An Enhanced Topology Optimization Approach Based on the Combined MMC and NURBS-Curve Boundaries

Rongzhen Zheng,Cheol Kim 한국정밀공학회 2020 International Journal of Precision Engineering and Vol.21 No.8

An efficient topology optimization method is developed newly in this study by combining the Non-uniform rational B-spline (NURBS) curves and moving morphable components (MMC). The MMC-based topology optimization is an explicit and geometrical method that utilizes a set of morphable components to create basic blocks for optimization. Optimum topologies may be obtained by optimizing shapes, lengths, thicknesses, orientations and layout of these components. The combined method adopts a different way in the creation of morphable components that consist of NURBS curves. Various kinds of complicated curved components can be built with NURBS curves or surfaces. Here, the NURBS curve is applied for shaping the geometries of structural basic components, and the coordinates of control points become design variables for topology optimization. A MATLAB optimization code has been developed. Four numerical examples of a short cantilever, a MBB beam, a simply supported beam with two point loadings, and a vehicle lower chassis structure subjected to crash loadings are provided to prove that the combined topology optimization approach coupled with NURBS curves and basic morphable components can get optimum topologies with clear topological boundaries successfully. As results of comparison study with other approaches, we can obtain the same topologies and faster convergence rates for the three separate cases. The combined approach can improve the smoothness of the topological boundaries that are similar to the shape optimization results obtained by post-optimization after the density-based topology optimization.

설계변수감소 위상최적설계기법을 활용한 자동차용 캘리퍼 강성 최대화 설계

김선용 한국소음진동공학회 2022 한국소음진동공학회 논문집 Vol.32 No.6

A brake caliper is crucial for control in automotives. One of the main design factors is stiffness in terms of fatigue and robustness. The topology optimization technique is adopted to obtain a conceptual design for a brake caliper. However, topology optimization requires a high computational expense. RDVM topology optimization was proposed to overcome the restriction and demonstrate the efficiency in benchmarking problems. This study presents the effectiveness of RDVM topology optimization for a real structure (i.e., brake caliper). The objective function is defined as the minimization of compliance, which is the converse of stiffness, and volume constrained. The objective function values were compared among an original brake caliper, conventionally topology optimized, and RDVM topology optimized. The objective function value by topology optimization was approximately 30% higher than the original one, which means the new design is 30% stiffer. The computational expenses were also compared between conventional and RDVM topology optimization. Although the optimal layouts were almost the same, the RDVM topology optimization only cost 42% of the conventional one.

Topology Optimization of the Decking Unit in the Aluminum Bass Boat and Strength Verification using the FEM-program

Kwang-Cheol Seo,Jin Gwak,Joo-Shin Park 해양환경안전학회 2018 해양환경안전학회지 Vol.24 No.3

The objective of this paper is to optimize the cross-section of aluminum decking units used in the bass boats under operating conditions, and to verify the optimized model from the results via by ANSYS software. Aluminum decking unit is needed to endure specific loading while leisure activity and sailing. For a stiffer and more cost-neutral aluminum decking unit, optimization is often considered in the naval and marine industries. This optimization of the aluminum decking unit is performed using the ANSYS program, which is based on the topology optimization method. The generation of finite element models and stress evaluations are conducted using the ANSYS Multiphysics module, which is based on the Finite Element Method (FEM). Through such a series of studies, it was possible to determine the most suitable case for satisfying the structural strength found among the phase-optimized aluminum deck units in bass boats. From these optimization results, CASE 1 shows the best solution in comparison with the other cases for this optimization. By linking the topology optimization with the structural strength analysis, the optimal solution can be found in a relatively short amount of time, and these procedures are expected to be applicable to many fields of engineering.

Topology optimization of compressor bracket

장정우,이영신 대한기계학회 2008 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.22 No.9

Topology optimization is very useful engineering technique especially at the concept design stage. It is common habit to design depending on the designer's experience at the early stage of product development. Structural analysis methodology of compressor bracket was verified on the static and dynamic loading condition with 2 bracket samples for the topology optimization base model. Topology optimization is able to produce reliable and satisfactory results with the verified structural model. Base bracket model for the topology optimization was modeled considering the interference with the adjacent vehicle parts. Objective function was to minimize combined compliance and the constraint was the first natural frequency over 250 Hz. Multiple load cases such as normal mode calculation and gravity load conditions with 3-axis direction were also applied for the optimization, expecting an even stress distribution and vibration durability performance. Commercial structural optimization code such as optistruct of Altair Engineering was used for the structural topology optimization. Optimization was converged after 14 iterations with the satisfaction of natural frequency constraint. New bracket shape was produced with the CATIA based on the topology optimization result. The new bracket from topology optimization result was compared with the traditional concept model and topology optimization base model under 4 load cases. 14 % 1’st natural frequency of new bracket with only 4 % mass increment increased compared to the concept model. 31 % mass decreased compared to the base model without the increment of stress under gravity load cases. It was analyzed thata new bracket would not fail during a vibration durability test, and these results were verified with a fabricated real sample under the durability condition.

Topology optimization based on the harmony search method

이승민,한석영 대한기계학회 2017 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.31 No.6

A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to staticstiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those intopology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimizedtopology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW)was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme,simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was alsoimplemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS withthose of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclusionscould be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms ofstability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that theHS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces asolid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topologyoptimization.

Shape optimization and its extension to topological design based on isogeometric analysis

Seo, Y.D.,Kim, H.J.,Youn, S.K. Pergamon Press ; Elsevier Science Ltd 2010 International journal of solids and structures Vol.47 No.11

In most of structural optimization approaches, finite element method (FEM) has been employed for structural response analysis and sensitivity calculation. However, the approaches generally suffer certain drawbacks. In shape optimization, cumbersome parameterization of design domain is required and time consuming remeshing task is also necessary. In topology optimization, design results are generally restricted on the initial design space and additional post-processing is required for communication with CAD systems. These drawbacks are due to the use of different mathematical languages in design or geometric modeling and numerical analysis: spline basis functions are used in design and geometric modeling whereas Lagrangian and Hermitian polynomials in analysis. Isogeometric analysis is a very attractive and promising alternative to overcome the limitations resulting from the use of the conventional FEM in structural optimization. In isogeometric analysis, the same spline information such as control points and spline basis functions which represent geometries in CAD systems are also used in numerical analysis. Such unification of the mathematical languages in CAD, analysis and design optimization can resolve the issues mentioned above. In this work, structural shape optimization using isogeometric analysis is studied on 2D and shell problems. The proposed framework is extended to topology optimization using trimming techniques. New inner fronts are introduced by trimming spline curves in topology optimization. Trimmed surface analysis which was recently proposed to analyze arbitrary complex topology problems is employed for topology optimization. Some benchmarking problems in shape and topology optimization are treated using the proposed approach.

Efficient three-dimensional topology optimization of heat sinks in natural convection using the shape-dependent convection model

Joo, Younghwan,Lee, Ikjin,Kim, Sung Jin Elsevier 2018 INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER - Vol.127 No.3

<P><B>Abstract</B></P> <P>In this study, heat sinks in natural convection are thermally optimized using the method of three-dimensional topology optimization. In order to perform three-dimensional topology optimization with low computational cost, a shape-dependent convection model is proposed. This model accounts for the variation of the heat transfer coefficient depending not only on the local shape of the fins but also on the development of the thermal boundary layer. The physical validity of the proposed model is confirmed by the fin geometry of the topology-optimized design that matches the multiscale structures proposed previously by the constructal theory. For further validation, the effective heat transfer coefficient evaluated by the proposed model is compared to that obtained from numerical simulations. Because the new topology-optimized design has a complicated fin geometry, design simplification is performed to yield a more manufacturable design. The thermal performance of the topology-optimized heat sink is compared to that of the radial plate-fin heat sink optimized analytically using an existing correlation. It is found that the topology-optimized heat sink has 13% lower thermal resistance and 48% less mass than the optimized radial plate-fin heat sink. This implies that the three-dimensional topology optimization method suggested in this study can provide a heat sink design with improved thermal performance and reduced mass for various practical applications.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A shape-dependent convection model for 3-D topology optimization was developed. </LI> <LI> The multiscale structures proposed by the constructal theory were obtained. </LI> <LI> The new design had 13% lower thermal resistance than an existing optimal design. </LI> <LI> Design simplification was performed to yield a more manufacturable design. </LI> </UL> </P>

A Modified Big Bang-Big Crunch Algorithm for Structural Topology Optimization

Hong-Kyun Ahn,한동석,한석영 한국정밀공학회 2019 International Journal of Precision Engineering and Vol.20 No.12

The purpose of this study is to develop a topology optimization scheme based on big bang–big crunch (BB–BC) algorithm, inspired from the evolution of the universe called big bang and big crunch theory. In order to apply the BB–BC algorithm to topology optimization for static and dynamic stiffness problems, the parameters of the algorithm were transformed to those of topology optimization scheme. In addition, some parameters such as big bang (BB) range, BB search, population and non-exchange limit were newly introduced to topology optimization scheme. Also, a parametric study for the parameters involved in the topology optimization scheme was performed to reduce the number of parameters, and find the appropriate ranges for topology optimization. Some examples were provided to examine the effectiveness of the developed topology optimization scheme for both static and dynamic stiffness problems throughout comparing with other metaheuristic topology optimization algorithms and the BESO (bi-directional evolutionary structural optimization) method. It was verified that the suggested algorithm shows superior to the compared typical metaheuristic topology optimization algorithms in the viewpoints of stability, robustness, accuracy and the convergence rate.

위상최적화를 위해 사용된 딥러닝 방법론 리뷰

신승연(Seungyeon Shin),신동주(Dongju Shin),류한영(Hanyoung Ryu),김민영(Minyoung Kim),강남우(Namwoo Kang) 대한기계학회 2021 대한기계학회 춘추학술대회 Vol.2021 No.8

Topology optimization is a method for determining optimal material distribution within a given design space under certain constraints on load and boundaries. Since topology optimization was introduced, various methodologies such as Solid Isotropic Microstructure with Penalization (SIMP), Evolutionary Structural Optimization (ESO), Level Set Method (LSM) have been studied. Recently, a lot of research has been done on data-driven topology optimization, and various machine learning techniques has been applied to effectively optimize design topologies. Especially, deep learning-based topology optimization complement the problems of conventional topology optimization by improving the optimization algorithms and reducing computational costs. The goal of this research is to review studies in the field of deep learning approach for topology optimization, based on the purpose of applying deep learning to topology optimization and the methodology applied.

Topology Optimization Scheme for Dynamic Stiffness Problems Using Harmony Search Method

이승민,한석영 한국정밀공학회 2016 International Journal of Precision Engineering and Vol.17 No.9

This paper suggests a new topology optimization scheme for natural frequency problems based on the harmony search (HS) method. The HS method is expected to be very effective since its topology optimization procedure is similar to the procedure for tuning the instruments found in an orchestra. To apply the HS method to dynamic topology optimization, an objective function is defined as a natural frequency, and the design domain is defined as harmony memory (HM) in the HS method. The harmony rate update rule is introduced to obtain a robust topology. Through a parametric study of the harmony memory considering rate (HMCR), pitch adjusting rate (PAR), and bandwidth (BW), the proper ranges of the search variables are determined and applied to numerical examples. Some examples are provided to examine the effectiveness of the HS method compared to the artificial bee colony algorithm (ABCA) in dynamic topology optimization. Properly selected parameters for the suggested algorithm with the harmony rate update rule provide a robust topology, a fast convergence rate and a stable optimization process. It can be effectively expanded to apply to shape and topological shape optimization algorithms.