• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 1997.10a
• /
• pp.23-27
• /
• 1997

This paper introduces the structural design optimization of a high speed machining center using multi-step optimization combined with G.A.(Genetic Algorithm) and Weighted Method. In this case, the design problem is to find out the best design variables which minimize the static compliance, the dynamic compliance, and the weight of the machine structure simultaneously. Dimensional thicknesses of the thirteen structural members of the machine structure are adopted as design variables. The first step is the cross-section configuration optimization, in which the area moment of inertia of the cross-section for each structural member is maximized while its area is kept constant The second step is a static design optimization, In which the static compliance and the weight of the machine structure are minimized under some dimensional and safety constraints. The third step IS a dynamic design optimization, where the dynamic compliance and the structure weight are minimized under the same constraints. After optunization, static and dynamic compliances were reduced to 62.3% and 95.7% Eorn the initial design, while the weight of the moving bodies are also in the feaslble range.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.39 no.3
• /
• pp.311-318
• /
• 2015

A nonlinear dynamic response structural optimization process is proposed for the television (TV) packing system that protects the damage from a drop situation using the equivalent static loads (ESLs). Topology optimization using ESLs is carried out for conceptual design, and shape optimization using stress ESLs for a virtual model is performed for detailed design. Stress ESLs are static loads that generate the same displacement as well as the stress fields of linear static analysis as those of nonlinear dynamic analysis. Thus, the response of nonlinear dynamic analysis can be utilized as a constraint in the linear static structural optimization. An actual example is solved to validate the process. The drop test of a television packaging system is analyzed by LS-DYNA, and NASTRAN is used for optimization.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2004.10a
• /
• pp.1256-1261
• /
• 2004

Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is proposed to perform optimization of non-linear response structures. It is more expensive to carry out nonlinear response optimization than linear response optimization. The conventional method spends most of the total design time on nonlinear analysis. Thus, the NROESL algorithm makes the equivalent static load cases for each response and repeatedly performs linear response optimization and uses them as multiple loading conditions. The equivalent static loads are defined as the loads in the linear analysis, which generates the same response field as those in non-linear analysis. The algorithm is validated for the convergence and the optimality. The function satisfies the descent condition at each cycle and the NROESL algorithm converges. It is mathematically validated that the solution of the algorithm satisfies the Karush-Kuhn-Tucker necessary condition of the original nonlinear response optimization problem. The NROESL algorithm is applied to two structural problems. Conventional optimization with sensitivity analysis using the finite difference method is also applied to the same examples. The results of the optimizations are compared. The proposed method is very efficient and derives good solutions.

• Proceedings of the KSME Conference
• /
• 2004.04a
• /
• pp.1011-1016
• /
• 2004

All the loads in the real world are dynamic loads and it is well known that structural optimization under dynamic loads is very difficult. Thus the dynamic loads are often transformed to the static loads using dynamic factors. However, due to the difference of load characters, there can be considerable differences between the results from static and dynamic analyses. When the natural frequency of a structure is high, the dynamic analysis result is similar to that of static analysis due to the small inertia effect on the behavior of the structure. However, if the natural frequency is low, the inertia effect should not be ignored. Then, the behavior of the dynamic system is different from that of the static system. The difference of the two cases can be explained from the relationship between the homogeneous and the particular solutions of the differential equation that governs the behavior of the structure. Through various examples, the difference between the dynamic analysis and the static analysis are shown. Also the optimization results considering dynamic loads are compared with static loads.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.9
• /
• pp.1314-1319
• /
• 2004

In this study, parameter optimization of micro-static mixer with a cantilever beam was accomplished for maximizing the mixing efficiency by using successive response surface approximations. Variables were chosen as the length of cantilever beam and the angle between horizontal and the cantilever beam. Sequential approximate optimization method was used to deal with both highly nonlinear and non-smooth characteristics of flow field in a micro-static mixer. Shape optimization problem of a micro-static mixer can be divided into a series of simple subproblems. Approximation to solve the subproblems was performed by response surface approximation, which does not require the sensitivity analysis. To verify the reliability of approximated objective function and the accuracy of it, ANOVA analysis and variables selection method were implemented, respectively. It was verified that successive response surface approximation worked very well and the mixing efficiency was improved very much comparing with the initial shape of a micro-static mixer.

• International Journal of Automotive Technology
• /
• v.8 no.3
• /
• pp.337-342
• /
• 2007

A multi-objective optimization technique was implemented to obtain optimal topologies of the inner reinforcement for a vehicle's hood simultaneously considering the static stiffness of bending and torsion and natural frequency. In addition, a smoothing scheme was used to suppress the checkerboard patterns in the ESO method. Two models with different curvature were chosen in order to investigate the effect of curvature on the static stiffness and natural frequency of the inner reinforcement. A scale factor was employed to properly reflect the effect of each objective function. From several combinations of weighting factors, a Pareto-optimal topology solution was obtained. As the weighting factor for the elastic strain efficiency went from 1 to 0, the optimal topologies transmitted from the optimal topology of a static stiffness problem to that of a natural frequency problem. It was also found that the higher curvature model had a larger static stiffness and natural frequency than the lower curvature model. From the results, it is concluded that the ESO method with a smoothing scheme was effectively applied to topology optimization of the inner reinforcement of a vehicle's hood.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.16 no.1
• /
• pp.69-74
• /
• 2007

Topology optimization of the inner reinforcement for a vehicle's hood has been performed by evolutionary structural optimization(ESO) using a smoothing scheme. The purpose of this study is to obtain optimal topology of the inner reinforcement for a vehicle's hood considering the static stiffness of bending and torsion simultaneously. To do this, the multiobjective optimization technique was implemented. Optimal topologies were obtained by the ESO method. From several combinations of weighting factors, a Pareto-optimal solution was obtained. Also, a smoothing scheme was implemented to suppress the checkerboard pattern in the procedure of topology optimization. It is concluded that ESO method with a smoothing scheme is effectively applied to topology optimization of the inner reinforcement of a vehicle's hood considering the static stiffness of bending and torsion.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.33 no.12
• /
• pp.1401-1409
• /
• 2009

All the forces in the real world act dynamically on structures. Design and analysis should be performed based on the dynamic loads for the safety of structures. Dynamic (transient or vibrational) responses have many peaks in the time domain. Topology optimization, which gives an excellent conceptual design, mainly has been performed with static loads. In topology optimization, the number of design variables is quite large and considering the peaks is fairly costly. Topology optimization in the frequency domain has been performed to consider the dynamic effects; however, it is not sufficient to fully include the dynamic characteristics. In this research, linear dynamic response topology optimization is performed in the time domain. First, the necessity of topology optimization to directly consider the dynamic loads is verified by identifying the relationship between the natural frequency of a structure and the excitation frequency. When the natural frequency of a structure is low, the dynamic characteristics (inertia effect) should be considered. The equivalent static loads (ESLs) method is proposed for linear dynamic response topology optimization. ESLs are made to generate the same response field as that from dynamic loads at each time step of dynamic response analysis. The method was originally developed for size and shape optimizations. The original method is expanded to topology optimization under dynamic loads. At each time step of dynamic analysis, ESLs are calculated and ESLs are used as the external loads in static response topology optimization. The results of topology optimization are used to update the design variables (density of finite elements) and the updated design variables are used in dynamic analysis in a cyclic manner until the convergence criteria are satisfied. The updating rules and convergence criteria in the ESLs method are newly proposed for linear dynamic response topology optimization. The proposed updating rules are the artificial material method and the element elimination method. The artificial material method updates the material property for dynamic analysis at the next cycle using the results of topology optimization. The element elimination method is proposed to remove the element which has low density when static topology optimization is finished. These proposed methods are applied to some examples. The results are discussed in comparison with conventional linear static response topology optimization.

• Journal of the Korean Society for Precision Engineering
• /
• v.22 no.3 s.168
• /
• pp.146-153
• /
• 2005

In this paper, a multi-step optimization using genetic algorithm with variable penalty function is introduced to the structural design optimization of a grinding machine. The design problem, in this study, is to find out the optimum configuration and dimensions of structural members which minimize the static compliance, the dynamic compliance, and the weight of the machine structure simultaneously under several design constraints such as dimensional constraints, maximum deflection limit, safety criterion, and maximum vibration amplitude limit. The first step is shape optimization, in which the best structural configuration is found by getting rid of structural members that have no contributions to the design objectives from the given initial design configuration. The second and third steps are sizing optimization. The second design step gives a set of good design solutions having higher fitness for lightweight and minimum static compliance. Finally the best solution, which has minimum dynamic compliance and weight, is extracted from the good solution set. The proposed design optimization method was successfully applied to the structural design optimization of a grinding machine. After optimization, both static and dynamic compliances are reduced more than 58.4% compared with the initial design, which was designed empirically by experienced engineers. Moreover the weight of the optimized structure are also slightly reduced than before.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.27 no.5
• /
• pp.421-427
• /
• 2014

Most of the structure of the real world is influenced under dynamic loads. However, when structure analysis and the structural optimization is performed, it is assumed that the static load acts on structure. When considering the actual load of dynamic loads in order to take into account a variety of loads, computational resources and time becomes a big burden in terms of cost. However, considering only the simple static load condition is not preferable for structural safety. For this reason, a lot of studies have been conducted trying to compensate this trouble by applying weight factor or replacing dynamic load with the equivalent static load. In this study, structural optimization techniques for structures under dynamic loads is proposed by applying the equivalent static load. From previous study, after determining the positions of equivalent static load based on primary degrees of freedom, the equivalent static load is calculated through the optimization process. In this process, the equivalent static load optimization of previous research is complemented by adding constraints to avoid excessively large load extraction. In numerical examples, dynamic load is applied to the truss structure and the plate. Then, the reliability of the proposed optimization technique is verified by carrying out size optimization with the equivalent static load.