Shape and topology optimization for electrothermomechanical microactuators using level set methods

In this short note, a shape and topology optimization method is presented for multiphysics actuators including geometrically nonlinear modeling based on an implicit free boundary parameterization method. A level set model is established to describe structural design boundary by embedding it into the zero level set of a higher-dimensional level set function. The compactly supported radial basis functions (CSRBF) are introduced to parameterize the implicit level set surface with a high level of accuracy and smoothness. The original more difficult shape and topology optimization driven by the Hamilton–Jacobi partial differential equation (PDE) is transferred into a relatively easier parametric (size) optimization, to which many well-founded optimization algorithms can be applied. Thus the structural optimization is transformed to a numerical process that describes the design as a sequence of motions of the design boundaries by updating the expansion coefficients of the size optimization. Two widely studied examples are chosen to demonstrate the effectiveness of the proposed method.     

Shape optimization of 3D curved slots and its application to the squirrel-cage elastic support design

The squirrel-cage elastic support is one of the most important components of an aero-engine rotor system.A proper structural design will favor the static and dynamic performances of the system.In view of the deficiency of the current shape optimization techniques,a new mapping approach is proposed to define shape design variables based on the parametric equations of 3D curves and surfaces.It is then applied for the slot shape optimization of a squirrel-cage elastic support.To this end,an automatic design procedure that integrates the Genetic Algorithm (GA) is developed to solve the problem.Two typical examples with different shape constraints are considered.Numerical results provide reasonable optimum designs for the improvement of stiffness and strength of the squirrel-cage elastic support.     

Shape and topology optimization of compliant mechanisms using a parameterization level set method

In this paper, a parameterization level set method is presented to simultaneously perform shape and topology optimization of compliant mechanisms. The structural shape boundary is implicitly embedded into a higher-dimensional scalar function as its zero level set, resultantly, establishing the level set model. By applying the compactly supported radial basis function with favorable smoothness and accuracy to interpolate the level set function, the temporal and spatial Hamilton–Jacobi equation from the conventional level set method is then discretized into a series of algebraic equations. Accordingly, the original shape and topology optimization is now fully transformed into a parameterization problem, namely, size optimization with the expansion coefficients of interpolants as a limited number of design variables.Design of compliant mechanisms is mathematically formulated as a general optimization problem with a nonconvex objective function and two additionally specified constraints. The structural shape boundary is then advanced as a process of renewing the level set function by iteratively finding the expansion coefficients of the size optimization with a sequential convex programming method. It is highlighted that the present method can not only inherit the merits of the implicit boundary representation, but also avoid some unfavorable features of the conventional discrete level set method, such as the CFL condition restriction, the re-initialization procedure and the velocity extension algorithm. Finally, an extensively investigated example is presented to demonstrate the benefits and advantages of the present method, especially, its capability of creating new holes inside the design domain.     

Shape and topology optimization based on the phase field method and sensitivity analysis

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to two-dimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.     

CFD/CSD耦合飞行器多学科优化设计新方法

文章以飞行器巡航外形为设计对象, 构建了一种新的飞行器的气动和结构特性评估方法, 即结构模型反迭代方法.该方法较传统的松耦合静气动弹性方法效率提高了4倍以上.以此为基础建立了一种新的飞行器气动/结构耦合多学科优化设计框架, 将优化效率提高4倍以上.采用数值求解N-S方程和结构有限元方程方法作为气动和结构学科的分析工具, 保证了设计结果的可信性.算例表明以巡航外形作为设计对象能够获得与传统方法一致的飞行器气动与结构特性, 以此为基础开展的无人机气动外形优化设计也获得了良好的设计结果.      

Nodal line optimization and its application to violin top plate design

In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.     

基于本征正交分解的气动优化设计外形数据挖掘

气动外形的全局优化设计会产生大量的过程数据,其中隐含的设计知识具有较高的挖掘价值.数据挖掘有助于获取直观、可定性描述的设计知识.本文采用基于本征正交分解的数据挖掘方法从气动优化设计的过程数据中获取设计知识,数据挖掘对象为跨音速压气机转子叶片NASA Rotor 37的优化过程数据,该数据由基于粒子群方法的绝热效率最大化优化设计产生.结果表明:基于本文数据挖掘方法获取的设计知识能够直接反映气动外形的变化规律,为叶片的气动外形设计提供参考;数据挖掘的设计知识成功地验证了优化设计结果的有效性.     

A new method for inverse electromagnetic casting problems based on the topological derivative

The inverse electromagnetic casting problem consists in looking for a suitable set of electric wires such that the electromagnetic field induced by an alternating current passing through them makes a given mass of liquid metal acquire a predefined shape. In this paper we propose a new method for the topology design of such inductors. The inverse electromagnetic casting problem is formulated as an optimization problem, and topological derivatives are considered in order to locate new wires in the right position. Several numerical examples are presented showing that the proposed technique is effective to design suitable inductors.     

逐级优化制定离轴三反射光学系统加工装调公差

逐级优化法是根据离轴三反射光学系统结构参数的像差灵敏度系数大小来确定主镜、次镜和第三反射镜的加工次序的。其方法是逐级优化确定各光学零件的加工公差,加工完成后测量光学元件结构参数,代入光学设计软件进行优化,进而确定光学系统的装调公差。采用该方法制定三反射系统的加工装调公差时将加工和设计过程有机的结合起来,在满足设计要求的前提下使系统的加工和装调公差得到最大程度地放松。     

Structural topology optimization on sound radiation at resonance frequencies in thermal environments

Thermal and acoustic environments pose severe challenges to the structural design of hypersonic vehicles.One of them is to find optimal design that exhibits ideal acoustic characteristics in a frequency band,which is discussed in this paper through topology optimization aiming at resonance sound radiation in thermal environments.The sound radiation at resonance frequencies is the main component of response,minimization on which is likely to provide a satisfactory design.A bi-material plate subjected to uniform temperature rise and excited by harmonic loading is studied here.Thermal stress is first evaluated and considered as prestress in the following dynamic analysis;radiated sound power is then calculated through Rayleigh integral.Sensitivity analysis is carried out through adjoint method considering the complicated relationship between stress-induced geometric stiffness and design variables.As the resonance frequency is constantly changing during the optimization,its sensitivity should be considered.It is also noticed that mode switching may occur,so mode tracking technique is employed in this work.Some numerical examples are finally discussed.     

Shape design sensitivity analysis for the radiated noise from the thin-body

Many industrial applications generally use thin-body structures in their design. To calculate the radiated noise from vibrated structure including thin bodies, the conventional boundary element method (BEM) using the Helmholtz integral equation is not an effective resolution. Thus, many researchers have studied to resolve the thin-body problem in various physical fields. No major study in the design sensitivity analysis (DSA) fields for thin-body acoustics, however, has been reported.A continuum-based shape DSA method is presented for the radiated noise from the thin-body. The normal derivative integral equation is employed as an analysis formulation. And, for the acoustic shape design sensitivity formulation, the equation is differentiated directly by using material derivative concept. To solve the normal derivative integral equation, the normal velocities on the surface should be calculated. In the acoustic shape sensitivity formulation, not only the normal velocities on the surface are required but also derivative coefficients of the normal velocities (structural shape design sensitivity) are also required as the input. Hence, the shape design sensitivity of structural velocities on the surface, with respect to the shape change, should be calculated. In this research, the structural shape design sensitivities are also obtained by using a continuum approach. And both a modified interpolation function and the Cauchy principle value are used to regularize the singularities generated from the acoustic shape design sensitivity formulation.A simple annular disk is considered as a numerical example to validate the accuracy and efficiency of the shape design sensitivity equations derived in this research. The commercial BEM code, SYSNOISE, is utilized to confirm the results of the developed in-house code based on a normal derivative integral equation. To validate the calculated design sensitivity results, central finite difference method (FDM) is employed. The error between FDM and the analytical result are less than 3%. This comparison demonstrates that the proposed design sensitivities of the radiated pressure are very accurate.     

大口径主镜轻量化结构参数的优化设计

针对空间遥感器中大口径主镜的轻量化结构设计引入了基于Kriging近似模型的多目标遗传优化方法,以2 m口径SiC主镜为例对其轻量化结构参数进行了优化设计。采用拉丁超立方法对优化参数进行试验设计,建立了Kriging模型,并用多目标遗传算法迭代求得了最优解。优化后得到了质量为243 kg的2 m口径SiC主镜,其面形精度达到了25.7 nm PV,4.7 nm RMS,轻量化率为84%。试验结果验证了此优化设计方法的可行性,为大口径主镜的轻量化结构参数优化设计提供了借鉴和参考。     

基于Kriging代理模型的飞行器结构刚度气动优化设计

大飞机具有轻质大柔性特点,使得气动/结构耦合作用增强,在设计过程中需要考虑这种耦合效应,直接调用CSD/CFD方法计算周期长,无法满足工程需要.代理模型方法由于能显著提高工程优化设计的效率,已广泛应用于飞行器气动外形优化设计中.采用Kriging方法建立代理模型,通过求解EI函数最大值得到需添加的样本点以更新代理模型,提高代理模型的拟合精度,结合改进的粒子群最优化方法对大飞机的结构刚度进行了优化设计.结果表明,该优化方法能够处理复杂目标的全局优化问题,在保证升力系数及纵向稳定性能不恶化的前提下,降低飞机巡航状态的飞行阻力.      

小阻尼封闭空间声压级灵敏度分析与优化设计

本文研究了小阻尼界面封闭空间低频声学有限元分析、灵敏度分析和优化设计问题。分别用模态法和直接法计算了封闭空间内声压级响应，并推导了声压级响应对声空间边界形状控制参数的灵敏度分析公式，在此基础上建立了小阻尼空间声学问题的优化模型，同时给出了优化求解算法，并在JIFEX软件中进行了程序实现。本文提出的灵敏度分析和优化设计方法可以使声场的边界布局更为合理，从而达到改进小阻尼界面封闭空间声学性能的目的。数值算例验证了本文提出的灵敏度分析和优化算法的有效性。     

空间光学遥感器次镜参数化设计

根据某空间遥感器次镜设计指标要求,采用ANASYS多参数优化设计功能对次镜轻量化进行优化设计。利用UG软件建立反射镜体结构的参数化模型,在ANSYS中将有关结构参数变量指定为优化设计变量,以反射镜体在地面重力作用下的镜面变形误差以及反射镜支撑孔位移为零作为约束条件,结合有限元法对镜体轻量化结构的尺寸参数进行优化分析,得到了轻量化率达到80.635%,镜面面形精度RMS为6.953 nm,PV值为31.317 nm,满足设计要求的反射镜。     

Differential toolbox to shape dispersion behavior in photonic crystal fibers

We present an analytical procedure to compute the first derivatives of the propagation constants with respect to several structural parameters in photonic crystal fibers (PCFs). From them we can easily evaluate the same derivatives of other directly related magnitudes. The above derivatives provide the trend of the magnitude at issue, which allows us to take advantage of a gradient-based algorithm to shape the properties of the guiding structure. In this way we implement an optimization process to carry out real inverse design in PCFs. We focus our attention on designing PCFs with a specific chromatic dispersion behavior. Likewise, the same approach makes it possible to analyze their fabrication tolerances.     

电流变力矩放大器

设计和开发一种电流变力矩放大器,介绍其工作原理、结构特点。在此基础上,研究结构设计参数间隙、圆盘内外径对机构性能的影响,并提出多目标规划的电流变力矩放大器的优化设计模型,从提高放大器放大倍数或提高动态响应速度的角度,规定权重和子目标的追求值,从而设计出性能优良的放大器。采用实验拟合方法,识别放大力矩与控制电场成抛物线关系;利用阶跃和脉冲电场信号研究这种装置的动态性能,结果表明,通过多目标规划的优化模型得到的电流变力矩放大器,具有良好的动态性能。     

Truss optimization on shape and sizing with frequency constraints based on orthogonal multi-gravitational search algorithm

Structural optimization on shape and sizing with frequency constraints is well-known as a highly nonlinear dynamic optimization problem with several local optimum solutions. Hence, efficient optimization algorithms should be utilized to solve this problem. In this study, orthogonal multi-gravitational search algorithm (OMGSA) as a meta-heuristic algorithm is introduced to solve truss optimization on shape and sizing with frequency constraints. The OMGSA is a hybrid approach based on a combination of multi-gravitational search algorithm (multi-GSA) and an orthogonal crossover (OC). In multi-GSA, the population is split into several sub-populations. Then, each sub-population is independently evaluated by an improved gravitational search algorithm (IGSA). Furthermore, the OC is used in the proposed OMGSA in order to find and exploit the global solution in the search space. The capability of OMGSA is demonstrated through six benchmark examples. Numerical results show that the proposed OMGSA outperform the other optimization techniques.     

Shape optimization towards stability in constrained hydrodynamic systems

Hydrodynamic stability plays a crucial role for many applications. Existing approaches focus on the dependence of the stability properties on control parameters such as the Reynolds or the Rayleigh number. In this paper we propose a numerical method which aims at solving shape optimization problems in the context of hydrodynamic stability. The considered approach allows to guarantee hydrodynamic stability by modifying parts of the underlying geometry within a certain flow regime. This leads to a formulation of a shape optimization problem with constraints on the eigenvalues related to the linearized Navier–Stokes equations. In that context the eigenvalue problem is generally non-symmetric and may involve complex eigenvalues. To validate the proposed numerical approach we consider the flow around a body in a channel. The shape of the body is parameterized and can be changed by means of a discrete number of design variables. It is our aim to find a design which minimizes the drag force and ensures at the same time hydrodynamic stability while keeping the volume of the body constant. The numerical results show that a transition from an unstable design to a stable one is attainable by considering an adequate change of the body shape. The resulting bodies are long and flat which corresponds to common intuition.