Design of Electromagnetic Actuators Using Layout Optimization With Distributed Current Source Models

A metal-only reflectarray (MOR) antenna for 77 [GHz] was analyzed with the equivalent surface current sources. The equivalent current sources can be used to produce the incident fields radiated from a feed. When a feed is an open-ended rectangular waveguide (OERW), the calculated antenna gains for the equivalent current sources, point source, and CST Microwave Studio (MWS) are 31.8, 30.0, and 31.6 [dBi], respectively. The simulated results of the equivalent current sources and CST MWS are in good agreement with each other in terms of the antenna gain.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

It is of great importance for the development of new products to find the best possible topology or layout for given design objectives and constraints at a very early stage of the design process (the conceptual and project definition phase). Thus, over the last decade, substantial efforts of fundamental research have been devoted to the development of efficient and reliable procedures for solution of such problems. During this period, the researchers have been mainly occupied with two different kinds of topology design processes; the Material or Microstructure Technique and the Geometrical or Macrostructure Technique. It is the objective of this review paper to present an overview of the developments within these two types of techniques with special emphasis on optimum topology and layout design of linearly elastic 2D and 3D continuum structures. Starting from the mathematical-physical concepts of topology and layout optimization, several methods are presented and the applicability is illustrated by a number of examples. New areas of application of topology optimization are discussed at the end of the article. This review article includes 425 references.

In this study, an efficient topology optimization method under crash loads is proposed by combining the equivalent static loads with a model order reduction method, which is referred as the reduced model–based equivalent static loads method for nonlinear dynamic response topology optimization method. Considering that some parts of the vehicle experience large nonlinear deformations, whereas others exhibit only small linear deformations in a vehicle crash scenario, the linear and nonlinear behavior parts are identified and the whole model of the complete structure is divided into nonlinear and linear sub-models. At each cycle, the model order reduction method is used in the linear sub-model during crash analysis to solve the low-density-elements-induced mesh distortion problem and accelerate this process. In the linear static topology optimization, the nonlinear sub-model that was initially used to describe the nonlinear behavior part is linearized by the equivalent static loads method and then reduced by the Guyan reduction method. Then, the reduced equivalent static load model is assembled into the linear sub-model that is defined as the design space to formulate a reduced topology optimization model of the complete structure and the reduced equivalent static loads that only act on master degrees of freedom are calculated. Finally, the linear static topology optimization is performed based on the reduced topology optimization model with the reduced equivalent static loads to enhance the efficiency and improve the numerical stability. The process is repeated until the convergence criterion is satisfied. The effectiveness of the proposed method is demonstrated by investing a numerical example. The results show that the proposed method provides a feasible strategy for the topology optimization under crash loads, which can effectively improve the numerical stability and convergence.

In this paper, an optimum rib layout design method for reducing radiated noise is proposed based on topology optimization and acoustic contribution analysis. According to radiated noise depends on acoustic transfer vector (ATV) and normal velocity, the influence of rib layout on ATV is analyzed and it is found rib layout has little influence on ATV. Only if a region has maximum acoustic contribution, the normal velocities on this region can have the most remarkable influence on radiated noise. So the determination procedure of region with maximum acoustic contribution is introduced. Based on this, the topology optimization model is established to minimize the normal velocities on this region. Ribs can be arranged according to the optimum topologies to reduce the normal velocities, which in turn results in a reduction of radiated noise. The topology optimization model is used to obtain the optimal rib layout by taking a plate-like structure as an example. The plate is fixed along all side edges and excited by a time-harmonic external point load with different prescribed frequencies. The radiated noise is simulated using the finite element method and boundary element method. Four plates are manufactured according to the optimal rib layouts for different single frequency excitation. Modal test and sound measurement are conducted to validate the proposed method. The influence of loading position on the topology optimization results is also investigated and discussed.

Simultaneously multi-material layout, and connectivity optimization of truss structures via an Enriched Firefly Algorithm

Integrated topology and shape optimization software for compliant MEMS mechanism design

Topology optimization of structures and composite continua has two main subfields: Layout Optimization (LO) deals with grid-like structures having very low volume fractions and Generalized Shape Optimization (GSO) is concerned with higher volume fractions, optimizing simultaneously the topology and shape of internal boundaries of porous or composite continua. The solutions for both problem classes can be exact/analytical or discretized/FE-based. This review article discusses FE-based generalized shape optimization, which can be classified with respect to the types of topologies involved, namely Isotropic-Solid/Empty (ISE), Anisotropic-Solid/Empty (ASE), and Isotropic-Solid/Empty/Porous (ISEP) topologies. Considering in detail the most important class of (i.e. ISE) topologies, the computational efficiency of various solution strategies, such as SIMP (Solid Isotropic Microstructure with Penalization), OMP (Optimal Microstructure with Penalization) and NOM (NonOptimal Microstructures) are compared. The SIMP method was proposed under the terms "direct approach" or "artificial density approach" by Bendsoe over a decade ago; it was derived independently, used extensively and promoted by the author's research group since 1990. The term "SIMP" was introducted by the author in 1992. After being out of favour with most other research schools until recently, SIMP is becoming generally accepted in topology optimization as a technique of considerable advantages. It seems, therefore, useful to review in greater detail the origins, theoretical background, history, range of validity and major advantages of this method.

In the design synthesis process, it has become a prime focus of all modern enterprises to optimal design an initial layout of the component that fulfill aesthetics, quality, and manufacturing constraints. Topology optimization is used to design an optimal initial layout of the component and computer simulations in CAE environment have also become vital tools to shorter product development time by reducing experimentation with prototypes. In this research, an integrated approach is implemented to design a multi pocket beam type component in CAE environment using topology optimization. CATIA is used for part modeling, machining constraints and to check machineability via virtual machining module. ANSYS is used to simulate the post machining distortions by using element deactivation technique firstly by developing an initial residual stress field through Sequential Coupled Field analysis. Material removal simulations are done by different sequences to determine the optimal machining process route. Comparison of simulated results with actual experimentation validates that optimization enabled design with computer simulations are very convenient for better product designs.

The performance of the cage can directly affect the service life of the bearing. This paper presents a cage topology optimization method for improving the heat dissipation and structural stiffness. Firstly, a multi-objective structural topology optimization model is established based on the SIMP method and MMA algorithm, the effects of force and thermal load are considered comprehensively. Secondly, considering the centrifugal force and frictional heat, under the conditions of a given volume constraint, the bearing cage topology optimization model is carried out with heat dissipation weakness and compliance as the optimization objectives. Using iterative calculations based on the MMA algorithm and boundary smoothing processing, the structure with the optimal material layout is obtained. Finally, compared with the initial structures, the maximum temperature reduces about 27% and the maximum stress reduces about 14.8%. The results show that topology optimization can provide a reference for the design of bearing cages, which can improve the structural performance while reducing weight.

The output of a proton exchange membrane fuel cell (PEMFC) relies on the transport behavior within the cathode gas channels, which is largely determined by their design features. Current designs remain inadequate, as they often rely on heuristic modifications of existing layouts or designer intuition with suboptimal performance. In this study, topology optimization is proposed to redesign the PEMFC cathode gas channel layout without a priori assumptions. The optimization aims to maximize the reactant concentration and minimize power dissipation along the flow path. A density-based topology optimization framework is adopted and coupled with a gradient-based optimizer. The problem is solved within a three-dimensional half-cell model. For computational tractability, a reduced-order, depth-averaged 2D model is also implemented. The optimized topology yields an enhanced current density with lower energy dissipation over the conventional benchmarks. At an inlet velocity of 0.15 m/s, the pressure drop is reduced by 46.7% compared to the serpentine layout, though it is 28.2% higher than that of the parallel case. Within the optimized channels, oxygen flows at higher local velocities, which allows more homogeneous reactant delivery across the domain. Compared to the serpentine layout, the optimized design increases the mean current density by 20.9% and lowers its standard deviation by 4.9%; relative to the parallel layout, the improvement in the mean current density reaches 39.7%. Placing more emphasis on dissipation minimization during optimization produces more intricate and tortuous channel topologies. Such design flexibility enables the discovery of unconventional yet efficient layouts that can be readily manufactured thanks to additive manufacturing (AM).

The purpose of this paper is to give an overall introduction of the structural optimization research works in ESAC group in 2011. Four main topics are involved, i.e. 1) topology optimization with multiphase materials, 2) integrated layout and topology optimization, 3) prediction of effective material properties and 4) composite design. More detailed techniques and some numerical results are also presented and discussed here.

Covariance matrix adaptation evolution strategy for topology optimization of foundations under static and dynamic loadings

The energy function method developed from Lyapunov theory is a typical direct method to evaluate the transient synchronous stability of traditional power grids. Different from grid‐forming (GFM) converters mimicking characteristics of synchronous generators (SGs), grid‐following (GFL) converters behave like current sources. The integration of multiple GFL converters poses challenges of constructing energy functions for transient synchronous stability assessment, which is analysed in this paper. In addition, the damping terms of GFL converters are highly dependent on phase angles. Due to the indefinite damping terms of GFL converters, assessment results might be optimistic or conservative, if neglecting damping terms to construct energy functions. Thus, based on manifold theory, an alternative without constructing energy functions is proposed for transient synchronous stability assessment of multi‐converter‐based power grids. Firstly, a hybrid modelling with equivalent voltage and current sources is built to accommodate different network topologies and types of converters. Then, benefiting from the first‐order approximation of manifolds and the geometrical analysis of the region of attraction (ROA) boundary, a criterion designed by manifold theory is proposed and employed for transient synchronous stability evaluation. In addition, the transient synchronous stability margin k rel ζ is defined to avoid optimistic results. Finally, modified IEEE 4‐generator 11‐bus and IEEE 10‐generator 39‐bus systems are built on the MATLAB/Simulink platform to validate the effectiveness of the method.

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.