Topology synthesis of electrothermal compliant mechanisms using line elements

This paper presents a line-element-based approach to the topology synthesis of electrothermal compliant (ETC) mechanisms. A line element is a one-dimensional model of the electrical, thermal, and elastic behavior of a beam-like continuum. In contrast to topology synthesis of ETC mechanisms by a continuum-element-based approach, the line-element-based approach offers significant conceptual and practical advantages. The line element allows for straightforward modeling of surface heat transfer in the topology optimization framework. It also obviates the need to interpolate electrical and thermophysical properties in the topology synthesis procedure. Moreover, this approach results in clean geometries that are easy to fabricate directly in their optimized form. Solutions obtained from this procedure are compared with results from continuum-based optimal synthesis procedures as well as intuitive designs reported in the literature. A number of design examples are used to demonstrate the ability of the procedure to generate nonintuitive topologies. The synthesis procedure is also used to study the influence of the direction of output and the electrical and thermal resistance of the workpiece on the resulting optimal topologies.     

An alternative interpolation scheme for minimum compliance topology optimization

We consider the discretized zero-one continuum topology optimization problem of finding the optimal distribution of two linearly elastic materials such that compliance is minimized. The geometric complexity of the design is limited using a constraint on the perimeter of the design. A common approach to solve these problems is to relax the zero-one constraints and model the material properties by a power law which gives noninteger solutions very little stiffness in comparison to the amount of material used. We propose a material interpolation model based on a certain rational function, parameterized by a positive scalar q such that the compliance is a convex function when q is zero and a concave function for a finite and a priori known value on q. This increases the probability to obtain a zero-one solution of the relaxed problem. Received July 20, 2000     

Two-stage compliant microleverage mechanism optimization in a resonant accelerometer

Compliant microleverage mechanisms can be used in micro-electro-mechanical systems (MEMS) to transfer an input force/displacement to an output to achieve mechanical/geometrical advantages. By stacking multiple stages of microlevers together, a compound microleverage mechanism is obtained with a higher amplification factor. This paper presents the analysis and optimization of a two-stage microleverage mechanism in a resonant output micro-accelerometer for force amplification. It is found that the compliance of the two-stage mechanism needs to be appropriately distributed in order for both stages to have the desired amplification effect. June 13, 2000     

Applications of regional strain energy in compliant structure design for energy absorption

Topology optimization of regional strain energy is studied in this paper. Unlike the conventional mean compliance formulation, this paper considers two main functions of structure: rigidity and compliance. For normal usages, rigidity is chosen as the design objective. For compliant design, a portion of the structure absorbs energy, while another part maintains the structural integrity. Therefore, we implemented a regional strain energy formulation for topology optimization. Sensitivity to regional strain energy is derived from the adjoint method. Numerical results from the proposed formulation are presented.     

Integration of topology and shape optimization for design of structural components

This paper presents an integrated approach that supports the topology optimization and CAD-based shape optimization. The main contribution of the paper is using the geometric reconstruction technique that is mathematically sound and error bounded for creating solid models of the topologically optimized structures with smooth geometric boundary. This geometric reconstruction method extends the integration to 3-D applications. In addition, commercial Computer-Aided Design (CAD), finite element analysis (FEA), optimization, and application software tools are incorporated to support the integrated optimization process. The integration is carried out by first converting the geometry of the topologically optimized structure into smooth and parametric B-spline curves and surfaces. The B-spline curves and surfaces are then imported into a parametric CAD environment to build solid models of the structure. The control point movements of the B-spline curves or surfaces are defined as design variables for shape optimization, in which CAD-based design velocity field computations, design sensitivity analysis (DSA), and nonlinear programming are performed. Both 2-D plane stress and 3-D solid examples are presented to demonstrate the proposed approach. Received January 27, 2000 Communicated by J. Sobieski     

Topology optimization of structures with integral compliant mechanisms for mid-frequency response

The purpose of this paper is to present a method for developing new truss-like sandwich structures that exhibit desirable mid-frequency vibratory characteristics. Specifically, a genetic algorithm optimization routine is used to determine candidate small scale structural topologies, i.e. unit cells, that may be used in the design of larger scale periodic sandwich structures. This multi-scale procedure is demonstrated starting with several unit cell topology optimization examples. From these examples a specific optimal unit cell is selected for further investigation and integration into a periodic sandwich beam. Computational results indicate that the proposed optimization approach is effective when used to design new structures for reduced mid-frequency vibratory response.     

Reliability-based topology optimization

The objective of this work is to integrate reliability analysis into topology optimization problems. The new model, in which we introduce reliability constraints into a deterministic topology optimization formulation, is called Reliability-Based Topology Optimization (RBTO). Several applications show the importance of this integration. The application of the RBTO model gives a different topology relative to deterministic topology optimization. We also find that the RBTO model yields structures that are more reliable than those produced by deterministic topology optimization (for the same weight).     

A web-based topology optimization program

The paper presents a web-based interface for a topology optimization program. The program is accessible over the World Wide Web at the address http://www.topopt.dtu.dk. The paper discusses implementation issues and educational aspects as well as statistics and experience with the program. Received September 29, 2000     

悬置支架强度分析和拓扑优化

在项目研发阶段用Abaqus对某轿车的发动机悬置支架进行强度分析,发现悬置支架不满足强度要求,通过拓扑优化的方法对其结构进行改进,在不增加质量的情况下,使悬置支架达到强度设计目标.     

Constrained adaptive topology optimization for vibrating shell structures

This paper describes an algorithm for structural topology optimization entitled Constrained Adaptive Topology Optimization or CATO which is applied here to produce the optimum design of shell structures under free vibration conditions. The algorithm, based on an artificial material model and an updating scheme, combines ideas from the more mathematically rigorous homogenization (h) methods and the more intuitive evolutionary (e) methods. Thus, CATO can be seen as a hybrid h/e method. The optimization problem is defined as maximizing or minimizing a chosen frequency with a constraint on the structural volume/mass by redistributing the material through the structure. The efficiency of the proposed algorithm is illustrated through several numerical examples. Received February 17, 2000     

Handling variable string lengths in GA-based structural topology optimization

Binary coded genetic algorithms (GAs) have been used effectively in topological design of discrete structural systems. In a majority of such applications, the structural topology is extracted from a pre-defined structural universe, a set of all permissible joints and elements that can be used in the development of the optimal design. In the presence of a dense structural universe, the GA search process must contend with very long string lengths, with the attendant degradation in the effectiveness of the search process. The present paper presents a novel approach for handling variable string lengths in GA-based topological design. Varying string lengths in a population requires a redefinition of the crossover process, and both inter- and intra-species crossover mechanisms are explored in the present paper. The use of micro-GAs is proposed as an approach to increasing the search efficiency in problems involving a large number of candidate topologies. The proposed strategies are implemented in representative algebraic problems, truss topology design, and the layout of a stiffened composite panel.     

多无人船通信网络拓扑优化控制算法

为构建有效、可靠的多无人船网络拓扑结构,本文提出一种基于改进粒子群优化的多无人船网络拓扑优化控制算法.该算法通过综合考虑网络连通度、链路通信质量、网络连接收益和网络连接成本构建多无人船网络拓扑优化模型.为确保模型与应用对象的适配性,重点分析海上无线电波的传播特性,并在此基础上,完成链路通信质量、网络连接收益和网络连接成本的表征.为获得模型的全局最优解,加快模型的收敛速度,在粒子群优化算法的迭代寻优过程中,借鉴电磁场中带电粒子间的相互作用,利用粒子的电荷量动态自适应调整算法的控制参数,当粒子种群多样性小于给定的阈值时,将粒子种群中适应度值最小的粒子作为扰动粒子,引导粒子向未搜索区域移动,克服算法的早熟收敛.仿真结果证明了该算法的有效性.     

A note on stress-constrained truss topology optimization

The purpose of this brief note is to demonstrate that general-purpose optimization methods and codes should not be discarded when dealing with stress-constrained truss topology optimization. By using a disaggregated formulation of the considered problem, such methods may find also “singular optima”, without using perturbation techniques like the ε-relaxed approach. Received February 19, 2002     

A new multi-objective programming scheme for topology optimization of compliant mechanisms

This paper presents an alternative method in implementing multi-objective optimization of compliant mechanisms in the field of continuum-type topology optimization. The method is designated as “SIMP-PP” and it achieves multi-objective topology optimization by merging what is already a mature topology optimization method—solid isotropic material with penalization (SIMP) with a variation of the robust multi-objective optimization method—physical programming (PP). By taking advantages of both sides, the combination causes minimal variation in computation algorithm and numerical scheme, yet yields improvements in the multi-objective handling capability of topology optimization. The SIMP-PP multi-objective scheme is introduced into the systematic design of compliant mechanisms. The final optimization problem is formulated mathematically using the aggregate objective function which is derived from the original individual design objectives with PP, subjected to the specified constraints. A sequential convex programming method, the method of moving asymptotes (MMA) is then utilized to process the optimization evolvement based on the design sensitivity analysis. The main findings in this study include distinct advantages of the SIMP-PP method in various aspects such as computation efficiency, adaptability in convex and non-convex multi-criteria environment, and flexibility in problem formulation. Observations are made regarding its performance and the effect of multi-objective optimization on the final topologies. In general, the proposed SIMP-PP method is an appealing multi-objective topology optimization scheme suitable for “real world” problems, and it bridges the gap between standard topological design and multi-criteria optimization. The feasibility of the proposed topology optimization method is exhibited by benchmark examples.     

Metamorphic development: a new topology optimization method for continuum structures

An effective optimization procedure for finding structural shapes and topologies that minimize structural compliance and weight subject to stress and deflection constraints is presented. This new approach, called “Metamorphic Development” (MD), can allow a structure to grow and degenerate towards an optimum topological layout. In this method, the optimization can start from the simplest possible geometry (layout) or any degree of development of the structure rather than from a complex ground mesh. The structure is then developed metamorphically using rectangular and triangular elements that can be of any specified sizes. Examples demonstrate the potential of the MD optimization procedure to generate innovative solutions to structural design problems. Results are given and the growth and degeneration histories during optimization are illustrated. Received August 20, 1999     

Checkerboard and minimum member size control in topology optimization

Checkerboard-like material distributions are frequently encountered in topology optimization of continuum structures, especially when first order finite elements are used. It has been shown that this phenomenon is caused by errors in the finite element formulation. Minimum member size control is closely related to the problem of mesh dependency of solutions in topology optimization. With increasing mesh density, the solution of a broad class of problems tends to form an increasing number of members with decreasing size. Different approaches have been developed in recent years to overcome these numerical difficulties. However, limitations exist for those methods, either in generality or in efficiency. In this paper, a new algorithm for checkerboard and direct minimum member size control has been developed that is applicable to the general problem formulation involving multiple constraints. This method is implemented in the commercial software Altair OptiStruct. March 22, 2000