Integrated topology and shape optimization software for compliant MEMS mechanism design

Random variable of thermo-mechanical coupling (TMC) structure is analyzed first, then the topology optimization model of TMC compliant mechanism is established. According to the uncertainty factors such as temperature, load, volume ratio and thermal expansion coefficient in the process of topology optimization, the robust reliability optimal design method is introduced into the topology optimization process. The various factors on the sensitivity of topology optimization process is analyzed, the best match between various factors is find out, which make the product has robust reliability for the change of the uncertainty. The residual analysis for the most sensitive factors is carried out. Finally the correctness and validity of the method is verified with an example. Introduction When we study the compliant mechanisms by adopting topological optimization method, we only need to give design domain and allocate input and output position, no need from the perspective of a known rigidity. The mechanism come from this method have a input and output relationship of optimized “force—displacement”, thus it attracts people’s attention. Topology optimization research is developing from certain topology optimization direction to reliable topology optimization direction. Jinqing Zhan proposed a reliable topology optimization method of compliant mechanism based on infrastructure method. KHARMANDA proposed a reliable topology optimization method. Zhaokun Li proposed a geometric nonlinear topology optimization research method based on reliable compliant mechanism. Their research turned out that the mechanism based on reliable topology optimization is more reasonable than the mechanism based on certain topology optimization. Yongcong Kuang build a level set function to design variable, stiffness minimization, and proposed corresponding optimization algorithm. Mingtao Cui established a monolithic compliant mechanism multi-target reliable topology optimization design dual mathematical model. This paper combines topology optimization process of compliant mechanism and robust reliability optimal design, analyzes the sensitivity of uncertainty random variables such as design domain’s size, external load and temperature in topology optimization process. Then get the best combination among these random variables. Random Variable Coupling Field Analysis Hot objects will produce thermal expansion, thus caused by the thermal deformation and displacement of combined action of mechanical load and temperature load structure called a hot solid coupling structure, the finite element balance equation :

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.

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

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.

Exploring the influence of initial design domain dependencies in concurrent multiscale topology optimization for heat conductivity maximization

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.

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 paper presents a microgripper design and utilizes the topology optimum method to obtain larger output force and displacement. The goal of this study is to obtain the sharpest topology layout by simulation and computing. The difference between compliant mechanisms and traditional mechanisms is that compliant mechanisms have flexible pieces to transmit force or deliver motion. When we apply different forces, we use the flexibility to generate expectably related effects to fulfil our special functional purposes. In addition, the shape obtained from topology optimal design can be further refined by shape optimization. This research combines insights from the topology optimum compliant mechanism and the piezoelectric microactuator to design a microgripper and to analyze the effects with different parameters in topology optimization

Inspired by nature’s multi-material compliant designs and the capability of modern manufacturing methods to make multi-material components without assembly, and motivated by the versatility and enhanced functionality with multi-material designs, we formalize the notion and the design of heterogeneous compliant mechanisms. In the topology optimization of compliant mechanisms, a fictitious density function is often used for material interpolation to overcome the computational difficulties encountered in the large “0-1” type integer programming problem. In this paper, we illustrate that a gradually formed continuous peak function can be used for material interpolation. One of the advantages of introducing the peak function is that multiple materials can easily be incorporated into the topology optimization without increasing the number of design variables. By using the peak function and the optimality criteria method, we synthesize compliant mechanisms with multiple materials with and without the material resource constraint. The numerical examples include the two, three, and four material designs where void is treated as one material. This new design method enables us to optimally juxtapose stiff and flexible materials in heterogeneous compliant mechanisms that can be built using a variety of modern manufacturing methods.

Although compliant mechanism design is a thoroughly studied field, surprisingly little information can be found in literature regarding selection of optimal materials. This paper is intended to fill this gap. Density-based, geometrically robust, stress constrained topology optimization based on a total Lagrangian FEM formulation is used for investigation of a compliant inverter and a compliant gripper example. Changes in handling of the projection parameters and the stress constraints are proposed for improved algorithmic stability and accurate representation of the stresses and material stiffness in topology optimization. Large-scale optimization studies are carried out, varying elastic modulus and allowable stress in a wide range. A comparison with an Ashby chart shows the characteristics of the best suited material. It is shown, that an optimal Young’s modulus and a minimum required material strength (depending on the modulus) can be identified from the results. Altering critical optimization parameters, e.g. allowable volume fraction and the minimum length scale, their influence on the optimal material choice is investigated. Guidelines for compliant mechanism designers for efficient selection of suited materials are developed.

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.

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.

Mathematical optimization theories are employed for the design of structures in structural optimization. Structural optimization is being widely utilized for practical problems due to well-developed commercial software systems. Three representative structural optimization systems such as Genesis, MSC Nastran and OptiStruct are investigated and evaluated by solving various test examples in different scales. The design capabilities of three software systems are explored and the performances of the systems are compared. The performance of structural optimization depends on the quality of the optimum solution and the computational time, and these aspects are compared from an application viewpoint. For a fair comparison, the same formulations are utilized, and the same optimization methods are employed for each example. Also, the same system environment is prepared, and the same optimization parameters are used. Additionally, various design options of each software system are tested for the best performance. Linear static response size, shape, topology, topometry and topography optimizations are applied to the examples and the results are compared. No system seems to be the best in all cases and each system has advantages and disadvantages depending on the application. In general, Genesis is excellent in computational time while OptiStruct gives excellent optimum solutions, in size, topometry and topology optimizations. Meanwhile, MSC Nastran presents good solutions in shape and topography optimizations.

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.

The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples are presented: the first one compares topological optimization with standard shape optimization, and the second one, issued from a lake oxygenation problem, illustrates the use of the new asymptotic expansion.