设计参数包括连续变量(换能器的尺寸)和离散变量(材料类型),利用基于分析模型的传递矩阵法对压电换能器进行建模,进而导出优化问题的数学描述式,最后应用多目标进化算法NSGA-Ⅱ,估算一系列的pareto优化设计值,分析优化结构,并确定最优设计参数.     

基于ANSYS的自行车车架拓扑优化设计

 为了寻求自行车车架的最佳结构形状,对其进行拓扑优化设计.首先介绍拓扑优化的研究现状和数学模型,接着应用有限元分析软件ANSYS 110对自行车车架进行拓扑优化设计,得出自行车车架的最佳结构形状为2个三角形,并对目前的自行车车架提出了改进措施.     

一种联合优化的水声通信网路由算法设计

针对传统的无线网络路由建立算法在水下小型网络中时延及能耗代价高的问题,提出了改进的DSDV(Destination Sequenced Distance Vector)路由过程,并在此基础上设计出与拓扑结构、MAC层联合优化的算法。该算法建立了以改进的DSDV路由建立时间、能耗及路由信息的完整性为代价函数,以MAC层的包长度、包间隔、拓扑结构中的点和边数等为矢量参数的数学模型,并结合无向图的广度优先搜索算法及最短路径算法,提出了在上述矢量参数条件下代价函数的最优化设计,形成一套适用于小规模区域性观测应用背景的水声通信网的路由建立方法。仿真结果表明,在相同的物理层条件下,联合优化的算法与未优化的DSDV相比,在相同的时间内建立完整的全网路由的概率最大可提高30%。     

Compliant mechanism design with non-linear materials using topology optimization

In this paper, compliant mechanism design with non-linear materials using topology optimization is presented. A general displacement functional with non-linear material model is used in the topology optimization formulation. Sensitivity analysis of this displacement functional is derived from the adjoint method. Optimal compliant mechanism examples for maximizing the mechanical advantage are presented and the effect of non-linear material on the optimal design are considered.     

尺度关联的微结构构型与排布的材料/结构动力学设计

考虑微观尺度和宏观尺度的关联, 将微结构胞元设计和多尺度均匀化设计结合, 建立了由相同尺寸和内部构型的微结构胞元组成的复合材料结构的材料/结构一体化动力学优化设计方法, 给出了相应的算例。方法中引入了微观和宏观两个尺度上的独立密度变量, 采用材料属性的合理近似模型对密度进行惩罚, 利用有限元超单元技术建立材料与结构的联系。基于算例获得了超单元尺寸与微观、宏观材料用量对结构拓扑构型的影响规律。将算例结果与已有方法的结果比较, 表明本文方法具有合理有效性, 可作为对轻质结构进行动力学设计的一种新方法。      

A methodology to reduce variability during vacuum infusion with optimized design of distribution media

Seemann Composites Resin Infusion Molding Process (SCRIMP) is a widely used version of Vacuum Assisted Resin Transfer Molding (VARTM) in which a highly permeable layer (distribution media) is placed on top of the dry preform to distribute the resin with very low flow resistance to reduce the filling and hence the manufacturing time. The flow patterns during filling may vary from part to part due to the variability associated with the material, part geometry, and layup of the assembly, which may result in race-tracking channels. The process is considered as reliable and robust only if the resin completely saturates the preform despite changing filling patterns caused by flow disturbances.The resin flow pattern can be manipulated with a tailored distribution media layout as it does impact the flow patterns significantly. The continuous distribution media layout over the entire part surface works well for very simple geometries with no to little potential for race-tracking along the edges. In this study we address complex cases, which require placement of an insert within the assembly, which will introduce race-tracking along its edges, and hence uniform placement of distribution media over the entire top surface will fail to yield a void free part. We introduce a methodology using a predictive tool to design an optimal shape of distribution media, which accounts for the flow variability introduced due to race-tracking along the edges of the inserts. This iterative approach quickly converges to provide the placement of distribution media on selective areas of the preform surface that ensures complete filling of the preform despite the variability. This approach has been validated with an experimental example and will help mitigate risk involved in manufacturing complex composites components with Liquid Molding.     

Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements

This paper focuses on topology optimization utilizing incompressible materials under both small‐ and finite‐deformation kinematics. To avoid the volumetric locking that accompanies incompressibility, linear and nonlinear mixed displacement/pressure (u/p) elements are utilized. A number of material interpolation schemes are compared, and a new scheme interpolating both Young's modulus and Poisson's ratio (E ‐ν interpolation) is proposed. The efficacy of this proposed scheme is demonstrated on a number of examples under both small‐ and finite‐deformation kinematics. Excessive mesh distortions that may occur under finite deformations are dealt with by extending a linear energy interpolation approach to the nonlinear u/p formulation and utilizing an adaptive update strategy. The proposed optimization framework is demonstrated to be effective through a number of representative examples.     

Integrated structures and materials design

This paper introduces the concept of␣Integrated Structures and Materials Design (ISMD). ISMD combines materials engineering and structural engineering for the purpose of more effectively achieving targeted structural performance, by adopting material composite properties as the shared link. An application example, design of a bridge deck link-slab, is used to illustrate the essential elements of ISMD. It is shown that the composite hardened properties—tensile strain capacity, microcrack width, and Young’s Modulus, as well as composite self-consolidating fresh properties, are amongst the most important composite parameters that govern the targeted structural performance of safety, durability and ease of design and implementation. These are also properties that can be controlled in an Engineered Cementitious Composite—an ultra ductile concrete, by tailoring the ingredients for desired fiber, matrix and interface micromechanical parameters. Broad implications of ISMD on educational approach, research collaboration, and next generation infrastructure development, are briefly discussed.     

Simplified design of composite materials

An internally consistent theory of micro- and macromechanics has been formulated to link materials, geometric and environmental parameters that affect the stiffness and strength ofstructural elements made of multidirectional composite laminates. Design simplifications are presented and other unique features ofthis integrated framework are discussed. The framework has been implemented on a personal computer in a spreadsheetformat and validated using organic fibre-matrix composite materials data.