Entire Design Domain Research Articles

希薄気体流れを対象としたトポロジー最適化

We construct a topology optimization method for two dimensional rarefied gas flow problems, based on level-set boundary expressions. The degree of rarefaction is expressed by the Knudsen number, which is the ratio of the mean free path and the characteristic length of the system. As the Knudsen number approaches 0 in the limit, flow behaviors can be described by Navier-Stokes equations and topology optimization methods for such flows have already been proposed. On the other hand, the governing equation for flows which have a large rarefaction is the Boltzmann equation and topology optimization methods for such flows have not been seen. This paper presents the topology optimization method for rarefied gas flows whose Knudsen number is approximately 1, aiming at an application for the design of flow channels in micromachines. We use the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and extend it to the entire design domain that includes both rarefied gas and solid domains. First, we briefly discuss the Boltzmann equation and the level set-based topology optimization method. Second, an optimization problem is formulated to address the design of flow channels that aim to maximize the flow velocity induced along a temperature gradient. Finally, several numerical examples demonstrate the validity and usefulness of the proposed method.

Simultaneous design of components layout and supporting structures using coupled shape and topology optimization technique

The purpose of this paper was to study the layout design of the components and their supporting structures in a finite packing space. A coupled shape and topology optimization (CSTO) technique is proposed. On one hand, by defining the location and orientation of each component as geometric design variables, shape optimization is carried out to find the optimal layout of these components and a finite-circle method (FCM) is used to avoid the overlap between the components. On the other hand, the material configuration of the supporting structures that interconnect components is optimized simultaneously based on topology optimization method. As the FE mesh discretizing the packing space, i.e., design domain, has to be updated itertively to accommodate the layout variation of involved components, topology design variables, i.e., density variables assigned to density points that are distributed regularly in the entire design domain will be introduced in this paper instead of using traditional pseudo-density variables associated with finite elements as in standard topology optimization procedures. These points will thus dominate the pseudo-densities of the surrounding elements. Besides, in the CSTO, the technique of embedded mesh is used to save the computing time of the remeshing procedure, and design sensitivities are calculated w.r.t both geometric variables and density variables. In this paper, several design problems maximizing structural stiffness are considered subject to the material volume constraint. Reasonable designs of components layout and supporting structures are obtained numerically.

Bi-Directional Evolutionary Topology Optimization Using Element Replaceable Method

In the present paper, design problems of maximizing the structural stiffness or natural frequency are considered subject to the material volume constraint. A new element replaceable method (ERPM) is proposed for evolutionary topology optimization of structures. Compared with existing versions of evolutionary structural optimization methods, contributions are twofold. On the one hand, a new automatic element deletion/growth procedure is established. The deletion of a finite element means that a solid element is replaced with an orthotropic cellular microstructure (OCM) element. The growth of an element means that an OCM element is replaced with a solid element of full materials. In fact, both operations are interchangeable depending upon how the value of element sensitivity is with respect to the objective function. The OCM design strategy is beneficial in preventing artificial modes for dynamic problems. Besides, the iteration validity is greatly improved with the introduction of a check position (CP) technique. On the other hand, a new checkerboard control algorithm is proposed to work together with the above procedure. After the identification of local checkerboards and detailed structures over the entire design domain, the algorithm will fill or delete elements depending upon the prescribed threshold of sensitivity values. Numerical results show that the ERPM is efficient and a clear and valuable material pattern can be achieved for both static and dynamic problems.

Radial basis functions and level set method for structural topology optimization

AbstractLevel set methods have become an attractive design tool in shape and topology optimization for obtaining lighter and more efficient structures. In this paper, the popular radial basis functions (RBFs) in scattered data fitting and function approximation are incorporated into the conventional level set methods to construct a more efficient approach for structural topology optimization. RBF implicit modelling with multiquadric (MQ) splines is developed to define the implicit level set function with a high level of accuracy and smoothness. A RBF–level set optimization method is proposed to transform the Hamilton–Jacobi partial differential equation (PDE) into a system of ordinary differential equations (ODEs) over the entire design domain by using a collocation formulation of the method of lines. With the mathematical convenience, the original time dependent initial value problem is changed to an interpolation problem for the initial values of the generalized expansion coefficients. A physically meaningful and efficient extension velocity method is presented to avoid possible problems without reinitialization in the level set methods. The proposed method is implemented in the framework of minimum compliance design that has been extensively studied in topology optimization and its efficiency and accuracy over the conventional level set methods are highlighted. Numerical examples show the success of the present RBF–level set method in the accuracy, convergence speed and insensitivity to initial designs in topology optimization of two‐dimensional (2D) structures. It is suggested that the introduction of the radial basis functions to the level set methods can be promising in structural topology optimization. Copyright © 2005 John Wiley & Sons, Ltd.

Design of Cooling Systems for Electronic Equipment Using Both Experimental and Numerical Inputs

This paper presents a methodology for the design and optimization of cooling systems for electronic equipment. In this approach, inputs from both experimentation and numerical modeling are to be used concurrently to obtain an acceptable or optimal design. The experimental conditions considered are driven by the numerical simulation and vice versa. Thus, the two approaches are employed in conjunction, rather than separately, as is the case in traditional design methods. Numerical simulation is used to consider different geometries, materials, and dimensions, whereas experiments are used for obtaining results for different flow rates and heat inputs, as these can often be varied more easily in experiments than in simulations. Also, transitional and turbulent flows are more accurately and more conveniently investigated experimentally. Thus, by using both approaches concurrently, the entire design domain is covered, leading to a rapid, convergent, and realistic design process. Two simple configurations of electronic cooling systems are used to demonstrate this approach.

Sensitivity-based scaling for approximating structural response

This article presents a sensitivity-based linearly varying scale factor used to reconcile results from simple and refined models for analysis of the same structure. The improved accuracy of the linear scale factor compared to a constant scale factor, as well as the commonly used tangent approximation, is demonstrated. A wing-box structure is used as an example, with displacements, stresses, and frequencies correlated. The linear scale factor could permit the use of a simplified model in an optimization procedure during preliminary design to approximate the response given by a refined model over a considerable range of design changes. HE design optimization of an engineering system typi- cally requires hundreds of analyses of that system. The use of approximation s to the objective function and con- straints during portions of the design process is quite com- mon,1 because of the high computational cost of these detailed analyses. Such design approximations can be divided into two classes. First there are local, derivative-based approximations such as the linear approximation based on a Taylor-series expansion about a design point. These approximations are typically based on an accurate model to obtain the system response and its derivatives. Second, there are global ap- proximations that try to capture the behavior of the objective function or constraints over the entire design domain. Such approximations can be based on a response surface which is constructed on the basis of many analyses.2 However, global approximations are often based on a simplified theory, a coarser model, or both.3 Such global approximations are referred to here as simple-model approximations. Local approximations are typically very accurate near the design point where they are generated, but since they are based on an extrapolation procedure their accuracy can deteriorate catastrophically at a distance. Simple-model approximations are intended to cap- ture the physics of the problem at some lower, but acceptable level of accuracy over the entire design domain. Therefore, at a particular design point the simple-model approximations are generally less accurate than local approximations, but on the other hand, they typically do not experience the cata-