• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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• pp.2568-2580
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• 2000

This paper presents a quasi-static optimization technique for elastic structures under dynamic loads. An equivalent static load (ESL) set is defined as a static load set which generates the same displacement field as that from a dynamic load at a certain time. Multiple ESL sets calculated at every time step are employed to represent the various states of the structure under the dynamic load. They can cover every critical state that might happen at an arbitrary time. Continuous characteristics of dynamic load are simulated by multiple discontinuous ones of static loads. The calculated sets of ESLs are applied as a multiple loading condition in the optimization process. A design cycle is defined as a circulated process between an analysis domain and a design domain. Design cycles are repeated until a design converges. The analysis domain gives a loading condition necessary for the design domain. The design domain gives a new updated design to be verified by the analysis domain in the next design cycle. This iterative process is quite similar to that of the multidisciplinary optimization technique. Even though the global convergence cannot be guaranteed, the proposed technique makes it possible to optimize the structures under dynamic loads. It has also applicability, flexibility, and reliability.

• Wind and Structures
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• v.25 no.5
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• pp.493-506
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• 2017

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

• Structural Engineering and Mechanics
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• v.4 no.5
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• pp.497-511
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• 1996

The equivalent static force procedure and the response spectrum analysis method are widely used for seismic analyses of multi-story buildings. The equivalent static force procedure is one of the most simple but less accurate method in predicting possible seismic response of a structure. The response spectrum analysis method provides more accurate results while it takes much longer computational time. In the response spectrum method, dynamic response of a multi-story building is obtained by combining modal responses through a proper procedure such as SRSS or CQC method. Since all of the analysis results are expressed in absolute values, structural engineers have difficulties to combine them with the results obtained from the static analysis. Design automation is interrupted at this stage because of the difficulty in the decision of the most critical design load. Pseudo-dynamic analysis method proposed in this study provides more accurate seismic analysis results than those of the equivalent static force procedure since the dynamic characteristics of a structure is considered. And the proposed method has an advantage in combination of the analysis results due to gravity loads and seismic loads since the direction of the forces can be considered.

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

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1344-1349
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• 2007

Biped humanoids maintain their stability through precise controls during locomotion or operation. Dynamic forces are applied to the humanoid structure during locomotion or operation. If the humanoid has weakness from a structural viewpoint, these forces cause severe deformation or vibration of the structure, which can make the humanoid unstable. In this research, a design scenario is proposed to design a robust humanoid structure under the dynamic loads. The pelvis part is selected for design practice. Multibody dynamics is adopted to calculate the dynamic loads and a structural optimization technique is employed to design the pelvis structures. Since it is extremely difficult directly consider the dynamic loads in the optimization process, equivalent static loads are evaluated from the dynamic loads and the design result are discussed.

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

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.8 s.239
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• pp.1061-1069
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• 2005

In part I of this papter Nonlinear Response Optimization using Equivalent Static Loads (NROESL) method/algorithm is developed to conduct optimization for nonlinear behavior structures. The method/algorithm is also verified to show its convergency and optimality. In this present paper, the NROESL algorithm is applied to several structural problems with geometric and/or material nonlinearity. 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.

• Wind and Structures
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• v.34 no.2
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• pp.161-171
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• 2022

This paper presents a failure type assessment curve method to judge the failure type of transmission tower segments. This novel method considers the equivalent static wind load characteristics and the transmission tower members' load-bearing capacities based on numerical simulations. This method can help judge the failure types according to the relative positions between the actual state points and the assessment curves of transmission tower segments. If the extended line of the actual state point intersects with the horizontal part's assessment curve, the segment would lose load-bearing capacity due to the diagonal members' failure. Another scenario occurs when the intersection point is in the oblique part, indicating that the broken main members have caused the tower segment to fail. The proposed method is verified by practical engineering case studies and static tests on the scaled tower segments.

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

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.321-326
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• 2007

The joined-wing is a new concept of the airplane wing. The fore-wing and the aft-wing arc joined together in the joined-wing. The range and loiter are longer than those of a conventional wing. The joined-wing can lead to increased aerodynamic performances and reduction of the structural weight. The structural behavior of the joined-wing has a high geometric nonlinearity according to the external loads. The gust loads are the most critical loading conditions in the structural design of the joined-wing. The nonlinear behavior should be considered in the optimization of the joined-wing. It is well known that conventional nonlinear response optimization is extremely expensive: therefore, the conventional method is almost impossible to use in large scale structures such as the joined-wing. In this research, geometric nonlinear response structural optimization is carried out using equivalent loads. Equivalent loads are the load sets which generate the same response field in linear analysis as that from nonlinear analysis. In the equivalent loads method, the external loads are transformed to the equivalent loads (EL) for linear static analysis, and linear response optimization is carried out based on the EL.