• Proceedings of the KSME Conference
• /
• 2008.11a
• /
• pp.412-417
• /
• 2008

In a traditional topology optimization method, material properties are usually distributed by finite element density and visualized by a gray level image. The distribution method based on element density is adequate for a great mass of 2-D topology optimization problems. However, when it is used for 3-D topology optimization, it is always difficult to obtain a smooth model representation, and easily appears a virtualconnect phenomenon especially in a low-density domain. The 3-D structural topology optimization method has been developed using the node density instead of the element density that is based on SIMP (solid isotropic microstructure with penalization) algorithm. A computer code based on Matlab was written to validate the proposed method. When it was compared to the element density as design variable, this method could get a more uniform density distribution. To show the usefulness of this method, several typical examples of structure topology optimization are presented.

• Journal of the Korean Society of Manufacturing Technology Engineers
• /
• v.9 no.5
• /
• pp.112-118
• /
• 2000

In case ESO(evolutionary structural optimization) which is one of topology optimization methods, the element removal ratio is fixed throughout topology optimization by 1 or 2%. As a result it has no flexibility for various types of structures and thus the rate of convergence might not be efficient. Thus various element removal methods were developed in order to improve the efficiency of ESO. In this paper, various element removal methods for ESO are compared with each other for a bracket and a short cantilever. In addition, a new improved bi-directional element removal method is suggested in order to obtain much better optimized topology. From the comparative results of the examples, it is verified that all of the developed various element removal methods are very effective, and the suggested element removal method is the most effective.

• Journal of Mechanical Science and Technology
• /
• v.14 no.9
• /
• pp.913-919
• /
• 2000

The purpose of this study was to develop a new element removal method for ESO (Evolutionary Structural Optimization), which is one of the topology optimization methods. ESO starts with the maximum allowable design space and the optimal topology emerges by a process of removal of lowly stressed elements. The element removal ratio of ESO is fixed throughout topology optimization at 1 or 2%. BESO (bidirectional ESO) starts with either the least number of elements connecting the loads to the supports, or an initial design domain that fits within the maximum allowable domain, and the optimal topology evolves by adding or subtracting elements. But the convergence rate of BESO is also very slow. In this paper, a new element removal method for ESO was developed for improvement of the convergence rate. Then it was applied to the same problems as those in papers published previously. From the results, it was verified that the convergence rate was significantly improved compared with ESO as well as BESO.

• Structural Engineering and Mechanics
• /
• v.51 no.5
• /
• pp.793-808
• /
• 2014

The goal of this study is to evaluate and design steel plates with optimal material distributions achieved through a specific material topology optimization by using a CCARAT (Computer Aided Research Analysis Tool) as an optimizer, topologically optimally updating node densities as design variables. In typical material topology optimization, optimal topology and layouts are described by distributing element densities (from almost 0 to 1), which are arithmetic means of node densities. The average element densities are employed as material properties of each element in finite element analysis. CCARAT may deal with material topology optimization to address the mean compliance problem of structural mechanical problems. This consists of three computational steps: finite element analysis, sensitivity analysis, and optimality criteria optimizer updating node densities. The present node density based design via CCARAT using node densities as design variables removes jagged optimal layouts and checkerboard patterns, which are disadvantages of classical material topology optimization using element densities as design variables. Numerical applications that topologically optimize reinforcement material distribution of steel plates of a cantilever type are studied to verify the numerical superiority of the present node density based design via CCARAT.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.22 no.3
• /
• pp.259-265
• /
• 2009

This paper studies the Element Connectivity Parameterization Method(ECP method) for topology optimization considering dynamic compliance. The previous element density based topology optimization method interpolates Young's modulus with respect to design variables defined in each element for topology optimization. Despite its various applications, these element density based methods suffer from numerical instabilities for nonlinear structure and multiphysics systems. To resolve these instabilities, recently a new numerical method called the Element Connectivity Parameterization(ECP) Method was proposed. Unlike the existing design methods, the ECP method optimizes the connectivities among plane or solid elements and it shows some advantages in topology optimization for both nonlinear structure and multiphysics systems. In this study, the method was expanded for topology optimization for the dynamic compliance by developing a way to model the mass matrix in the framework of the ECP method.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
• /
• 2000.04a
• /
• pp.46-51
• /
• 2000

In case of ESO(evolutionary structural optimization) which is one of topology optimization methods, the element removal ratio is fixed throughout topology optimization by 1 or 2 %. As a result it has no flexibility for various types of structures and thus the rate of convergence might not be efficient. Thus various element removal methods are developed in order to improve the efficiency of ESO. In this paper, various element removal methods for ESO are compared with each other. Each element removal method is explained, and applied to a bracket and a Michell type of beam. In addition, a new bi-directional element removal method is suggested in order to obtain much better optimized topology. From the results of stress, displacement and the rate of convergence for the examples under the same mass constraints, it is verified that the suggested element removal method is the most effective. .

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.8
• /
• pp.779-785
• /
• 2009

This paper is concerned with a computational approach for topology optimization of geometrically nonlinear structures following specific load-displacement trajectories. In our previous works, attention was paid to stabilize topology optimization involving large displacement and a method called the element connectivity parameterization was developed. Here, we aimed to extend the element connectivity parameterization method to find an optimal geometrically nonlinear structure yielding a specific load-displacement trajectory. In contrast to designing a stiffest structure, the trajectory design problem requires special consideration in topology optimization formulation and solution procedure. Some numerical problems were considered to test the developed element connectivity parameterization based formulation.

• Journal of Korean Association for Spatial Structures
• /
• v.24 no.1
• /
• pp.57-64
• /
• 2024

This study numerically compares optimum solutions generated by element- and node-wise topology optimization designs for free vibration structures, where element-and node-wise denote the use of element and nodal densities as design parameters, respectively. For static problems optimal solution comparisons of the two types for topology optimization designs have already been introduced by the author and many other researchers, and the static structural design is very common. In dynamic topology optimization problems the objective is in general related to maximum Eigenfrequency optimization subject to a given material limit since structures with a high fundamental frequency tend to be reasonable stiff for static loads. Numerical applications topologically maximizing the first natural Eigenfrequency verify the difference of solutions between element-and node-wise topology optimum designs.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2001.10a
• /
• pp.183-190
• /
• 2001

Topology optimization. has been evolved into a very efficient conceptual design tool and has been utilized into design engineering processes in many industrial parts. In recent years, topology optimization has become the focus of structural optimization design and has been researched and widely applied both in academy and industry. Traditional topology optimization has been using homogenization method and optimality criteria method. Homogenization method provides relationship equation between structure which includes many holes and stiffness matrix in FEM. Optimality criteria method is used to update design variables while maintaining that volume fraction is uniform. Traditional topology optimization has advantage of good convergence but has disadvantage of too much convergency time and additive checkerboard prevention algorithm is needed. In one way to solve this problem, element remove method is presented. Then, it is applied to many examples. From the results, it is verified that the time of convergence is very improved and optimal designed results is obtained very similar to the results of traditional topology using 8 nodes per element.

• Korean Journal of Computational Design and Engineering
• /
• v.14 no.4
• /
• pp.281-289
• /
• 2009

Topology optimization has been widely used for the optimal structure design for weight reduction and high performance. Since the result of three-dimensional topology optimization is represented by the discrete material distribution in finite elements, it is hard to interpret from a design point of view. In this paper, the method for interpreting three-dimensional topology optimization resuIt into a series of cross-sectional curve representation is proposed and interfaced with the existing CAD system for the practical use. The concept of node density and virtual grid is introduced to transform element density values into grid density and material boundaries in each cross section are identified based on the element volume rate to satisfy the amount of material specified in the original design intent. Design exampIes show that three-dimensional topology result can be converted into a form of curve CAD model and the seamless interface with CAD software can be achieved.