• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.4
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• pp.642-651
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• 1988

The present paper develops finite element procedures to calculate displacements, strains and stresses in initially stressed elastic solids subjected to static or time-dependent loading conditions. As a point of departure, we employ Hamilton's principle to obtain nonlinear equations of motion characterizing the displacement in a solid. The equations of motion reduce to linear equations of motion if incremental stresses are assumed to be infinitesimal. In the case of linear problem, finite element solutions are obtained by Newmark's direct integration method and by modal analysis. An analytic solution is referred to compare with the linear finite element solution. In the case of nonlinear problem, finite element solutions are obtained by Newton-Raphson iteration method and compared with the linear solution. Finally, the effect of the order of Gauss-Legendre numerical integration on the nonlinear finite element solution, has been investigated.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.8
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• pp.899-904
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• 2014

Thickness profiled blank is designed using optimization techniques for maximizing the bulged heights during the free bulging of Inconel 718. The thickness of the blank was described by the Bezier curve and the locations of the control points were used as the design variables for optimization. The maximization of the bulged heights within the limited strain range served as the objective function and constraints for optimization. The equivalent static loads method for non-linear static response structural optimization (ESLSO) was used and the result of the optimization revealed 22 increased bulged heights. A free bulging test using a blank with an optimized profile was conducted to verify the optimization process. The results were compared with those of numerical analysis in terms of bulged height and deformed shape.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.5 s.248
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• pp.585-594
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• 2006

The joined-wing is a new concept of the airplane wing. The fore-wing and the aft-wing are joined together in a joined-wing. The range and loiter are longer than those of a conventional wing. The joined-wing can lead to increased aerodynamic performance and reduction of the structural weight. In this research, dynamic response optimization of a joined-wing is carried out by using equivalent static loads. Equivalent static loads are made to generate the same displacement field as the one from dynamic loads at each time step of dynamic analysis. The gust loads are considered as critical loading conditions and they dynamically act on the structure of the aircraft. It is difficult to identify the exact gust load profile. Therefore, the dynamic loads are assumed to be (1-cosine) function. Static response optimization is performed for the two cases. One uses the same design variable definition as dynamic response optimization. The other uses the thicknesses of all elements as design variables. The results are compared.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.8 s.179
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• pp.1949-1957
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• 2000

All the loads in the real world act dynamically on structures. Since dynamic loads are extremely difficult to handle in analysis and design, static loads are utilized with dynamic factors. The dyna mic factors are generally determined based on experiences. Therefore, the static loads can cause problems in precise analysis and design. An analytical method based on modal analysis has been proposed for the transformation of dynamic loads into equivalent static load sets. Equivalent static load sets are calculated to generate an identical displacement field in a structure with that from dynamic loads at a certain time. The process is derived and evaluated mathematically. The method is verified through numerical tests. Various characteristics are identified to match the dynamic and the static behaviors. For example, the opposite direction of a dynamic load should be considered due to the vibration response. A dynamic bad is transformed to multiple equivalent static loads according to the number of the critical times. The places of the equivalent static load can be different from those of the dynamic load. An optimization method is defined to use the equivalent static loads. The developed optimization process has the same effect as the dynamic optimization which uses the dynamic loads directly. Standard examples are solved and the results are discussed

• 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.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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.10 s.253
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• pp.1194-1201
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• 2006

All the loads in the real world are dynamic loads and structural optimization under dynamic loads is very difficult. Thus the dynamic loads are often transformed to static loads by dynamic factors, which are believed equivalent to the dynamic loads. However, due to the difference of load characteristics, 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 of the structure 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 dynamic response optimization results are compared with the results with static loads transformed from dynamic loads by dynamic factors, which show the necessity of the design considering dynamic loads.

• Journal of the Korea institute for structural maintenance and inspection
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• v.10 no.4
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• pp.97-107
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• 2006

This study is structural analysis and continuous, discrete optimum design of braced steel frame structures under earthquake loads considering soil condition. The program which is able to perform simultaneously structural analysis and continuous, discrete optimum design, it is applied steel frame structures using unbraced, Z-braced, and X-braced types and analyze the program about static loads and seismic loads. The purpose of this study is to present proper braced type for seismic effects by comparing and analyzing results of analytic method about various cases using specially Newmark-Hall design spectrum, ATC design spectrum and ATC equivalent static analysis and finding minimum weight and design variables which satisfy the ultimate strength requirements of AISC-ASD specifications, the serviceability requirements and allowable story drift requirements of ATC-3-06 and various constraints.