Light-weight design of automobile suspension components using topology and shape optimization techniques

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

The study of reactive silencers by shape and parametric optimization techniques

Structural topology optimization.- On basic properties of Michell's structures.- Validation of numerical method by analytical benchmarks and verification of exact solutions by numerical methods.- Introduction to shape and topology optimization.- Homogenization method for shape and topology optimization.- Level set method for shape and topology optimization.- Compliance minimization of two-material elastic structures.- Some notes on topology optimization of vibrating continuum structures.- Topology optimization of vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps.- On optimum shape design and periodicity of band-gape beam structures.- Topological design for minimum dynamic compliance of continuum structures subjected to forced vibration.- Topological design for minimum sound emission from bi-material structures subjected to forced vibration.- Discrete material optimization of vibrating laminated composite plates for minimum sound emission.- Optimization of diffusive transport problems.- Fluid topology optimization: stokes and Navier-stokes models.- Topology optimization of coupled multi-physics problems.- Topology optimization based on the extended finite element method.- Topology optimization of meso- and nano-scale problems.- Topology optimization under uncertainty.- A brief review of numerical methods of structural topology optimization.- The free material design in planar elasticity.

Most robotic applications demand lightweight and high-speed manipulators for considerably reducing the consumed power and achieving high production rates. The two ways for seeking such high-speed arms are; applying advanced control algorithms and/or performing an extensive optimization of the arm structure itself. Therefore, the topology optimization technique is proposed here for obtaining an optimal robot arm design from both structure and control viewpoints. Results of some researches, that have been previously accomplished by size and shape optimization, were encouraging enough to extend and propose this optimization approach. The method of moving asymptotes (MMA) as an optimization algorithm, the finite element analysis (FEA) by ANSYS, and the time-optimal control method are integrated to gain an optimum design capable of attaining the minimum traveling time. The proposed methodology focuses on performing different comparisons between the proposed optimum topological designs and their initial designs for different robot arms’ sizes and materials. It also distinguishes between the proposed optimum design and the previously achieved one by size optimization under the same operational conditions. Therefore, the significance of the proposed technique is emphasized. It shows that the traveling time is reduced by 44.8%, while the previous work only achieved 23.5%. In addition, the mass is reduced to nearly half of its initial value, taking into account the air damping as the real case in all terrestrial applications.

<div class="htmlview paragraph">In various practical structural design problems, decision of a layout of material or stiffeners in the given design space satisfying some design constraints is the most difficult task for design engineers. Also, they must consider many possible cases for safety, performance and some other requirements. But it is very difficult to solve this type of layout (topology) problem by any conventional structural optimization techniques because its mathematical modeling of topology is so complex. To solve this problem, we employed the new topology optimization technique using the homogenization method that was recently introduced by Bensøe and Kikuchi. The method gives the minimum compliance design under certain material constraint. This technique was also extended to three dimensional shells and three dimensional solids by Suzuki and Kikuchi.</div> <div class="htmlview paragraph">In this paper, shape and topology optimization problem under multi-loading conditions is discussed. Various car body design problems are solved to justify the validity and the strength of the present approach for engineering applications.</div>

In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.

In order to achieve a low vibration design of engine block,verify the correctness of finite element model based on the test method,ensure the undertake of different levels of optimization model using the method of topology and shape optimization,modal frequency and vibration intensity of engine block are taken as optimization objectives,vibration analysis of engine block is made in the simulation,and the body vibration condition distribution are identified in the optimization design.The four cylinder engine block is set as the design objective,the optimal solution design variables are got through the topology optimization and shape optimization method,and then the final optimization scheme with whole layout and detailed design are obtained.The results of optimized structure show that frequencies of each mode are improved,and the vibration intensity value of engine block decreases by 34.8%,then vibration intensity of improved engine block is minimized in a safe area subject to rigidity and strength constraints.Efficiency and precision of the combination method of topology and shape optimization has an obvious enhance,and the feasibility and efficiency of the proposed methods are demonstrated by the experiment.

Integrated topology and shape optimization software for compliant MEMS mechanism design

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.

Simple and effective strategies for achieving diverse and competitive structural designs

This paper deals with simultaneous topology and shape optimization of elastic contact problems. The structural optimization problem for an elastic contact problem is formulated. Shape as well as topological derivatives formulae of the cost functional are provided using material derivative and asymptotic expansion methods, respectively. These derivatives are employed to formulate necessary optimality condition for simultaneous shape and topology optimization and to calculate a descent direction in numerical algorithm. Level set based numerical algorithm for the solution of this optimization problem is proposed. Numerical examples are provided and discussed.

This chapter is the printed matter of a series of lectures on shape optimization given in Udine (Italy) in June 2012. It is mainly focused on the optimal design problem in elasticity.It is well known, since the pioneer work of Tartar and Murat in the late 70’s, that this problem – as well as the scalar shape optimization problem in conductivity – is ill posed and does not always admit solutions. If the goal is to construct numerical methods to address this optimal design problem, this illposedness will lead to algorithms showing instabilities and erratic behaviours.Two ways are possible to slightly change the initial problem so that it may be solved in an efficient and reliable way by numerical methods. The first one consists in enlarging the set of admissible shapes and allow, as solutions, “generalized shapes” that may contain fine mixtures of the initial material and void. This process is called “relaxation” and the main mathematical tool involved is the homogenization theory. It leads to the so called “homogenization method for shape optimization”. It is described in Section 2, both from theoretical and numerical point of views, including practical issues necessary to write a numerical code.The second approach consists in restricting the set of admissible solutions. A few theorems prove the existence of solutions under further geometrical, topological or regularity constraints. The classical domain variation method is revisited using the level set representation, that may be seen as a constraint on the set of admissible solutions. The main tool is here the shape derivative. The level set algorithm is presented in Section 3.Of course this chapter is too short to develop new results and methods and present extensive proofs. Its goal is rather to give an overview on different parts of our work on this topics. Interested readers should check the references cited to have further details.KeywordsTopology OptimizationShape OptimizationHomogenization MethodAdmissible SolutionOptimal Design ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The application of optimization design in stomatology: A literature review

As an increasing need for metal implant species and quantities in the clinical application, the demands of structure for the implants have been increased, accompanying the rapid development of 3D printing technology and the progress of medical combination with engineering also made it possible to fabricate complex implants. On this basis, the topology optimization of structure in the finite element analysis technique has been developed gradually, and the application of this technique has greatly improved the biomechanical properties of implants. This review introduces the applications of topology optimization technology in implant structure design, and summarizes the researches of topology optimization technique in the field of medical implant mainly on the department of maxillofacial surgery and orthopedics. In the field of orthopedics, topology optimization technique is most widely used, and in the structural design of joint prosthesis, internal fixation and spinal implant, the obvious progress was obtained in both theory and practice. Finally, the paper put forward the prospect of the trend for the topology optimization design of metal implants in the future. Key words: Topology optimization; Implants; Maxillofacial surgery; Orthopedics.

The goal of this research is to obtain the optimum design of a new interbody fusion implant for use in lumbar spine fixation. A new minimally invasive surgical technique for interbody fusion is currently in development. The procedure makes use of an interbody implant that is inserted between two vertebral bodies. The implant is packed with bone graft material that fuses the motion segment. The implant must be capable of retaining bone graft and supporting spinal loads while fusion occurs. Finite element-based optimization techniques are used to drive the design. The optimization process is performed in two stages: topology optimization and then shape optimization. The different load conditions analyzed include: flexion, extension, and lateral bending.