• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.19-28
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• 2007

Discrete topology optimization processes of structures start from an initial design domain which is described by the topology of constant material densities. During optimization procedures, the structural topology changes in order to satisfy optimization problems in the fixed design domain, and finally, the optimization produces material density distributions with optimal topology. An introduction of initial holes in a design domain presented by Eschenauer et at. has been utilized in order to improve the optimization convergence of boundary-based shape optimization methods by generating finite changes of design variables. This means that an optimal topology depends on an initial topology with respect to topology optimization problems. In this study, it is investigated that various optimal topologies can be yielded under constraints of usable material, when partial solid phases are deposited in an initial design domain and thus initial topology is finitely changed. As a numerical application, structural topology optimization of a simple MBB-Beam is carried out, applying partial circular solid phases with varying sizes to an initial design domain.

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

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.119-126
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• 2004

A continuum-based design sensitivity analysis and topology optimization methods are developed for power flow analysis. Efficient adjoint sensitivity analysis method is employed and further extended to topology optimization problems. Young's moduli of all the finite elements are selected as design variables and parameterized using a bulk material density function. The objective function and constraint are an energy compliance of the system and an allowable volume fraction, respectively. A gradient-based optimization, the modified method of feasible direction, is used to obtain the optimal material layout. Through several numerical examples, we notice that the developed design sensitivity analysis method is very accurate and efficient compared with the finite difference sensitivity. Also, the topology optimization method provides physically meaningful results. The developed is design sensitivity analysis method is very useful to systematically predict the impact on the design variations. Furthermore, the topology optimization method can be utilized in the layout design of structural systems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.3
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• pp.281-290
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• 2003

Co Evolutionary Structural Design(CESD) Framework is presented, which can deal with the load design and structural topology design simultaneously. The load design here is the exploration algorithm that finds the critical load patterns of the given structure. In general, the load pattern is a crucial factor in determining the structural topology and being selected from the experts어 intuition and experience. However, if any of the critical load patterns would be excluded during the process of problem formation, the solution structure might show inadequate performance under the load pattern. Otherwise if some reinforcement method such as safety factor method would be utilized, the solution structure could result in inefficient conservativeness. On the other hand, the CESD has the ability of automatically finding the most critical load patterns and can help the structural solution evolve into the robust design. The CESD is made up of a load design discipline and a structural topology design discipline both of which have the fully coupled relation each other. This coupling is resolved iteratively until the resultant solution can resist against all the possible load patterns and both disciplines evolve into the solution structure with the mutual help or competition. To verify the usefulness of this approach, the 10 bar truss and the jacket type offshore structure are presented. SORA(Sequential Optimization & Reliability Assessment) is adopted in CESD as a probabilistic optimization methodology, and its usefulness in decreasing the computational cost is verified also.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.291-298
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• 2006

A parallelized topology design optimization method is developed on a distributed memory system. The parallelization is based on a domain decomposition method and a boundary communication scheme. For the finite element analysis of structural responses and design sensitivities, the PCG method based on a Krylov iterative scheme is employed. Also a parallelized optimization method of optimality criteria is used to solve large-scale topology optimization problems. Through several numerical examples, the developed method shows efficient and acceptable topology optimization results for the large-scale problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1210-1216
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• 2003

Topology optimization is applied to determine the layout of a structural component with a specified frequency by minimizing the difference between the specified structural frequency and a given frequency. The homogenization design method is employed and the topology design problem is solved by the optimality criteria method. The value of a weighting factor in the optimality criteria plays an important role in this topology design problem. The modified optimality criteria method approximated by using the binomial expansion is suggested to determine the suitable value of the weighting factor, which makes convergence stable. If a given frequency is set as an excited frequency, it is possible to avoid resonance by moving away the specified structural frequency from the given frequency. The results of several test problems are compared with previous works and show the validity of the proposed algorithm.

• Structural Engineering and Mechanics
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• v.36 no.1
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• pp.79-94
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• 2010

This study shows how uncertainties of data like material properties quantitatively have an influence on structural topology optimization results for dynamic problems, here such as both optimal topology and shape. In general, the data uncertainties may result in uncertainties of structural behaviors like deflection or stress in structural analyses. Therefore optimization solutions naturally depend on the uncertainties in structural behaviors, since structural behaviors estimated by the structural analysis method like FEM need to execute optimization procedures. In order to quantitatively estimate the effect of data uncertainties on topology optimization solutions of dynamic problems, a so-called interval analysis is utilized in this study, and it is a well-known non-stochastic approach for uncertainty estimate. Topology optimization is realized by using a typical SIMP method, and for dynamic problems the optimization seeks to maximize the first-order eigenfrequency subject to a given material limit like a volume. Numerical applications topologically optimizing dynamic wall structures with varied supports are studied to verify the non-stochastic interval analysis is also suitable to estimate topology optimization results with dynamic problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.8
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• pp.786-792
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• 2009

Topology optimization is to find the optimal material distribution of the specified design domain minimizing the objective function while satisfying the design constraints. Since the genetic algorithm (GA) has its advantage of locating global optimum with high probability, it has been applied to the topology optimization. To guarantee the structural connectivity, the concept of compliance pattern is proposed and to improve the convergence rate, small number of population size and variable probability in genetic operators are incorporated into GA. The rank sum weight method is applied to formulate the fitness function consisting of compliance, volume, connectivity and checkerboard pattern. To substantiate the proposed method design examples in the previous works are compared with respect to the number of function evaluation and objective function value. The comparative study shows that the compliance pattern based GA results in the reduction of computational cost to obtain the reasonable structural topology.

• Journal of Ocean Engineering and Technology
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• v.34 no.4
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• pp.263-271
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• 2020

In this study, we performed a three-dimensional (3D) topology optimization of a fixed offshore structure to enhance its structural stiffness. The proposed topology optimization is based on the solid isotropic material with penalization (SIMP) method, where a volume constraint is applied to utilize an equivalent amount of material as that used for the rule-based scantling design. To investigate the effects of the main legs of the fixed offshore structure on its structural stiffness, the leg region is selectively considered in the design domain of the topology optimization problem. The obtained optimal designs and the rule-based scantling design of the structure are manufactured by 3D metal printing technology to experimentally validate the topology optimization. The behaviors under compressive loading of the obtained optimal designs are compared with those of the rule-based scantling design using a universal testing machine (UTM). Based on the structural experiments, we concluded that by employing the topology optimization method, the structural stiffness of the structure was enhanced compared to that of the rule-based scantling design for an equal amount of the fabrication material. Furthermore, by effectively combining the topology optimization and rule-based scantling methods, we succeeded in enhancing the structural stiffness and improving the breaking load of the fixed offshore structure.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.45-58
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• 2017

This paper presents the application of topology optimization as a design tool for a steel railway bridge. The choice of a steel railway bridge is dictated by the particular situation that it is suitable for topology optimization design. On the one hand, the current manufacturing techniques for steel structures (additive manufacturing techniques not included) are highly appropriate for material optimization and weight reduction to improve the overall structural efficiency, improve production efficiency, and reduce costs. On the other hand, the design of a railway bridge, especially at higher speeds, is dominated by minimizing the deformations, this being the basic principle of compliance optimization. However, a classical strategy of topology optimization considers typically only one or a very limited number of load cases, while the design of a steel railway bridge is characterized by relatively concentrated convoy loads, which may be present or absent at any location of the structure. The paper demonstrates the applicability of considering multiple load configurations during topology optimization and proves that a different and better optimal layout is obtained than the one from the classical strategy.