• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.175-178
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• 2010

동하중의 영향을 받는 구조물의 효율적인 구조 해석 및 최적화 수행을 위해 동하중을 등가정하중으로 변환하는 방법이 요구된다. 이 때 적절한 자유도를 선정하여 등가정하중을 부여하는 것이 중요하다. 기존방법에서는 시스템 축소기법을 통해 일정 개수 이상의 주자유도를 선택하여 등가정하중을 부여하고 그 결과 변위가 동하중 하에서의 변위와 같도록 하였다. 그러나 보수적인 결과를 얻기 위한 제한 조건의 지배적인 성격으로 인하여 등가정하중 하에서의 변위가 지나치게 크게 나타나 그 효율성이 떨어지게 되었다. 본 연구에서는 등가정하중의 변환에 있어서 효율성을 높이는 방안을 제안한다. 제안기법은 보수적 결과를 얻는 범위 내에서 과도응답해석 결과와의 오차를 크게 줄일 수 있다. 수치예제를 통해 제안기법의 결과를 기존 기법의 결과와 비교해본다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.6
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• pp.619-627
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• 2014

An optimization method is proposed for the simultaneous design of structural and control systems using the equivalent static loads. In the past researches, the control parameters of such feedback gains are obtained to improve some performance in the steady-state. However, the actuators which have position and velocity feedback gains should be designed to exhibit a good performance in the time domain. In other words, the system analysis should be conducted for the transient-state in dynamic manner. In this research, a new equivalent static loads method is presented to treat the control variables as the design variables. The equivalent static loads (ESLs) set is defined as a static load set which generates the same displacement field as that from dynamic loads at a certain time. The calculated sets of ESLs are applied as multiple loading conditions in the optimization process. Several examples are solved to validate the proposed method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.2
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• pp.165-171
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• 2013

Due to the difficulty in considering dynamic load in the view point of a computer resource and computing time, it is common that external load is assumed as ideal static loads. However, structural analysis under static load cannot guarantee the safety of design of the structures under dynamic loadings. Recently, the systematic method to construct equivalent static load from the given dynamic load has been proposed. Previous study has calculated equivalent static load through the optimization procedure under displacement constraints. However, previously reported works to distribute equivalent static load were based on ad-hoc methods. Improper selection of equivalent static loading positions may results in unreliable prediction of structural design. The present study proposes the selection method of the proper locations of equivalent static loads to dynamically applied loads when we consider transient dynamic structural problems. Moreover, it is appropriate to take into account the stress constraint as well as displacement constraint condition for the safety design. But the previously reported studies of equivalent static load design methods considered only displacement constraint conditions but not stress constraint conditions. In the present study we consider not only displacement constraint but also stress constraint conditions. Through a few numerical examples, the efficiency and reliability of proposed scheme is verified by comparison of the equivalent stress between equivalent static loading and dynamic loading.

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

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.11
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• pp.1361-1370
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• 2012

A shape optimization is proposed to obtain the desired final shape of forming and forging products in the manufacturing process. The final shape of a forming product depends on the shape parameters of the initial blank shape. The final shape of a forging product depends on the shape parameters of the billet shape. Shape optimization can be used to determine the shape of the blank and billet to obtain the appropriate final forming and forging products. The equivalent static loads method for non linear static response structural optimization (ESLSO) is used to perform metal forming and forging optimization since nonlinear dynamic analysis is required. Stress equivalent static loads (stress ESLs) are newly defined using a virtual model by redefining the value of the material properties. The examples in this paper show that optimization using the stress ESLs is quite useful and the final shapes of a forming and forging products are identical to the desired shapes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.1
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• pp.1-10
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• 2011

An optimization method is proposed for preform and billet shape designs in the forging process by using the Equivalent Static Loads (ESLs). The preform shape is an important factor in the forging process because the quality of the final forging is significantly influenced by it. The ESLSO is used to determine the shape of the preform. In the ESLSO, nonlinear dynamic loads are transformed to the ESLs and linear response optimization is performed using the ESLs. The design is updated in linear response optimization and nonlinear analysis is performed with the updated design. The examples in this paper show that optimization using the ESLs is useful and the design results are satisfactory. Consequently, the optimal preform and billet shapes which produce the desired final shape have been obtained. Nonlinear analysis and linear response optimization of the forging process are performed using the commercial software LS-DYNA and NASTRAN, respectively.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.216.2-216.2
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• 2005

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.57-63
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• 2007

The systematic method to construct equivalent static load from a given dynamic load is proposed in the present study. Previously reported works to construct equivalent static load were based on ad hoc methods. Due to improper selection of loading position, they may results in unreliable structural design. The present study proposes the employment of primary degrees of freedom for imposing the equivalent static loads. The degrees of freedom are selected by two-level condensation scheme with reliability and efficiency. In several numerical examples, the efficiency and reliability of the proposed scheme is verified by comparison displacement for equivalent static loading and dynamic loading at the critical time.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.39 no.3
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• pp.259-268
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• 2015

An optimization method for the tube hydroforming process is developed using the equivalent static loads method for non linear static response structural optimization (ESLSO). The aims of the tube hydroforming optimization are to determine the axial forces (axial feedings) and the internal pressures, and to obtain the desired shape without failures after hydroforming analysis. Therefore, the magnitude of the forces should be design variables in the optimization process. Also, some tube hydroforming optimization needs to consider the result of the thickness in nonlinear dynamic analysis as responses. However, the external forces are considered as constants and the thickness is not a response in the linear response optimization process of the original ESLSO. Thus, a new ESLSO process is proposed to overcome the difficulties and some examples are solved to validate the proposed method.

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